Publications

We consider the emergence of edge states in a finite optical lattice and show that the boundaries of the lattice play a decisive role for their location in the corresponding energy spectrum. We introduce a simple parametrization of the boundaries of the optical lattice and demonstrate the existence of an optimal choice of the values of the parameters which leads to an approximate restoration of chiral symmetry. A crucial property of this optimization is the suppression of tunneling between next-nearest-neighboring wells of the lattice. This in turn allows the mapping of the optical lattice setup to a finite SSH model. The topological character of the emerging edge states is discussed

Symmetries play a paramount role in many aspects of topological physics. A particularly illuminating example is the Su-Schrieffer-Heeger (SSH) chain, whose reflection and chiral symmetry endow the quantization of the Zak phase and winding number, subsequently guaranteeing the existence of topological edge states. Here, we harness recent graph-theoretical results to construct families of setups whose unit cells feature neither of these symmetries, but instead a so-called latent or hidden reflection symmetry. This causes the isospectral reduction—akin to an effective Hamiltonian—of the resulting lattice to resemble an SSH model. These latent SSH models exhibit features such as multiple topological transitions, edge states, a quantized Zak phase, and, counterintuitively, immunity to orientational disorder. We confirm our findings through electric circuit experiments, where the topological edge states can be directly observed. Serving as a first proof of principle, our paper demonstrates the wealth and generality of a stroboscopic point of view, taking advantage of hidden properties such as symmetries.

We explore the ground-state properties of a lattice of classical dipoles spanned on the surface of a Möbius strip. The dipole equilibrium configurations depend significantly on the geometrical parameters of the Möbius strip, as well as on the lattice dimensions. As a result of the variable dipole spacing on the curved surface of the Möbius strip, the ground state can consist of multiple domains with different dipole orientations which are separated by domain-wall-like boundaries. We analyze in particular the dependence of the ground-state dipole configuration on the width of the Möbius strip and highlight two crossovers in the ground state that can be correspondingly tuned. A first crossover changes the dipole lattice from a phase which resists compression to a phase that favors it. The second crossover leads to an exchange of the topological properties of the two involved domains. We conclude with a brief summary and an outlook on more complex topologically intricate surfaces.

Solitons are nonlinear solitary waves which maintain their shape over time and through collisions, occurring in a variety of nonlinear media from plasmas to optics. We present an experimental and theoretical study of hydrodynamic phenomena in a two-component atomic Bose-Einstein condensate where a soliton array emerges from the imprinting of a periodic spin pattern by a microwave pulse-based winding technique. We observe the ensuing dynamics which include shape deformations, the emergence of dark-antidark solitons, apparent spatial frequency tripling, and decay and revival of contrast related to soliton collisions. For the densest arrays, we obtain soliton complexes where solitons undergo continued collisions for long evolution times providing an avenue towards the investigation of soliton gases in atomic condensates.

Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behavior has, however, remained elusive. We provide here an analysis of a local reflection symmetric tight-binding Hamiltonian which attempts at identifying the key features that lead to the localized eigenstates. A weak coupling expansion of closed-form expressions for the eigenvectors demonstrates that the degeneracy of on-site energies occurring at the center of the locally symmetric domains represents the nucleus for eigenstates spreading across the domain. Since the symmetry-related subdomains constituting a locally symmetric domain are isospectral, we encounter pairwise degenerate eigenvalues that split linearly with an increasing coupling strength of the subdomains. The coupling to the (nonsymmetric) environment in an extended setup then leads to the survival of a certain system specific fraction of linearly splitting eigenvalues. The latter go hand in hand with the eigenstate localization on the locally symmetric domain. We provide a brief outlook addressing possible generalizations of local symmetry transformations while maintaining isospectrality.

We provide a non-unit-disk framework to solve combinatorial optimization problems such as maximum cut and maximum independent set on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at timescales well within the system lifetime and with approximation ratios close to one. The nonblockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.

We demonstrate the failure of the adiabatic Born-Oppenheimer approximation to describe the ground state of a quantum impurity within an ultracold Fermi gas despite substantial mass differences between the bath and impurity species. Increasing repulsion leads to the appearance of nonadiabatic couplings between the fast bath and slow impurity degrees of freedom, which reduce the parity symmetry of the latter according to the pseudo Jahn-Teller effect. The presence of this mechanism is associated to a conical intersection involving the impurity position and the inverse of the interaction strength, which acts as a synthetic dimension. We elucidate the presence of these effects via a detailed ground-state analysis involving the comparison of ab initio fully correlated simulations with effective models. Our study suggests ultracold atomic ensembles as potent emulators of complex molecular phenomena.

We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and a trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

We experimentally realize the Peregrine soliton in a highly particle-imbalanced two-component repulsive Bose-Einstein condensate in the immiscible regime. The effective focusing dynamics and resulting modulational instability of the minority component provide the opportunity to dynamically create a Peregrine soliton with the aid of an attractive potential well that seeds the initial dynamics. The Peregrine soliton formation is highly reproducible, and our experiments allow us to separately monitor the minority and majority components, and to compare with the single component dynamics in the absence or presence of the well with varying depths. We showcase the centrality of each of the ingredients leveraged herein. Numerical corroborations and a theoretical basis for our findings are provided through three-dimensional simulations emulating the experimental setting and via a one-dimensional analysis further exploring its evolution dynamics.

We study the out-of-equilibrium dynamics of noninteracting atoms confined within a one-dimensional harmonic trap triggered by dragging an external long-range potential through the system. The symmetry-breaking nature of this moving potential couples adjacent eigenstates in the atoms' effective potential, leading to an energy landscape reminiscent of systems exhibiting trap-induced shape resonances. These couplings may be exploited to selectively excite the atoms into higher vibrational states of the harmonic trap by controlling the motion of the dragged potential. To this end, we consider two protocols designs: The first protocol strives to maintain adiabaticity at critical points during the atoms' dynamics, while the second protocol utilizes the fast tunneling of the atoms within their effective double-well potential. These protocols take place in the few to many millisecond regime and achieve high-fidelity excitation of the atoms into pure vibrational states and superpositions thereof. Overall, our study highlights the significance of dragged potentials for controlling and manipulating atom dynamics and offers intuitive protocols for achieving desired excitations.

The concept of local symmetry dynamics has recently been used to demonstrate the evolution of discrete symmetries in one-dimensional chains leading to emergent periodicity. Here we go one step further and show that the unboundedness of this dynamics can lead to chains that consist of subunits of ever-increasing lengths which results in a scaled chain. Mapping this scaled chain onto a corresponding tight-binding Hamiltonian we investigate its spectral and transmission properties. Varying the off-diagonal coupling the eigenvalue spectrum shows different branches with characteristic transitions and peaks in the corresponding density of states. The fluctuations of the energy levels exhibit a hierarchy of minigaps each one accompanied by a characteristic sequence of energy spacings. We develop a local resonator model to describe the spectral properties and gain a deeper understanding of it in the weak-to-intermediate coupling regime. Eigenstate maps together with the inverse participation ratio are used to unravel the characteristic (de)localization properties of the scaled chain with varying coupling strength. Finally, we probe the energy-dependent transmission profile of the scaled chain.

We investigate the ground state (GS) properties of rectangular dipole lattices on curved surfaces. The curved geometry can 'distort' the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the surface. We find that the system's GS can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls (DWs) locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the DWs to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the DW acts as a boundary that traps low-energy excitations within a domain.

Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the Van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.

We demonstrate that an interferometer based on modulated magnetic field pulses enables precise characterization of the energies and lifetimes of Efimov trimers irrespective of the magnitude and sign of the interactions in 85Rb thermal gases. Despite thermal effects, interference fringes develop when the dark time between the pulses is varied. This enables the selective excitation of coherent superpositions of trimer, dimer, and free-atom states. The interference patterns possess two distinct damping timescales at short and long dark times that are either equal to or twice as long as the lifetime of Efimov trimers, respectively. Specifically, this behavior at long dark times provides an interpretation of the unusually large damping timescales reported in a recent experiment with 7Li thermal gases [Yudkin et al., Phys. Rev. Lett. 122, 200402 (2019)]. Apart from that, our results constitute a stepping stone towards a high precision few-body state interferometry for dense quantum gases.

We explore the scattering of waves in designed asymmetric one-dimensional waveguide networks. We show that the reflection between two ports of an asymmetric network can be identical over a broad frequency range, as if the network was mirror-symmetric, under the condition of so-called latent symmetry between the ports. This broadband equireflectionality is validated numerically for acoustic waveguides and experimentally through measurements on microwave transmission-line networks. In addition, introducing a generalization of latent symmetry, we study the properties of an N-port scattering matrix S. When the powers of S fulfill certain relations, which we coin scaled cospectrality, the setup is guaranteed to possess at least one zero eigenvalue of S, so that the setup features coherent perfect absorption. More importantly, scaled cospectrality introduces a scaling factor which controls the asymmetry of the incoming wave to be absorbed. Our findings introduce a novel approach for designing tunable wave manipulation devices in asymmetric setups. As evidenced by our acoustic simulations and microwave experiments, the generality of our approach extends its potential applications to a wide range of physical systems.

Cold atomic gases have become a paradigmatic system for exploring fundamental physics, which at the same time allows for applications in quantum technologies. The accelerating developments in the field have led to a highly advanced set of engineering techniques that, for example, can tune interactions, shape the external geometry, select among a large set of atomic species with different properties, or control the number of atoms. In particular, it is possible to operate in lower dimensions and drive atomic systems into the strongly correlated regime. In this review, we discuss recent advances in few-body cold atom systems confined in low dimensions from a theoretical viewpoint. We mainly focus on bosonic systems in one dimension and provide an introduction to the static properties before we review the state-of-the-art research into quantum dynamical processes stimulated by the presence of correlations. Besides discussing the fundamental physical phenomena arising in these systems, we also provide an overview of the calculational and numerical tools and methods that are commonly used, thus delivering a balanced and comprehensive overview of the field. We conclude by giving an outlook on possible future directions that are interesting to explore in these correlated systems.

We explore Fermi acceleration in a stochastic oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a transition from limited to unlimited energy growth taking place while detuning the corresponding restitution coefficient responsible for the degree of dissipation. A corresponding order parameter is suggested, and its susceptibility is shown to diverge at the critical point. We show that this order parameter is also be applicable to the periodically driven oval billiard and discuss the elementary excitation of the controlled diffusion process.

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a symmetry that holds only in a finite domain of space, can be either the result of a self-organization process or a structural ingredient into a synthetically prepared physical system. Applying local symmetry operations to extend a given finite chain we show that the resulting one-dimensional lattice consists of a transient followed by a subsequent periodic behavior. Due to the fact that, by construction, the implanted local symmetries strongly overlap the resulting lattice possesses a dense skeleton of such symmetries. We proof this behavior on the basis of a class of local symmetry operations allowing us to conclude upon the “asymptotic” properties such as the final period, decomposition of the unit cell and the length and appearance of the transient. As an example case, we explore the corresponding tight-binding Hamiltonians. Their energy eigenvalue spectra and eigenstates are analyzed in some detail, showing in particular the strong variability of the localization properties of the eigenstates due to the presence of a plethora of local symmetries.

We study analytically an armchair graphene nanoribbon (AGNR) in the presence of a bichromatic light wave, consisting of intense low-frequency and perturbative high frequency modes. The electric fields of both waves are directed parallel to the ribbon axis. The Dirac equation describing the electron-nonstationary field interaction is employed and solved in the resonant approximation. This allows us to calculate in an explicit form the Rabi frequency of the resonant transitions between the hole and electron size-quantized subbands, induced by the weak wave. The dependencies of the Rabi frequency on the parity of the low frequency photon numbers, magnitudes of the electric fields and ribbon width are examined and found to be in line with those obtained by numerical methods. We show that the Rabi frequency associated with the additional weak wave exceeds that generated by only the strong mode.

We investigate spin-charge separation of a spin-12 Fermi system confined in a triple well where multiple bands are occupied. We assume that our finite fermionic system is close to fully spin polarized while being doped by a hole and an impurity fermion with opposite spin. Our setup involves ferromagnetic couplings among the particles in different bands, leading to the development of strong spin-transport correlations in an intermediate interaction regime. Interactions are then strong enough to lift the degeneracy among singlet and triplet spin configurations in the well of the spin impurity but not strong enough to prohibit hole-induced magnetic excitations to the singlet state. Despite the strong spin-hole correlations, the system exhibits spin-charge deconfinement allowing for long-range entanglement of the spatial and spin degrees of freedom.

The Fibonacci chain, i.e. a tight-binding model where couplings and/or on-site potentials can take only two different values distributed according to the Fibonacci word, is a classical example of a one-dimensional quasicrystal. With its many intriguing properties, such as a fractal eigenvalue spectrum, the Fibonacci chain offers a rich platform to investigate many of the effects that occur in three-dimensional quasicrystals. In this work, we study the eigenvalues and eigenstates of two identical Fibonacci chains coupled to each other in different ways. We find that this setup allows for a rich variety of effects. Depending on the coupling scheme used, the resulting system (i) possesses an eigenvalue spectrum featuring a richer hierarchical structure compared to the spectrum of a single Fibonacci chain, (ii) shows a coexistence of Bloch and critical eigenstates, or (iii) possesses a large number of degenerate eigenstates, each of which is perfectly localized on only four sites of the system. If additionally, the system is infinitely extended, the macroscopic number of perfectly localized eigenstates induces a perfectly flat quasi band. Especially the second case is interesting from an application perspective, since eigenstates that are of Bloch or of critical character feature largely different transport properties. At the same time, the proposed setup allows for an experimental realization, e.g. with evanescently coupled waveguides, electric circuits, or by patterning an anti-lattice with adatoms on a metallic substrate.

Ultralong-range Rydberg molecules (ULRMs) are highly imbalanced bound systems formed via the low-energy scattering of a Rydberg electron with a ground-state atom. We investigate for 23Na the d state and the energetically close-by trilobite state, exhibiting avoided crossings that lead to the breakdown of the adiabatic Born-Oppenheimer (BO) approximation. We develop a coupled-channel approach to explore the nonadiabatic interaction effects between these electronic states. The resulting spectrum exhibits stark differences in comparison to the BO spectra, such as the existence of above-threshold resonant states without any adiabatic counterparts, and a significant rearrangement of the spectral structure as well as the localization of the eigenstates. Our study motivates the use of 23Na ULRMs, as a probe to explore vibronic interaction effects on exaggerated timescales and length scales.

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this paper, we employ a numerical technique referred to as multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multilayering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

We unravel the correlated quantum quench dynamics of a single impurity immersed in a bosonic environment confined in an one-dimensional double-well potential. A particular emphasis is placed on the structure of the time-evolved many-body (MB) wave function by relying on a Schmidt decomposition whose coefficients directly quantify the number of configurations that are macroscopically populated. For a non-interacting bosonic bath and weak postquench impurity-bath interactions, we observe the dynamical formation of a two-fold fragmented MB state which is related to intra-band excitation processes of the impurity and manifests as a two-body phase separation (clustering) between the two species for repulsive (attractive) interactions. Increasing the postquench impurity-bath coupling strength leads to the destruction of the two-fold fragmentation since the impurity undergoes additional inter-band excitation dynamics. By contrast, a weakly interacting bath suppresses excitations of the bath particles and consequently the system attains a weakly fragmented MB state. Our results explicate the interplay of intra- and inter-band impurity excitations for the dynamical generation of fragmented MB states in multi-well traps and for designing specific entangled impurity states.

We address the existence and dynamics of one-dimensional harmonically confined quantum droplets appearing in two-component mixtures by deploying a nonperturbative approach. We find that, in symmetric homonuclear settings, beyond-Lee-Huang-Yang correlations result in flat-top droplet configurations for either decreasing intercomponent attraction or larger atom number. Asymmetric mixtures feature spatial mixing among the involved components with the more strongly interacting or heavier one exhibiting flat-top structures. Applying quenches on the harmonic trap we trigger the lowest-lying collective droplet excitations. The interaction-dependent breathing frequency, being slightly reduced in the presence of correlations, shows a decreasing trend for stronger attractions. Semianalytical predictions are also obtained within the Lee-Huang-Yang framework. For relatively large quench amplitudes the droplet progressively delocalizes and higher-lying motional excitations develop in its core. Simultaneously, enhanced intercomponent entanglement and long-range two-body intracomponent correlations arise. In sharp contrast, the dipole motion remains robust irrespective of the system parameters. Species-selective quenches lead to a correlation-induced dephasing of the droplet or to irregular dipole patterns due to intercomponent collisions.

Latent symmetries are hidden symmetries which become manifest by performing a reduction of a given discrete system into an effective lower-dimensional one. We show how latent symmetries can be leveraged for continuous wave setups in the form of acoustic networks. These are systematically designed to possess latent-symmetry induced pointwise amplitude parity between selected waveguide junctions for all low frequency eigenmodes. We develop a modular principle to interconnect latently symmetric networks to feature multiple latently symmetric junction pairs. By connecting such networks to a mirror symmetric subsystem, we design asymmetric setups featuring eigenmodes with domain-wise parity. Bridging the gap between discrete and continuous models, our work takes a pivotal step towards exploiting hidden geometrical symmetries in realistic wave setups.

Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterized by their unique electronic structures resulting from the ion-induced admixture of quantum defect-split Rydberg nP states with different low-field-seeking high-l states. We predict that in both cases, these diatomic molecular states can bind additional ground-state atoms lying within the orbit of the Rydberg electron, thereby forming charged ultralong-range Rydberg molecules (ULRMs) with binding energies similar to that of conventional nonpolar ULRMs. To demonstrate this, we consider a Rydberg atom interacting with a single ground-state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalization over a finite basis and the vibrational structure is determined using the multiconfiguration time-dependent Hartree method. Due to the lobelike structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.

The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail, evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion, and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes accessible in contemporary cold atom experiments.

Magnetic monopoles have been realized as emergent quasiparticles in both condensed matter and ultracold atomic platforms, with growing interest in the coupling effects between the monopole and different magnetic quasiparticles. In this work, interaction effects between monopoles and magnons are investigated for an atomic pseudospin chain. We reveal that the monopole can excite a virtual magnon cloud in the paramagnetic chain, thereby giving rise to an unconventional type of polaron, the monopole-cored polaron (MCP). The MCP is composed of the monopole as the impurity core and the virtual magnon excitation as the dressing cloud. The magnon dressing facilitates the Dirac string excitation and impacts the monopole hopping. This induces an antitrapping effect of the MCP, which refers to the fact that the dressing enhances the mobility of the MCP, in contrast to the self-trapping of the common polarons. Moreover, heterogeneous bipolarons are shown to exist under the simultaneous doping of a north and a south monopole. The heterogeneous bipolaron possesses an inner degree of freedom composed of two identical impurities. Our investigation sheds light on the understanding of how the coupling between the impurity core and the dressing cloud can engineer the property of the polaron.

We explore the dynamical transport of an impurity between different embedding majority species, which are spatially separated in a double well. The transfer and storage of the impurity is triggered by dynamically changing the interaction strengths between the impurity and the two majority species. We find a simple but efficient protocol consisting of linear ramps of majority-impurity interactions at designated times to pin or unpin the impurity. Our study of this highly imbalanced few-body triple mixture is conducted with the multilayer multiconfiguration time-dependent Hartree method for atomic mixtures, which accounts for all interaction-induced correlations. We analyze the dynamics in terms of single-particle densities and entanglement growth and provide an effective potential description involving mean fields of the interacting components. The majority components remain self-trapped in their individual wells at all times, which is a crucial element for the effectiveness of our protocol. During storage times each component performs low-amplitude dipole oscillations in a single well. Unexpectedly, the interspecies correlations possess a stabilizing impact on the transport and storage properties of the impurity particle.

A scheme is proposed to dynamically excite distinct eigenstate superpositions in three-body Bose-Fermi mixtures confined in a two-dimensional harmonic trap. The system is initialized in a noninteracting state with a variable spatial extent, and the scattering lengths are subsequently quenched spanning the regime from weak to strong interactions. For spatial widths smaller than the three-body harmonic oscillator length, a superposition of trimers and atom-dimers is dynamically attained, otherwise trap states are predominantly populated, as inferred from the frequency spectrum of the fidelity. Accordingly, the Tan contacts evince the buildup of short-range two- and three-body correlations in the course of the evolution. A larger spatial extent of the initial state leads to a reduction of few-body correlations, endowed, however, with characteristic peaks at the positions of the avoided crossings in the energy spectra, thereby signaling the participation of atom-dimers. Our results expose ways to dynamically excite selectively trimers, atom-dimers, and trapped few-body states characterized by substantial correlations, and they are likely to be accessible within current experiments.

We investigate the formation of magnetic Bose polaron, an impurity atom dressed by spin-wave excitations, in a one-dimensional spinor Bose gas. Within an effective potential model, the impurity is strongly confined by the host excitations which can even overcome the impurity-medium repulsion leading to a self-localized quasi-particle state. The phase diagram of the attractive and self-bound repulsive magnetic polaron, repulsive non-magnetic (Fröhlich-type) polaron and impurity-medium phase-separation regimes is explored with respect to the Rabi-coupling between the spin components, spin–spin interactions and impurity-medium coupling. The residue of such magnetic polarons decreases substantially in both strong attractive and repulsive branches with strong impurity-spin interactions, illustrating significant dressing of the impurity. The impurity can be used to probe and maneuver the spin polarization of the magnetic medium while suppressing ferromagnetic spin–spin correlations. It is shown that mean-field theory fails as the spinor gas approaches immiscibility since the generated spin-wave excitations are prominent. Our findings illustrate that impurities can be utilized to generate controllable spin–spin correlations and magnetic polaron states which can be realized with current cold atom setups.

We investigate the classical equilibrium properties and metamorphosis of the ground state of interacting dipoles with fixed locations on a helix. The dipoles are shown to align themselves along separate intertwined dipole chains forming single, double, and higher-order helical chains. The number of dipole chains, and their properties such as chirality and length scale on which the chains wind around each other, can be tuned by the geometrical parameters. We demonstrate that all possible configurations form a self-similar bifurcation diagram which can be linked to the Stern–Brocot tree and the underlying Farey sequence. We describe the mechanism responsible for this behavior and subsequently discuss corresponding implications and possible applications.

We explore the connection between chaos, thermalization, and ergodicity in a linear chain of N interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with excess energy ΔK. The time evolution of the chaoticity of the system and the energy localization along the chain is analyzed by computing, up to a very long time, the statistical average of the finite-time Lyapunov exponent λ(t) and the participation ratio Π(t). For small ΔK, the evolution of λ(t) and Π(t) indicates that the system becomes chaotic at approximately the same time as Π(t) reaches a steady state. For the largest considered values of ΔK the system becomes chaotic at an extremely early stage in comparison with the energy relaxation times. We find that this fact is due to the presence of chaotic breathers that keep the system far from equipartition and ergodicity. Finally, we show numerically and analytically that the asymptotic values attained by the participation ratio Π(t) fairly correspond to thermal equilibrium.

We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS equation on the torus, a recently derived [N.-E. Guenther et al., Phys. Rev. A 101, 053606 (2020)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS equation evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and followed, using parameter continuation, along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontally and vertically aligned quadrupoles to rectangular and rhomboidal quadrupoles to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrupole solutions is monitored at both the NLS equation and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark-soliton stripes and their connection, through a series of bifurcation cascades, with steady-state vortex configurations.

The counterflow dynamics of two correlated impurities in a double well coupled to a one-dimensional bosonic medium is explored. We determine the ground-state phase diagram of the system according to the impurity-medium entanglement and the impurities' two-body correlations. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinement of the medium. Accordingly the impurities' dynamical response, triggered by suddenly ramping down the central potential barrier, is affected by the medium's trapping geometry. In particular, for a box-confined medium, repulsive impurity-medium couplings lead, due to attractive induced interactions, to the localization of the impurities around the trap center. In contrast, for a harmonically trapped medium the impurities perform a periodic collision and expansion dynamics further interpreted in terms of a two-body effective model. Our findings elucidate the correlation aspects of the collisional physics of impurities which should be accessible in recent cold-atom experiments.

Magnetic monopoles and kinks are topological excitations that have been extensively investigated in quantum spin systems, but usually, they are studied in different setups. We explore the conditions for the coexistence and interaction effects of these quasiparticles in the pseudospin chain of an atomic dipolar superlattice gas. In this chain, the magnetic kink is the intrinsic quasiparticle, and the particle (hole) defect takes over the role of the north (south) magnetic monopole, exerting monopolar magnetic fields on neighboring spins. A binding effect between the monopole and kink is revealed, which renormalizes the dispersion of the kink. The corresponding dynamical antibinding process is observed and arises due to the kink-antikink annihilation. The rich interaction effects of the two quasiparticles could stimulate corresponding investigations in bulk spin systems.

The present work is motivated by the recent experimental realization of the Townes soliton in an effective two-component Bose-Einstein condensate by B. Bakkali-Hassan et al. [Phys. Rev. Lett. 127, 023603 (2021)]. Here, we use a similar multicomponent platform to exemplify theoretically and numerically, within the mean-field Gross-Pitaevskii framework, the potential toward the experimental realization of a different fundamental wave structure, namely the Peregrine soliton. Leveraging the effective attractive interaction produced within the mixture's minority species in the immiscible regime, we illustrate how initialization of the condensate with a suitable power-law decaying spatial density pattern yields the robust emergence of the Peregrine wave in the absence and in the presence of a parabolic trap. We then showcase the spontaneous emergence of the Peregrine soliton via a suitably crafted wide Gaussian initialization, again both in the homogeneous case and in the trap scenario. It is also found that narrower wave packets may result in periodic revivals of the Peregrine soliton, while broader ones give rise to a cascade of Peregrine solitons arranged in a so-called Christmas-tree structure. Strikingly, the persistence of these rogue-wave structures is demonstrated in certain temperature regimes as well as in the presence of transversal excitations through three-dimensional computations in a quasi-one-dimensional regime. This proof-of-principle illustration is expected to represent a practically feasible way to generate and observe this rogue wave in realistic current ultracold atom experimental settings.

We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit of a vanishing helix radius, the governing equations of motion coincide with those of the well-known Kapitza pendulum—a classical pendulum with oscillating pivot—implying that the driven toroidal helix represents a corresponding generalization. It is shown that the two dominant static fixed points present in the Kapitza pendulum are also present for a finite helix radius. The dependence of the stability of these two fixed points on the helix radius, the driving amplitude, and the static potential are analyzed analytically. These analytical results are subsequently compared to results corresponding of numerical simulations. Additionally, the most prominent deviations of the driven helix from the Kapitza pendulum with respect to the resulting phase space are investigated and analyzed in some detail. These effects include an unusual transition to chaos and an effective directed transport due to the simultaneous presence of multiple chaotic phase space regions.

We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths, and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal postquench traps the employed protocol allows to couple states of different center-of-mass parity in contrast to species-symmetric trap quenches. Among the participating eigenstates we identify one having odd center-of-mass parity and even global parity. The breathing frequency induced by this state is a monotonically decreasing function of the coupling parameter. Importantly, in order to be numerically observable, it requires the entanglement between the species to be taken into account. We demonstrate this by comparing the numerically exact results obtained by means of the multilayer multiconfiguration time-dependent Hartree method for mixtures to the ones of a species mean-field ansatz. The entanglement-sensitive breathing frequency persists also for unequal postquench traps where the center of mass cannot be decoupled. Finally, we analyze the impact of global parity symmetry on the breathing dynamics by initializing a state of odd global parity. We evidence a striking resemblance to the breathing spectrum of the ground state, but find also some additional modes.

We present an analytical approach to the problem of the multiphoton absorption and Rabi oscillations in an armchair graphene nanoribbon (AGNR) in the presence of a time-oscillating strong electric field induced by a light wave directed parallel to the ribbon axis. The two-dimensional Dirac equation for the massless electron subject to the ribbon confinement is employed. In the resonant approximation the electron-hole pair production rate, associated with the electron transitions between the valence and conduction size-quantized subbands, the corresponding multiphoton absorption coefficient, and the frequency of the Rabi oscillations are obtained in an explicit form. We trace the dependencies of the above quantities on the ribbon width and electric field strength for both the multiphoton assisted and tunneling regimes relevant to the time-oscillating and practically constant electric field, respectively. A significant enhancement effect of the oscillating character of the electric field on the intersubband transitions is encountered. Our analytical results are in qualitative agreement with those obtained for the graphene layer by numerical methods. Estimates of the expected experimental values for the typically employed AGNR and laser parameters show that both the Rabi oscillations and multiphoton absorption are accessible in the laboratory. The data relevant to the intersubband tunneling makes the AGNR a one-dimensional condensed matter analog in which the quantum electrodynamic vacuum decay can be detected by applying an external laboratory electric field.

We investigate the polaronic properties of a single impurity immersed in a weakly interacting bosonic environment confined within a one-dimensional double-well potential using an exact diagonalization approach. We find that an increase of the impurity–bath coupling results in a vanishing residue, signifying the occurrence of the polaron orthogonality catastrophe. Asymptotic configurations of the systems' ground state wave function in the strongly interacting regime are obtained by means of a Schmidt decomposition, which in turn accounts for the observed orthogonality catastrophe of the polaron. We exemplify that depending on the repulsion of the Bose gas, three distinct residue behaviors appear with respect to the impurity–bath coupling. These residue regimes are characterized by two critical values of the bosonic repulsion and originate from the interplay between the intra- and the interband excitations of the impurity. Moreover, they can be clearly distinguished in the corresponding species reduced density matrices with the latter revealing a phase separation on either the one- or the two-body level. The impact of the interspecies mass-imbalance on the impurity's excitation processes is appreciated yielding an interaction shift of the residue regions. Our results explicate the interplay of intra- and interband excitation processes for the polaron generation in multiwell traps and for designing specific polaron entangled states motivating their exposure in current experiments.

The controlled creation of dark-bright (DB) soliton trains in multicomponent Bose-Einstein condensates (BECs) is a topic of ongoing interest. In this work we generalize earlier findings on the creation of dark soliton trains in single-component BECs [A. Romero-Ros et al., Phys. Rev. A 103, 023329 (2021)] to two-component BECs. By choosing suitable filled box-type initial configurations (FBTCs) and solving the direct scattering problem for the defocusing vector nonlinear Schrödinger equation with nonzero boundary conditions we obtain analytical expressions for the DB soliton solutions produced by a general FBTC. It is found that the size of the initial box and the amount of filling directly affect the number, size, and velocity of the solitons, while the initial phase determines the parity (even or odd) of the solutions. Our analytical results are compared to direct numerical integration of the coupled Gross-Pitaevskii equations, both in the absence and in the presence of a harmonic trap, and an excellent agreement between the two is demonstrated.

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.

We study the impact of beyond Lee-Huang-Yang (LHY) physics, especially due to intercomponent correlations, in the ground state and the quench dynamics of one-dimensional quantum droplets with an ab initio nonperturbative approach. It is found that the droplet Gaussian-shaped configuration arising for intercomponent attractive couplings becomes narrower for stronger intracomponent repulsion and transits towards a flat-top structure either for larger particle numbers or weaker intercomponent attraction. Additionally, a harmonic trap prevents the flat-top formation. At the balance point where mean-field interactions cancel out, we show that a correlation hole is present in the few-particle limit of LHY fluids as well as for flat-top droplets. Introducing mass imbalance, droplets experience intercomponent mixing and excitation signatures are identified for larger masses. Monitoring the droplet expansion (breathing motion) upon considering interaction quenches to stronger (weaker) attractions, we explicate that beyond LHY correlations result in a reduced velocity (breathing frequency). Strikingly, the droplets feature two-body anticorrelations (correlations) at the same position (longer distances). Our findings pave the way for probing correlation-induced phenomena of droplet dynamics in current ultracold-atom experiments.

We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analysed in terms of the eigenvalues and eigenstates of the underlying stationary Schrödinger equation up to several hundreds of excited states. A generalization of the superexponential self-interacting oscillator shows a scaling behaviour of the spacing of the eigenvalues which turns into an alternating behaviour for the power law modified oscillator. Superexponential potentials with an oscillating power show a very rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even–odd pairs which are interspersed into the spectrum of delocalized states. We provide an outlook on future perspectives including the possibility to use these features for applications in e.g. cold atom physics.

We study the statistical mechanics and the dynamical relaxation process of modulationally unstable one-dimensional quantum droplets described by a modified Gross–Pitaevskii equation. To determine the classical partition function thereof, we leverage the semi-analytical transfer integral operator (TIO) technique. The latter predicts a distribution of the observed wave-function amplitudes and yields two-point correlation functions providing insights into the emergent dynamics involving quantum droplets. We compare the ensuing TIO results with the probability distributions obtained at large times of the modulationally unstable dynamics as well as with the equilibrium properties of a suitably constructed Langevin dynamics. We find that the instability leads to the spontaneous formation of quantum droplets featuring multiple collisions and which are found to coalesce at large evolution times. Our results from the distinct methodologies are in good agreement aside from the case of low temperatures in the special limit where the droplet widens. In this limit, the distribution acquires a pronounced bimodal character, exhibiting a deviation between the TIO solution and the Langevin dynamics.

We unravel the polaronic properties of impurities immersed in a correlated trapped one-dimensional Bose-Bose mixture. This setup allows the impurities to couple either attractively or repulsively to a specific host, thus offering a highly flexible platform for steering the emergent polaronic properties. Specifically, the impurity residue peak and strength of induced interactions can be controlled by varying the coupling of the impurities to the individual bosonic components. In particular, it is possible to maintain the quasiparticle character for larger interaction strengths as compared to the case of impurities immersed in a single bosonic species. We explicate a hierarchy of the polaron binding energies in terms of the impurity-medium interactions, thereby elucidating the identification of the polaronic resonances in recent experimental radio-frequency schemes. For strong attractive impurity-medium couplings, bipolaron formation is captured. Our findings pave the way for continuously changing the quasiparticle character, under the impact of trap effects, while exposing the role of correlations in triple-mixture settings.

Few-body correlations emerging in two-dimensional harmonically trapped mixtures, are comprehensively investigated. The presence of the trap leads to the formation of atom-dimer and trap states, in addition to trimers. The Tan's contacts of these eigenstates are studied for varying interspecies scattering lengths and mass ratio, while corresponding analytical insights are provided within the adiabatic hyperspherical formalism. The two- and three-body correlations of trimer states are substantially enhanced compared to the other eigenstates. The two-body contact of the atom-dimer and trap states features an upper bound regardless of the statistics, treated semi-classically and having an analytical prediction in the limit of large scattering lengths. Such an upper bound is absent in the three-body contact. Interestingly, by tuning the interspecies scattering length the contacts oscillate as the atom-dimer and trap states change character through the existent avoided-crossings in the energy spectra. For thermal gases, a gradual suppression of the involved two- and three-body correlations is evinced manifesting the impact of thermal effects. Moreover, spatial configurations of the distinct eigenstates ranging from localized structures to angular anisotropic patterns are captured. Our results provide valuable insights into the inherent correlation mechanisms of few-body mixtures which can be implemented in recent ultracold atom experiments and will be especially useful for probing the crossover from few- to many-atom systems.

We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential can exhibit chaotic dynamics due to the presence of a single impurity. The nonequilibrium dynamics is triggered by a quench of the impurity-Bose interaction and is illustrated via the evolution of the population imbalance for the bosons between the two wells. While the increase of the postquench interaction strength always facilitates the irregular motion for the bosonic population imbalance, it becomes regular again when the impurity is initially populated in the highly excited states. Such an integrability to chaos (ITC) transition is fully captured by the transient dynamics of the corresponding linear entanglement entropy, whose infinite-time-averaged value additionally characterizes the edge of the chaos and implies the existence of an effective Bose-Bose attraction induced by the impurity. To elucidate the physical origin for the observed ITC transition, we perform a detailed spectral analysis for the mixture with respect to both the energy spectrum as well as the eigenstates. Specifically, two distinguished spectral behaviors upon a variation of the interspecies interaction strength are observed. While the avoided level crossings take place in the low-energy spectrum, the energy levels in the high-energy spectrum possess a bandlike structure and are equidistant within each band. This leads to a significant delocalization of the low-lying eigenvectors, which, in turn, accounts for the chaotic nature of the bosonic dynamics. By contrast, those highly excited states bear a high resemblance to the noninteracting integrable basis, which explains the recovery of the integrability for the bosonic species. Finally, we discuss the induced Bose-Bose attraction as well as its impact on the bosonic dynamics.

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with l-fold symmetry, ranging from quadrupole (l=2) to heptagon modes (l=7), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the l=6 mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.

We observe a series of conical intersections in the potential energy curves governing both the collision between a Rydberg atom and a ground-state atom and the structure of Rydberg molecules. By employing the electronic energy of the Rydberg atom as a synthetic dimension we circumvent the von Neumann–Wigner theorem. These conical intersections can occur when the Rydberg atom’s quantum defect is similar in size to the electron–ground-state atom scattering phase shift divided by π, a condition satisfied in several commonly studied atomic species. The conical intersections have an observable consequence in the rate of ultracold l-changing collisions of the type Rb(nf)+Rb(5s)→Rb(nl>3)+Rb(5s). In the vicinity of a conical intersection, this rate is strongly suppressed, and the Rydberg atom becomes nearly transparent to the ground-state atom.

Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies in hosting compactly localized eigenstates which originate from destructive interference induced by the lattice geometry, in turn often based on symmetry principles. We here show that flat bands can be generated from a hidden symmetry of the lattice unit cell, revealed as a permutation symmetry upon reduction of the cell over two sites governed by an effective dimer Hamiltonian. This so-called latent symmetry is intimately connected to a symmetry between possible walks of a particle along the cell sites, starting and ending on each of the effective dimer sites. The summed amplitudes of any eigenstate with odd parity on the effective dimer sites vanish on special site subsets called walk multiplets. We exploit this to construct flat bands by using a latently symmetric unit cell coupled into a lattice via walk multiplet interconnections. We demonstrate that the resulting flat bands are tunable by different parametrizations of the lattice Hamiltonian matrix elements which preserve the latent symmetry. The developed framework may offer fruitful perspectives to analyze and design flat band structures.

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split up of the chaotic part of the phase space, which prevents the particle from inverting its direction of motion. This allows for a nonzero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.

Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices of an undirected graph with real edge weights are cospectral if and only if the underlying weighted adjacency matrix M fulfills for all non-negative integer k, and as a result any eigenvector ϕ of M has (or, in the presence of degeneracies, can be chosen to have) definite parity on u and v. We here show that the powers of a matrix with cospectral vertices induce further local relations on its eigenvectors, and also can be used to design cospectrality preserving modifications. To this end, we introduce the concept of walk equivalence of cospectral vertices with respect to walk multiplets which are special vertex subsets of a graph. Walk multiplets allow for systematic and flexible modifications of a graph with a given cospectral pair while preserving this cospectrality. The set of modifications includes the addition and removal of both vertices and edges, such that the underlying topology of the graph can be altered. In particular, we prove that any new vertex connected to a walk multiplet by suitable connection weights becomes a so-called unrestricted substitution point (USP), meaning that any arbitrary graph may be connected to it without breaking cospectrality. Also, suitable interconnections between walk multiplets within a graph are shown to preserve the associated cospectrality. Importantly, we demonstrate that the walk equivalence of cospectral vertices imposes a local structure on every eigenvector ϕ obeying (in the case of degeneracies, a specific choice of the eigenvector basis is needed). Our work paves the way for flexibly exploiting hidden structural symmetries in the design of generic complex network-like systems.

Degeneracies in the energy spectra of physical systems are commonly considered to be either of accidental character or induced by symmetries of the Hamiltonian. We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian derived by subsystem partitioning. We provide an intuitive interpretation of such latent symmetries by relating them to corresponding local symmetries in the powers of the underlying Hamiltonian matrix. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-Abelian latent symmetry group. It is demonstrated that the rotational symmetries can be broken in a controlled manner while maintaining the underlying more fundamental latent symmetry. This opens up the perspective of investigating accidental degeneracies in terms of latent symmetries.

We investigate the crossover of the impurity-induced dynamics, in trapped one-dimensional Bose polarons subject to radio frequency (RF) pulses of varying intensity, from an adiabatic to a diabatic regime. Utilizing adiabatic pulses for either weak repulsive or attractive impurity-medium interactions, a multitude of polaronic excitations or mode-couplings of the impurity-bath interaction with the collective breathing motion of the bosonic medium are spectrally resolved. We find that for strongly repulsive impurity-bath interactions, a temporal orthogonality catastrophe manifests in resonances in the excitation spectra where impurity coherence vanishes. When two impurities are introduced, impurity–impurity correlations, for either attractive or strong repulsive couplings, induce a spectral shift of the resonances with respect to the single impurity. For a heavy impurity, the polaronic peak is accompanied by a series of equidistant side-band resonances, related to interference of the impurity spin dynamics and the sound waves of the bath. In all cases, we enter the diabatic transfer regime for an increasing bare Rabi frequency of the RF field with a Lorentzian spectral shape featuring a single polaronic resonance. The findings in this work on the effects of external trap, RF pulse and impurity–impurity interaction should have implications for the new generations of cold-atom experiments.

We unravel the many-body dynamics of a harmonically trapped impurity colliding with a bosonic medium confined in a double well upon quenching the initially displaced harmonic trap to the center of the double well. We reveal that the emerging correlation dynamics crucially depends on the impurity-medium interaction strength allowing for a classification into different dynamical response regimes. For strong attractive impurity-medium couplings the impurity is bound to the bosonic bath, while for intermediate attractions it undergoes an effective tunneling. In the case of weak attractive or repulsive couplings the impurity penetrates the bosonic bath and performs a dissipative oscillatory motion. Further increasing the impurity-bath repulsion results in the pinning of the impurity between the density peaks of the bosonic medium, a phenomenon that is associated with a strong impurity-medium entanglement. For strong repulsions, the impurity is totally reflected by the bosonic medium. To unravel the underlying microscopic excitation processes accompanying the dynamics, we employ an effective potential picture. We extend our results to the case of two bosonic impurities and demonstrate the existence of a qualitatively similar impurity dynamics.

We employ the multiconfiguration time-dependent Hartree method for bosons in order to investigate the correlated nonequilibrium quantum dynamics of two bosons confined in two colliding and uniformly accelerated Gaussian wells. As the wells approach each other an effective, transient double-well structure is formed. This induces a transient and oscillatory over-barrier transport. We monitor both the amplitude of the intrawell dipole mode in the course of the dynamics as well as the final distribution of the particles between the two wells. For fast collisions we observe an emission process which we attribute to two distinct mechanisms. Energy transfer processes lead to an untrapped fraction of bosons and a resonant enhancement of the deconfinement for certain kinematic configurations can be observed. Despite the comparatively weak interaction strengths employed in this work, we identify strong interparticle correlations by analyzing the corresponding von Neumann entropy.

We explore two-dimensional scattering off a potential that is invariant with respect to linear symmetry transformations such as rotations, reflections, and/or coordinate exchange. The common ansatz of an incoming wave, in general, does not respect the symmetries of the potential and, therefore, the solution of the corresponding Schrödinger equation is not an eigenstate of the operator representing the respective symmetry transform. This renders it difficult to conceptually account for the imprint of the potentials' symmetry on the scattered wave field, unless the limit of an infinite distance r→∞ is taken. In the latter case, the symmetries of the potential are expressed as conditions on the scattering amplitude. In the present work, we employ the recently derived, symmetry-induced, nonlocal and divergence-free currents, which are constructed from the wave field at a point r and its symmetry-related image \overline{r}, to derive general properties of the scattering solution and the associated scattering matrix. These properties originate from the requirement of a vanishing divergence for the nonlocal currents, which is in one-to-one correspondence with the presence of a symmetry in the scattering potential. In practice, they are expressed as conditions on the coefficients of the wave-field expansion with respect to the angular momentum basis in two dimensions. This, in turn, constrains the form of the related S-matrix eigenvectors. The obtained properties are also valid at finite r and can be used as a tool to check upon and improve the efficiency of numerical approaches to the quantum scattering problem of interest.

Superexponential systems are characterized by a potential where dynamical degrees of freedom appear in both the base and the exponent of a power law. We explore the scattering dynamics of many-body systems governed by superexponential potentials. Each potential term exhibits a characteristic crossover via two saddle points from a region with a confining channel to two regions of asymptotically free motion. With increasing scattering energy in the channel we observe a transition from a direct backscattering behaviour to multiple backscattering and recollision events in this channel. We analyze this transition in detail by exploring both the properties of individual many-body trajectories and of large statistical ensembles of trajectories. The recollision trajectories occur for energies below and above the saddle points and typically exhibit an intermittent oscillatory behaviour with strongly varying amplitudes. In case of statistical ensembles the distribution of reflection times into the channel changes with increasing energy from a two-plateau structure to a single broad asymmetric peak structure. This can be understood by analyzing the corresponding momentum-time maps which undergo a transition from a two-valued curve to a broad distribution. We close by providing an outlook onto future perspectives of these uncommon model systems.

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.

We consider a hybrid atom-ion system consisting of a pair of bosons interacting with a single ion in a quasi-one-dimensional trapping geometry. Building upon a model potential for the atom-ion interaction developed in earlier theoretical works, we investigate the behavior of the low-energy eigenstates for varying contact interaction strength g among the atoms. In particular, we contrast the two cases of a static ion and a mobile ion. Our study is carried out by means of the multilayer multiconfiguration time-dependent Hartree method for bosons, a numerically exact ab initio method for the efficient simulation of entangled mixtures. We find that repulsive atom interactions induce locally distinct modifications of the atomic probability distribution unique to each eigenstate. While the atoms on average separate from each other with increasing g , they do not necessarily separate from the ion. The mobility of the ion leads in general to greater separations among the atoms as well as between the atoms and the ion. Notably, we observe an exchange between the kinetic energy of the atoms and the atom-ion interaction energy for all eigenstates, which is both interaction and mobility induced. For the ground state, we provide an intuitive description by constructing an effective Hamiltonian for each species, which aptly captures the response of the atoms to the ion's mobility. Furthermore, the effective picture predicts enhanced localization of the ion, in agreement with our results from exact numerical simulations.

Matter-wave interference mechanisms in one-dimensional Bose-Einstein condensates that allow for the controlled generation of dark soliton trains upon choosing suitable box-type initial configurations are described. First, the direct scattering problem for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions and general box-type initial configurations is discussed, and expressions for the discrete spectrum corresponding to the dark soliton excitations generated by the dynamics are obtained. It is found that the size of the initial box directly affects the number, size and velocity of the solitons, while the initial phase determines the parity of the solutions. The analytical results obtained for the untrapped system are compared to those of numerical simulations of the Gross-Pitaevskii equation, both in the absence and in the presence of a harmonic trap. The numerical results bear out the analytical results with excellent agreement.

We investigate the quantum dynamics of ultra-long-range trilobite molecules exposed to homogeneous electric fields. A trilobite molecule consists of a Rydberg atom and a ground-state atom, which is trapped at large internuclear distances in an oscillatory potential due to scattering of the Rydberg electron off the ground-state atom. Within the Born-Oppenheimer approximation, we derive an analytic expression for the two-dimensional adiabatic electronic potential energy surface in weak electric fields valid up to 500 V/m. This is used to unravel the molecular quantum dynamics employing the multiconfigurational time-dependent Hartree method. Quenches of the electric field are performed to trigger the wave-packet dynamics including the case of field inversion. Depending on the initial wave packet, we observe radial intrawell and interwell oscillations as well as angular oscillations and rotations of the respective one-body probability densities. Opportunities to control the molecular configuration are identified, a specific example being the possibility to superimpose different molecular bond lengths by a series of periodic quenches of the electric field.

We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor F=1 Bose–Einstein condensate. Particularly, it is found that nonlinear excitations in the form of dark–dark–bright solitons exist in the antiferromagnetic and in the easy-axis phase of a spinor gas, being generally unstable in the former while possessing stability intervals in the latter phase. Dark–bright–bright solitons can be realized in the polar and the easy-plane phases as unstable and stable configurations respectively; the latter phase can also feature stable dark–dark–dark solitons. Importantly, the persistence of these types of states upon transitioning, by means of tuning the quadratic Zeeman coefficient from one phase to the other is unravelled. Additionally, the spin-mixing dynamics of stable and unstable matter waves is analyzed, revealing among others the coherent evolution of magnetic dark–bright, nematic dark–bright–bright and dark–dark–dark solitons. Moreover, for the unstable cases unmagnetized or magnetic droplet-like configurations and spin-waves consisting of regular and magnetic solitons are seen to dynamically emerge remaining thereafter robust while propagating for extremely large evolution times. Interestingly, exposing spinorial solitons to finite temperatures, their anti-damping in trap oscillation is showcased. It is found that the latter is suppressed for stronger bright soliton component 'fillings'. Our investigations pave the wave for a systematic production and analysis involving spin transfer processes of such waveforms which have been recently realized in ultracold experiments.

We study the correlated dynamics of few interacting bosonic impurities immersed in a one-dimensional harmonically trapped bosonic environment. The mixture is exposed to a time-dependent impurity-medium interaction pulse moving it across the relevant phase-separation boundary. For modulation frequencies smaller than the trapping one, the system successively transits through the miscible and immiscible phases according to the driving of the impurity-medium interactions. For strong modulations, and driving from the miscible to the immiscible regime, a significant fraction of the impurities is expelled to the edges of the bath. They exhibit a strong localization behavior and tend to equilibrate. Following the reverse driving protocol, the impurities perform a breathing motion while featuring a two-body clustering and the bath is split into two incoherent parts. Interestingly, in both driving scenarios, dark-bright solitons are nucleated in the absence of correlations. A localization of the impurities around the trap center for weak impurity-impurity repulsions is revealed, which subsequently disperse into the bath for increasing interactions.

We explore a model system with superexponential interactions that serves as a fundamental building block for more complex superexponential systems. While being of striking simplicity, this highly nonlinear interaction yields a plethora of intriguing properties and rich dynamics. It exhibits a spatial region where the dynamics occurs in a channel characterised by a transversally confined and longitudinally unbounded motion, and additionally two distinct regions where the dynamics is asymptotically free. A deconfinement transition via two saddle points connects the dynamics in the channel with the asymptotically free motion. The scattering functions show plateau and peak structures that can be interpreted in terms of the corresponding momentum-time maps. These are intimately related to the varying anharmonicity of the transverse motion while moving along the longitudinal dimension of the channel. We perform a comprehensive analysis of the scattering transition for energies below and above the saddle points. Possible variants and extensions of the superexponential interaction to many-body system are briefly discussed.

We demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential exhibits a population imbalance between the two wells at large timescales, when the depth of the wells is modulated by a time-dependent driving force. The specific form of the driving force is shown to break spatial parity and time-reversal symmetries, which leads to such an asymptotic population imbalance (API). The value of the API can be flexibly controlled by changing the phase of the driving force and the total number of particles. While the API is highly sensitive to the initial state in the few-particle regime, this dependence on the initial state is lost as we approach the classical limit of large particle numbers. We perform a Floquet analysis in the few-particle regime and an analysis based on a driven classical nonrigid pendulum in the many-particle regime. Although the obtained API values in the many-particle regime agree very well with those obtained in the classical limit, we show that there exists a significant disagreement in the corresponding real-time population imbalance due to quantum correlations.

We unravel the ground-state properties and the nonequilibrium quantum dynamics of two bosonic impurities immersed in a one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. A quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase separation between the impurities and their surrounding for strong repulsions. For attractive postquench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between noninteracting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

We demonstrate the control of vortical motion of neutral classical particles in driven superlattices. Our superlattice consists of a superposition of individual lattices whose potential depths are modulated periodically in time but with different phases. This driving scheme breaks the spatial reflection symmetries and allows an ensemble of particles to rotate with an average angular velocity. An analysis of the underlying dynamical attractors provides an efficient method to control the angular velocities of the particles by changing the driving amplitude. As a result, spatially periodic patterns of particles showing different vortical motions can be created. Possible experimental realizations include holographic optical lattice based setups for colloids or cold atoms.

A Faraday-wave-like parametric instability is investigated via mean-field and Floquet analysis in immiscible binary Bose-Einstein condensates. The condensates form a so-called ball-shell structure in a two-dimensional harmonic trap. To trigger the dynamics, the scattering length of the core condensate is periodically modulated in time. We reveal that in the dynamics the interface becomes unstable towards the formation of oscillating patterns. The interface oscillates subharmonically, exhibiting an m-fold rotational symmetry that can be controlled by maneuvering the amplitude and the frequency of the modulation. Using Floquet analysis we are able to predict the generated interfacial tension of the mixture and derive a dispersion relation for the natural frequencies of the emergent patterns. A heteronuclear system composed of 87Rb−85Rb atoms can be used for the experimental realization of the phenomenon, yet our results are independent of the specifics of the employed atomic species and of the parameters such as scattering lengths and trap strengths at which the driving is applied.

We propose and investigate a pump-probe spectroscopy scheme to unveil the time-resolved dynamics of fermionic or bosonic impurities immersed in a harmonically trapped Bose-Einstein condensate. In this scheme a pump pulse initially transfers the impurities from a noninteracting to a resonantly interacting spin state and, after a finite time in which the system evolves freely, the probe pulse reverses this transition. This directly allows us to monitor the nonequilibrium dynamics of the impurities as the dynamical formation of coherent attractive or repulsive Bose polarons and signatures of their induced interactions are imprinted in the probe spectra. We show that for interspecies repulsions exceeding the intraspecies ones a temporal orthogonality catastrophe occurs, followed by enhanced energy redistribution processes, independently of the impurity's flavor. This phenomenon takes place over the characteristic trap timescales. For much longer timescales a steady state is reached characterized by substantial losses of coherence of the impurities. This steady state is related to eigenstate thermalization and it is demonstrated to be independent of the system's characteristics.

We investigate the ground state properties and the nonequilibrium dynamics of a lattice trapped bosonic mixture consisting of an impurity species and a finite-sized medium. For the case of one as well as two impurities we observe that, depending on the lattice depth and the interspecies interaction strength, a transition from a strongly delocalized to a localized impurity distribution occurs. In the latter regime the two species phase separate, thereby forming a particle–hole pair. For two impurities we find that below a critical lattice depth they are delocalized among two neighboring outer lattice wells and are two-body correlated. This transition is characterized by a crossover from strong to a suppressed interspecies entanglement for increasing impurity-medium repulsion. Turning to the dynamical response of the mixture, upon quenching the interspecies repulsion to smaller values, we reveal that the predominant tunneling process for a single impurity corresponds to that of a particle–hole pair, whose dynamical stability depends strongly on the quench amplitude. During the time-evolution a significant increase of the interspecies entanglement is observed, caused by the build-up of a superposition of states and thus possesses a many-body nature. In the case of two bosonic impurities the particle–hole pair process becomes unstable in the course of the dynamics with the impurities aggregating in adjacent lattice sites while being strongly correlated.

We explore a few-body mixture of two bosonic species confined in quasi-one-dimensional parabolic traps of different length scales. The ground-state phase diagrams in the three-dimensional parameter space spanned by the harmonic length scale ratio, interspecies coupling strength, and particle-number ratio are investigated. As a first case study we use the mean-field ansatz (MF) to perform a detailed analysis of the separation mechanism. It allows us to derive a simple and intuitive rule predicting which of the immiscible phases is energetically more favorable at the miscible-immiscible phase boundary. We estimate the critical coupling strength for the miscible-immiscible transition and perform a comparison to correlated many-body results obtained by means of the multilayer multiconfiguration time-dependent Hartree method for bosonic mixtures (ML-X). At a critical ratio of the trap frequencies, determined solely by the particle-number ratio, the deviations between MF and ML-X are very pronounced and can be attributed to a high degree of entanglement between the components. As a result, we evidence the breakdown of the effective one-body picture. Additionally, when many-body correlations play a substantial role, the one-body density is in general not sufficient for deciding upon the phase at hand which we demonstrate exemplarily.

We report on the static and dynamical properties of multiple dark-antidark solitons (DADs) in two-component, repulsively interacting Bose-Einstein condensates. Motivated by experimental observations involving multiple DADs, we present a theoretical study which showcases that bound states consisting of dark (antidark) solitons in the first (second) component of the mixture exist for different values of interspecies interactions. It is found that ensembles of few DADs may exist as stable configurations, while for larger DAD arrays, the relevant windows of stability with respect to the interspecies interaction strength become progressively narrower. Moreover, the dynamical formation of states consisting of alternating DADs in the two components of the mixture is monitored. A complex dynamical evolution of these states is observed, leading either to sorted DADs or to beating dark-dark solitons depending on the strength of the interspecies coupling. This study demonstrates clear avenues for future investigations of DAD configurations.

We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied. Amorphous particle configurations for a vanishing electric field and crystalline order in the regime of a strong electric field are observed. We study the impact of parameter variations on the particle order and conclude that the crossover occurs for a wide range of parameter values and even holds for different helical systems.

We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two- and one-dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short-range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wave function, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction, and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions, while for fixed anisotropy quenches toward the noninteracting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher lying excited states.

We explore the stability of the phase separation phenomenon in few-fermion spin-1/2 systems confined in a double-well potential. It is shown that within the SU(2) symmetric case, where the total spin is conserved, the phase separation cannot be fully stabilized. An interaction regime characterized by metastable phase separation emerges for intermediate interactions which is inherently related with ferromagnetic spin–spin correlations emerging within each of the wells. The breaking of the SU(2) symmetry crucially affects the stability properties of the system as the phase separated state can be stabilized even for weak magnetic potential gradients. Our results imply an intricate relation between the phenomena of phase separation and ferromagnetism that lies beyond the view of the Stoner instability.

We investigate the spectral and eigenstate properties of the quantum superexponential oscillator. Our focus is on the quantum signatures of the recently observed transition of the energy dependent period of the corresponding classical superexponential oscillator. We show that the ground state exhibits a remarkable metamorphosis of decentering, asymmetrical squeezing and the development of a tail. Analyzing the central moments up to high order a characteristic transition from exponentially decaying moments to increasing moments is unravelled. A corresponding spectral analysis shows that, surprisingly, to a good approximation the spectrum is equidistant. A closer look, however, reveals a spectral scaling behaviour below the transition point which is replaced by irregular oscillations above the transition energy. Excited bound states are analyzed up to the continuum threshold. We discuss future perspectives and possible experimental realizations of the superexponential oscillator.

We unravel the correlation effects of the second-order quantum phase transitions emerging on the ground state of a harmonically trapped spin-1 Bose gas, upon varying the involved Zeeman terms, as well as its breathing dynamics triggered by quenching the trapping frequency. It is found that the boundaries of the associated magnetic phases are altered in the presence of interparticle correlations for both ferromagnetic and antiferromagnetic spin-spin interactions, an effect which becomes more prominent in the few-body scenario. Most importantly, we unveil a correlation-induced shrinking of the antiferromagnetic and broken-axisymmetry phases implying that ground states with bosons polarized in a single spin component are favored. Turning to the dynamical response of the spinor gas it is shown that its breathing frequency is independent of the system parameters while correlations lead to the formation of filamentary patterns in the one-body density of the participating components. The number of filaments is larger for increasing spin-independent interaction strengths or for smaller particle numbers. Each filament maintains its coherence and exhibits an anticorrelated behavior while distinct filaments show significant losses of coherence and are two-body correlated. Interestingly, we demonstrate that for an initial broken-axisymmetry phase an enhanced spin-flip dynamics takes place which can be tuned either via the linear Zeeman term or the quench amplitude.

We propose a scheme to realize a heavy Rydberg system (HRS), a bound pair of oppositely charged ions, from a gas of ultracold atoms. The intermediate step to achieve large internuclear separations is the creation of a unique class of ultra-long-range Rydberg molecules bound in a stairwell potential energy curve. Here, a ground-state atom is bound to a Rydberg atom in an oscillatory potential emerging due to attractive singlet p-wave electron scattering. The utility of our approach originates in the large electronic dipole transition element between the Rydberg and the ionic molecule, while the nuclear configuration of the ultracold gas is preserved. The Rabi coupling between the Rydberg molecule and the heavy Rydberg system is typically in the MHz range and the permanent electric dipole moments of the HRS can be as large as one kilo-Debye. We identify specific transitions which place the creation of the heavy Rydberg system within immediate reach of experimental realization.

The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find that, on ensemble average, the chain eigenstates become more fragmented spatially for intermediate average symmetry domain sizes, depending on the degree of disorder. This is caused by the partial formation of states with approximate local parity confined within fictitious, disorder-induced double wells and perturbed by the coupling to adjacent domains. The dynamical evolution of wave-packets shows that the average site-resolved transfer efficiency is enhanced between regions connected by local symmetry. The transfer may further be drastically amplified in the presence of spatial overlap between the symmetry domains, and in particular when global and local symmetry coexist. Applicable to generic discrete models for matter and light waves, our work provides a perspective to understand and exploit the impact of local order at multiple scales in complex systems.

The realization of mixtures of excitons and charge carriers in van der Waals materials presents a frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for quantum Monte Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

We explore the time evolution of two impurities in a trapped one-dimensional Bose gas that follows a change of the boson-impurity interaction. We study the induced impurity-impurity interactions and their effect on the quench dynamics. In particular, we report on the size of the impurity cloud, the impurity-impurity entanglement, and the impurity-impurity correlation function. The presented numerical simulations are based upon the variational multilayer multiconfiguration time-dependent Hartree method for bosons. To analyze and quantify induced impurity-impurity correlations, we employ an effective two-body Hamiltonian with a contact interaction. We show that the effective model consistent with the mean-field attraction of two heavy impurities explains qualitatively our results for weak interactions. Our findings suggest that the quench dynamics in cold-atom systems can be a tool for studying impurity-impurity correlations.

We investigate the nonequilibrium quantum dynamics of one and two heavy fermionic impurities being harmonically trapped and repulsively interacting with a finite ensemble of majority fermions. A quench of the potential of the majority species from a double-well to a harmonic trap is applied, enforcing its counterflow, which in turn perturbs the impurities. For weak repulsions, it is shown that the mixture undergoes a periodic mixing and demixing dynamics, while stronger interactions lead to a more pronounced dynamical spatial separation. In the presence of correlations, the impurity exhibits an expansion dynamics which is absent in the Hartree-Fock case, resulting in an enhanced degree of miscibility. We generalize our results to different impurity masses and demonstrate that the expansion amplitude of the impurity reduces for a larger mass. Furthermore, we showcase that the majority species is strongly correlated and a phase separation occurs on the two-body level. Most importantly, signatures of attractive impurity-impurity induced interactions mediated by the majority species are identified in the time evolution of the two-body correlations of the impurities, a result that is supported by inspecting their spatial size.

We study the ground state properties and non-equilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity–impurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastrophe of Bose polarons. We find that for an increasing postquench repulsion the impurities reside in a superposition of two distinct two-body configurations while at strong repulsions their corresponding two-body correlation patterns show a spatially delocalized behavior evincing the involvement of higher excited states. For attractive interspecies couplings, the impurities exhibit a tendency to localize at the origin and remarkably for strong attractions they experience a mutual attraction on the two-body level that is imprinted as a density hump on the bosonic bath.

We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown that PGST generally arises when a network's eigenvectors and the factors P± of its characteristic polynomial P fulfill certain conditions, where P± correspond to eigenvectors which have ±1 parity on the input and target sites. We combine this result with the so-called isospectral reduction of a network to obtain P± from a dimensionally reduced form of the Hamiltonian. Equipped with the knowledge of the factors P±, we show how a variety of setups can be equipped with PGST by proper tuning of P±. Having demonstrated a method of designing networks featuring pretty good state transfer of single site excitations, we further show how the obtained networks can be manipulated such that they allow for robust storage of qubits. We hereby rely on the concept of compact localized states, which are eigenstates of a Hamiltonian localized on a small subdomain, and whose amplitudes completely vanish outside of this domain. Such states are natural candidates for the storage of quantum information, and we show how certain Hamiltonians featuring pretty good state transfer of single site excitation can be equipped with compact localized states such that their transfer is made possible.

The concept of local symmetry has been shown to be a powerful tool in predicting and designing complex transport phenomena in stationary scattering off aperiodic media, in terms of symmetry‐adapted nonlocal currents. For time‐evolving wavepackets, the spatiotemporal correlations caused by local symmetries are more challenging to reveal. A recent formalism‐based nonlocal continuity equation shows how local symmetries are encoded into the dynamics of light propagation in discrete waveguide arrays governed by a Schrödinger equation. However, the experimental demonstration is elusive so far. Representative examples of locally symmetric, globally symmetric, and fully nonsymmetric configurations are fabricated in fs laser‐written photonic arrays and their dynamics are probed. The approach allows to distinguish all three types of structures.

We detail the rich electronic and vibrational structure of triatomic 'butterfly' molecules, ultra-long-range Rydberg molecules bound by resonant p-wave scattering. We divide these molecules into two sub-classes depending on their parity under reflection of the electronic wave function through the molecular plane. The trimers with odd reflection parity have smoothly varying, non-oscillatory potential energy surfaces except near the collinear configuration. Here, the vibrational wave function is confined tightly in the symmetric-stretch and bending modes, but only loosely in the asymmetric stretch mode. The trimers with even reflection parity exhibit far richer potential surfaces with abundant minima, but only a few of these are deep enough to localize the vibrational states. These minima are correlated with the electronic wave functions of the butterfly dimer, contributing to a building principle for trimers.

We demonstrate the directed transport of underdamped particles in two-dimensional lattices of arbitrary geometry driven by an unbiased AC driving force. The direction of transport can be controlled via the lattice geometry as well as the strength and orientation of the oscillating drive. The breaking of the spatial inversion symmetry, which is necessary for the emergence of directed transport, is achieved solely due to the structure and geometry of the lattice. The most important criterion determining the transport direction is shown to be the ballistic attractors underlying the phase space of our weakly dissipative nonlinear dynamical system. This allows the prediction of transport direction even for setups like driven oblique lattices where the standard symmetry arguments of transport control fail. Our results can be experimentally realized using holographic optical-lattice-based setups with colloids or cold atoms.

We propose an experimentally realizable scheme to produce triatomic ultralong-range Rydberg molecules (TURM), formed in ultracold KRb traps. A near resonant coupling of the non-zero quantum defect Rydberg levels with the KRb molecule in N = 0 and N = 2 rotational levels, is engineered which exploits the unique Rydberg electron–molecule anisotropic dipole interaction. This near resonant coupling enhances the TURM binding and produces favorable Franck–Condon factors. Schemes for both postassium and rubidium excitations are demonstrated.

We unravel the correlated tunneling dynamics of an impurity trapped in a double well and interacting repulsively with a majority species of lattice trapped bosons. Upon quenching the tilt of the double well it is found that the quench-induced tunneling dynamics depends crucially on the interspecies interaction strength and the presence of entanglement inherent in the system. In particular, for weak couplings the impurity performs a rather irregular tunneling process in the double well. Increasing the interspecies coupling it is possible to control the response of the impurity which undergoes a delayed tunneling while the majority species effectively acts as a material barrier. For very strong interspecies interaction strengths the impurity exhibits a self-trapping behavior. We showcase that a similar tunneling dynamics takes place for two weakly interacting impurities and identify its underlying transport mechanisms in terms of pair and single-particle tunneling processes.

We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components, we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings, the impurities decouple from their host, while if exposed to a high-frequency driving, they remain trapped in the bosonic gas. For continuous shaking, we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state, we unveil that for moderate driving frequencies the impurities feature a dispersive behavior while for a high-frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair.

We unravel the spontaneous generation of vortex-bright-soliton structures in binary Bose–Einstein condensates with a small mass imbalance between the species confined in a two-dimensional harmonic trap where one of the two species has been segmented into two parts by a potential barrier. To trigger the dynamics the potential barrier is suddenly removed and subsequently the segments perform a counterflow dynamics. We consider a relative phase difference of π between the segments, while a singly quantized vortex may be imprinted at the center of the other species. The number of vortex structures developed within the segmented species following the merging of its segments is found to depend on the presence of an initial vortex on the other species. In particular, a π phase difference in the segmented species and a vortex in the other species result in a single vortex-bright-soliton structure. However, when the non-segmented species does not contain a vortex the counterflow dynamics of the segmented species gives rise to a vortex dipole in it accompanied by two bright solitary waves arising in the non-segmented species. Turning to strongly mass imbalanced mixtures, with a heavier segmented species, we find that the same overall dynamics takes place, while the quench-induced nonlinear excitations become more robust. Inspecting the dynamics of the angular momentum we show that it can be transferred from one species to the other, and its transfer rate can be tuned by the strength of the interspecies interactions and the mass of the atomic species.

We demonstrate that directed transport of particles in a two dimensional driven lattice can be dynamically reversed multiple times by superimposing additional spatially localized lattices on top of a background lattice. The timescales of such current reversals can be flexibly controlled by adjusting the spatial locations of the superimposed lattices. The key principle behind the current reversals is the conversion of the particle dynamics from chaotic to ballistic, which allow the particles to explore regions of the underlying phase space which are inaccessible otherwise. Our results can be experimentally realized using cold atoms in driven optical lattices and allow for the control of transport of atomic ensembles in such setups.

We review ultralong-range Rydberg molecules (ULRMs), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.

The superexponential self-interacting oscillator (SSO) is introduced and analyzed. Its power law potential is characterized by the dependence of both the base and the exponent on the dynamical variable of the oscillator. Opposite to standard oscillators such as the (an-)harmonic oscillator the SSO combines both scattering and confined periodic motion with an exponentially varying nonlinearity. The SSO potential exhibits a transition point with a hierarchy of singularities of logarithmic and power law character leaving their fingerprints in the agglomeration of its phase space curves. The period of the SSO consequently undergoes a crossover from decreasing linear to a nonlinearly increasing behaviour when passing the transition energy. We explore its dynamics and show that the crossover involves a kick-like behaviour. A symmetric double well variant of the SSO is briefly discussed.

Motivated by recent developments in the realm of matter waves, we explore the potential of creating solitary waves on the surface of a torus. This is an intriguing perspective due to the role of curvature in the shape and dynamics of the coherent structures. We find different families of bright solitary waves for attractive nonlinearities including ones localized in both angular directions, as well as waves localized in one direction and homogeneous in the other. The waves localized in both angular directions have also been partitioned into two types: those whose magnitude decays to zero and those who do not. The stability properties of the waves are examined and one family is found to be spectrally stable in a suitable parametric regime while most are spectrally unstable, a feature that we comment on. Finally, the nature of the ensuing nonlinear dynamics is touched upon.

We present experimental evidence for spin-orbit interaction of an electron as it scatters from a neutral atom. The scattering process takes place within a Rb2 ultralong-range Rydberg molecule, consisting of a Rydberg atomic core, a Rydberg electron, and a ground state atom. The spin-orbit interaction leads to characteristic level splittings of vibrational molecular lines which we directly observe via photoassociation spectroscopy. We benefit from the fact that molecular states dominated by resonant p-wave interaction are particularly sensitive to the spin-orbit interaction. Our work paves the way for studying novel spin dynamics in ultralong-range Rydberg molecules. Furthermore, it shows that the molecular setup can serve as a microlaboratory to perform precise scattering experiments in the low-energy regime of a few meV.

We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole-dipole interaction in an external homogeneous electric field. In the field-free stable head-tail configuration, an excess energy is provided to one of the dipoles, and we explore the resulting complete dimensional classical dynamics. This dynamics is characterized in terms of the kinetic energy transfer between the dipoles, their orientation along the electric field, as well as their chaotic behavior. The field-free energy transfer mechanism shows an abrupt transition between equipartition and non-equipartition regimes, which is independent of the initial direction of rotation due to the existence of an infinite set of equivalent manifolds. The field-dressed dynamics is highly complex and strongly depends on the electric field strength and on the initial conditions. In the strong field regime, the energy equipartition and chaotic behavior dominate the dynamics.

We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynamics is initiated by suddenly lowering the repulsive interspecies interaction strength, thereby entering a different regime in the crossover diagram. For specific postquench interspecies interaction strengths we find that a single impurity tunnels first to the neighboring empty site and depending on the quench strength can further tunnel to the next-neighboring site. Interestingly, this effect is highly sensitive to the presence of the Bose gas and does not occur when the Bose gas does not interact with the impurity species throughout the dynamics. Moreover, we find that the tunneling process is accompanied by strong entanglement between the Bose gas and the impurity species as well as correlations among the impurities.

We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength and thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the stationary system, we derive a closed analytical form of the expansion coefficients of the time-evolved two-body wave function, whose dynamics is determined by an expansion over the postquench eigenstates. The emergent dynamical response of the system is analyzed in detail by inspecting several observables such as the fidelity, the reduced one-body densities, the radial probability density of the relative wave function in both real and momentum space, and the Tan contact, which unveils the existence of short range two-body correlations. When the system is initialized in its bound state, it is perturbed in the most efficient manner as compared to any other initial configuration. Moreover, starting from an interacting ground state, the two-boson response is enhanced for quenches toward the noninteracting limit.

We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose–Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.

We consider a degenerate Bose gas confined in a double-well potential in interaction with a trapped ion in one dimension and investigate the impact of two relevant sources of imperfections in experiments on the system dynamics: ion motion and thermal excitations of the bosonic ensemble. Particularly, their influence on the entanglement generation between the spin state of the moving ion and the atomic ensemble is analyzed. We find that the detrimental effects of the ion motion on the entanglement protocol can be mitigated by properly choosing the double-well parameters as well as timings of the protocol. Furthermore, thermal excitations of the bosons affect significantly the system's tunneling and self-trapping dynamics at moderate temperatures; i.e., thermal occupation of a few double-well quanta reduces the protocol performance by about 10%. Hence, we conclude that finite temperature is the main source of decoherence in such junctions and we demonstrate the possibility to entangle the condensate motion with the ion vibrational state.

We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel toward the edges of the bosonic cloud where they equilibrate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to draw conclusions on the spatial localization of the quench-induced fermionic density humps.

We propose modulation protocols designed to generate, store, and transfer compact localized states in a quantum network. Induced by parameter tuning or local reflection symmetries, such states vanish outside selected domains of the complete system and are therefore ideal for information storage. Their creation and transfer is here achieved either via amplitude phase flips or via optimal temporal control of intersite couplings. We apply the concept to a decorated, locally symmetric Lieb lattice where one sublattice is dimerized, and also demonstrate it for more complex setups. The approach allows for a flexible storage and transfer of states along independent paths in lattices supporting flat energetic bands. We further demonstrate a method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks. We show that these compact localized states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications. The generic network and protocols proposed can be utilized in various physical setups such as atomic or molecular spin lattices, photonic waveguide arrays, and acoustic setups.

The level structure of negative ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system that is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so-far unobserved fine structure of the 3PJ triplet of Rb− and allows us to extract parameters of the associated p-wave scattering resonances that deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.

We unveil the dynamical formation of multiple localized structures in the form of dark-bright and dark-antidark solitary waves that emerge upon quenching a one-dimensional particle-imbalanced Bose-Bose mixture. Interspecies interaction quenches drive the system out of equilibrium while the so-called miscible-immiscible threshold is crossed in a two-directional manner. Dark-bright entities are spontaneously generated for quenches towards the phase separated regime and dark-antidark states are formed in the reverse process. The distinct mechanisms of creation of the aforementioned states are discussed in detail and their controlled generation is showcased. In both processes, it is found that the number of solitary waves generated is larger for larger particle imbalances, a result that is enhanced for stronger postquench interspecies interactions. Additionally the confining geometry highly affects the production of both types of states with a decaying solitary wave formation occurring for tighter traps. Furthermore, in both of the aforementioned transitions, the breathing frequencies measured for the species differ significantly for highly imbalanced mixtures. Finally, the robustness of the dynamical formation of dark-bright and dark-antidark solitons is also demonstrated in quasi-one-dimensional setups.

The investigation of the nonequilibrium quantum dynamics of bosonic many-body systems is very challenging due to the excessively growing Hilbert space and poses a major problem for their theoretical description and simulation. We present a novel dynamical pruning approach in the framework of the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) to tackle this issue by dynamically detecting the most relevant number states of the underlying physical system and modifying the many-body Hamiltonian accordingly. We discuss two different number state selection criteria as well as two different ways to modify the Hamiltonian. Our scheme regularly re-evaluates the number state selection in order to dynamically adapt to the time evolution of the system. To benchmark our methodology, we study the nonequilibrium dynamics of bosonic particles confined either in an optical lattice or in a double-well potential. It is shown that our approach reproduces the unpruned MCTDHB results accurately while yielding a significant reduction of the simulation time. The speedup is particularly pronounced in the case of the optical lattice.

We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component, and spinor Bose-Einstein condensates. The formation of solitonic entities of the dark-bright type is based on the so-called matter-wave interference of spatially separated condensates. In all three cases, a systematic numerical study is carried out upon considering different variations of each system's parameters both in the absence and in the presence of a harmonic trap. It is found that manipulating the initial separation or the chemical potential of the participating components allows us to tailor the number of nucleated dark-bright states. Particularly, the number of solitons generated increases upon increasing either the initial separation or the chemical potential of the participating components. Similarities and differences of the distinct models considered herein are showcased, while the robustness of the emerging states is illustrated via direct numerical integration, demonstrating their long time propagation. Importantly, for the spinorial system, we unravel the existence of beating dark soliton arrays that are formed due to the spin-mixing dynamics. These states persist in the presence of a parabolic trap, often relevant for associated experimental realizations.

We investigate a temporal evolution of an impurity atom in a one-dimensional trapped Bose gas following a sudden change of the boson-impurity interaction strength. Our focus is on the effects of inhomogeneity due to the harmonic confinement. These effects can be described by an effective one-body model where both the mass and the spring constant are renormalized. This is in contrast to the classic renormalization, which addresses only the mass. We propose an effective single-particle Hamiltonian and apply the multilayer multiconfiguration time-dependent Hartree method for bosons to explore its validity. Numerical results suggest that the effective mass is smaller than the impurity mass, which means that it cannot straightforwardly be extracted from translationally invariant models.

We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied to the Fibonacci, Thue-Morse, and Rudin-Shapiro chains, representing different structural classes. Our approach is based on an analysis of the eigenstates at weak intersite coupling, where they are shown to generically localize on locally reflection-symmetric substructures, which we call local resonators. A perturbation theoretical treatment demonstrates the local symmetries of the eigenstates. Depending on the degree of spatial complexity of the chain, the proposed local resonator picture can be used to predict the occurrence of gap-edge states even for stronger couplings. Moreover, we connect the localization behavior of a given eigenstate to its energy, thus providing a quantitative connection between the real-space structure of the chain and its eigenvalue spectrum. This allows for a deeper understanding, based on local symmetries, of how the energy spectra of binary chains are formed. The insights gained allow for a systematic analysis of aperiodic binary chains and offers a pathway to control structurally induced edge states.

Quantum gas microscopes, which image the atomic occupations in an optical lattice, have opened a new avenue to the exploration of many-body lattice systems. Imaging trapped systems after freezing the density distribution by ramping up a pinning lattice leads, however, to a distortion of the original density distribution, especially when its structures are on the scale of the pinning lattice spacing. We show that this dynamics can be described by a filter, which we call in analogy to classical optics a quantum point spread function. Using a machine learning approach, we demonstrate via several experimentally relevant setups that a suitable deconvolution allows for the reconstruction of the original density distribution. These findings are both of fundamental interest for the theory of imaging and of immediate importance for current quantum gas experiments.

We monitor the correlated quench induced dynamical dressing of a spinor impurity repulsively interacting with a Bose-Einstein condensate. Inspecting the temporal evolution of the structure factor, three distinct dynamical regions arise upon increasing the interspecies interaction. These regions are found to be related to the segregated nature of the impurity and to the Ohmic character of the bath. It is shown that the impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold. In particular, for miscible components the polaron formation is imprinted on the spectral response of the system. We further illustrate that for increasing interaction an orthogonality catastrophe occurs and the polaron picture breaks down. Then a dissipative motion of the impurity takes place leading to a transfer of energy to its environment. This process signals the presence of entanglement in the many-body system.

We unravel the dynamical stability of a fully polarized one-dimensional ultracold few-fermion spin-1/2 gas subjected to inhomogeneous driving of the itinerant spins. Despite the unstable character of the total spin-polarization the existence of an interaction regime is demonstrated where the spin-correlations lead to almost maximally aligned spins throughout the dynamics. The resulting ferromagnetic order emerges from the build up of superpositions of states of maximal total spin. They comprise a decaying spin-polarization and a dynamical evolution towards an almost completely unpolarized NOON-like state. Via single-shot simulations we demonstrate that our theoretical predictions can be detected in state-of-the-art ultracold experiments.

We explore repulsive Fermi polarons in one-dimensional harmonically trapped few-body mixtures of ultracold atoms using as a case example a 6Li-40K mixture. A characterization of these quasiparticle-like states, whose appearance is signaled in the impurity's radiofrequency spectrum, is achieved by extracting their lifetime and residua. Increasing the number of 40K impurities leads to the occurrence of both single and multiple polarons that are entangled with their environment. An interaction-dependent broadening of the spectral lines is observed suggesting the presence of induced interactions. We propose the relative distance between the impurities as an adequate measure to detect induced interactions independently of the specifics of the atomic mixture, a result that we showcase by considering also a 6Li-173Yb system. This distance is further shown to be indicative of the generation of entanglement independently of the size of the bath (6Li) and the atomic species of the impurity. The generation of entanglement and the importance of induced interactions are revealed with an emphasis on the regime of intermediate interaction strengths.

We present an analytical investigation of the exciton optical absorption in a narrow armchair graphene nanoribbon (AGNR) in the presence of a longitudinal external electric field directed parallel to the ribbon axis. The two-body two-dimensional Dirac equation for the massless electron and hole subject to the ribbon confinement, Coulomb interaction, and electric field is employed. The ribbon confinement is assumed to be much stronger than the internal exciton electric field which in turn considerably exceeds the external electric field. In the single subband approximation of the isolated size-quantized subbands induced by the ribbon confinement, the exciton electroabsorption coefficient is determined in an explicit form. The pronounced dependencies of the exciton peak positions, widths, and intensities on the ribbon width and electric field strength are traced. The electron-hole exciton attraction enhances considerably the Franz-Keldysh electroabsorption in the frequency region below and significantly modifies it above the edges determined by the size-quantized energy levels. The ionization by increasing the ribbon width is shown to occur. In the double-subband approximation of the interacting ground and first excited subbands the total peak widths associated with the exciton electro- and autoionization caused by the electric field and intersubband coupling, respectively, are determined analytically. Our analytical results are in agreement with those obtained by numerical methods. Estimates of the expected experimental values for the typically employed AGNR show that for a weak electric field the exciton quasidiscrete states remain sufficiently stable to be observed in optical experiments, while relatively strong fields free the captured carriers to further restore their contribution to the transport.

The exciton absorption coefficient is determined analytically for a semiconductor superlattice in crossed electric and magnetic fields, for the magnetic field being parallel and the electric field being perpendicular to the superlattice axis. Our investigation applies to the case where the magnetic length, while being much smaller than the exiton Bohr radius, considerably exceeds the superlattice period. The optical absorption in superlattices displays a spectral fine structure related to the sequences of exciton states bound whose energies are adjacent to the Landau energies of the charge carriers in the magnetic field. We study effects of external fields and of the center-of-mass exciton motion on the fine structure peak positions and oscillator strengths. In particular, we find that the inversion of the orientation of the external fields and of the in-plane total exciton momentum notably affects the absorption spectrum. Conditions for the experimental observation of the exciton absorption are discussed.

We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a source term proportional to the potential difference. In case the potential landscapes are related by a linear symmetry transformation in a finite domain of the embedding space, the derived continuity equation leads to generalized currents which are divergence free within this spatial domain. In a single spatial dimension these generalized currents are invariant. In contrast to the standard continuity equation, originating from the abelian -phase symmetry of the standard Lagrangian, the generalized continuity equations derived here, are based on a non-abelian -transformation of a super-Lagrangian. Our approach not only provides a rigorous theoretical framework to study quantum mechanical systems in potential landscapes possessing local symmetries, but it also reveals a general duality between quantum states corresponding to different Schrödinger problems.

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs(nd3/2) atoms. The anisotropy of the atomic Rydberg state allows for the formation of angular trimers, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers coexist with Rydberg dimers. The existence of such effective three-body interactions is confirmed with the observation of asymmetric line profiles and interpreted by a theoretical approach that includes relativistic spin interactions. Simulations of the observed spectra with and without angular trimer lines lend convincing support to the existence of effective three-body interactions.

We investigate triatomic molecules that consist of two ground-state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of angstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential-energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and develop a simple building principle that predicts the triatomic equilibrium configurations. As a representative example we focus on 87Rb trimers correlated to the n=30 Rydberg state. Using an exact diagonalization scheme we determine and characterize localized vibrational states in these potential minima with energy spacings on the order of 100 MHz×h.

We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.

We unravel some peculiar properties of ultra-long-range Rydberg molecules formed by an s-state 87Rb Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the s-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open interesting possibilities for accessing the physics of relativistic electron-atom scattering experimentally.

Following the goal of using active particles as targeted cargo carriers aimed, for example, to deliver drugs towards cancer cells, the quest for the control of individual active particles with external fields is among the most explored topics in active matter. Here, we provide a scheme allowing to control collective behaviour in active matter, focusing on the fluctuating band patterns naturally occurring e.g. in the Vicsek model. We show that exposing these patterns to a travelling wave potential tames them, yet in a remarkably nontrivial way: the bands, which initially pin to the potential and comove with it, upon subsequent collisions, self-organize into a macroband, featuring a predictable transport against the direction of motion of the travelling potential. Our results provide a route to simultaneously control transport and structure, i.e. micro- versus macrophase separation, in polar active matter.

We investigate the spectral properties of a class of hard-wall bounded systems, described by potentials exhibiting domainwise different local symmetries. Tuning the distance of the domains with locally symmetric potential from the hard-wall boundaries leads to extrema of the eigenenergies. The underlying wave function becomes then an eigenstate of the local symmetry transform in each of the domains of local symmetry. These extrema accumulate towards eigenenergies which do not depend on the position of the potentials inside the walls. They correspond to perfect transmission resonances of the associated scattering setup, obtained by removing the hard walls. We argue that this property characterizes the duality between scattering and bounded systems in the presence of local symmetries. Our findings are illustrated through a numerical example with a potential consisting of two domains of local symmetry, each comprised of Dirac δ barriers.

We study the compact localized scattering resonances of periodic and aperiodic chains of dipolar nanoparticles by combining the powerful equitable partition theorem (EPT) of a graph theory with the spectral dyadic Green’s matrix formalism for the engineering of embedded quasi-modes in non-Hermitian open scattering systems in three spatial dimensions. We provide the analytical and numerical design of the spectral properties of compact localized states in electromagnetically coupled chains and establish a connection with the distinctive behavior of bound states in the continuum. Our results extend the concept of compact localization to the scattering resonances of open systems with an arbitrary aperiodic order beyond tight-binding models, and are relevant for the efficient design of novel photonic and plasmonic metamaterial architectures for enhanced light–matter interaction.

We explore the interspecies interaction quench dynamics of ultracold spin-polarized few-body mass-balanced Fermi-Fermi mixtures confined in a double well with an emphasis on the beyond Hartree-Fock correlation effects. It is shown that the ground state of particle-imbalanced mixtures exhibits a symmetry breaking of the single-particle density for strong interactions in the Hartree-Fock limit, which is altered within the many-body approach. Quenching the interspecies repulsion towards the strongly interacting regime, the two species phase separate within the Hartree-Fock approximation while remaining miscible in the many-body treatment. Despite their miscible character on the one-body level, the two species are found to be strongly correlated and exhibit a phase separation on the two-body level that suggests the antiferromagneticlike behavior of the few-body mixture. For particle-balanced mixtures we show that an intrawell fragmentation (filamentation) of the density occurs both for the ground state and upon quenching from weak to strong interactions, a result that is exclusively caused by the presence of strong correlations. By inspecting the two-body correlations, a phase separation of the two species is unveiled, being a precursor towards an antiferromagnetic state. Finally, we simulate in situ single-shot measurements and showcase how our findings can be retrieved by averaging over a sample of single-shot images.

We unravel the correlated tunneling dynamics of a mass imbalanced few-body Fermi-Fermi mixture upon quenching the tilt of a double well. The nonequilibrium dynamics of both species changes from Rabi oscillations close to the noninteracting limit to a delayed tunneling dynamics for moderate interspecies repulsions. Considering strong interspecies interactions, the lighter species experiences quantum self-trapping due to the heavier species which acts as an effective material barrier, while performing almost perfect Rabi oscillations. The degree of entanglement, inherent in the system, is analyzed and found to be significant at both moderate and strong repulsions. To relate our findings to possible experimental realizations, we simulate in situ single-shot measurements and discuss how a sampling of such images dictates the observed dynamics. Finally, the dependence of the tunneling behavior on the mass ratio, the particle number in each species, and the height of the barrier of the double well is showcased.

We investigate the localization pattern of interacting impurities, which are trapped in a lattice potential and couple to a Bose gas. For small interspecies interaction strengths, the impurities populate the energetically lowest Bloch state or localize separately in different wells with one extra particle being delocalized over all the wells, depending on the lattice depth. In contrast, for large interspecies interaction strengths we find that due to the fractional filling of the lattice and the competition of the repulsive contact interaction between the impurities and the attractive interaction mediated by the Bose gas, the impurities localize either pairwise or completely in a single well. Tuning the lattice depth, the interspecies and intraspecies interaction strength correspondingly allows for a systematic control and engineering of the two localization patterns. The sharpness of the crossover between the two states as well as the broad region of their existence supports the robustness of the engineering. Moreover, we are able to manipulate the ground state's degeneracy in the form of triplets, doublets and singlets by implementing different boundary conditions, such as periodic and hard wall boundary conditions.

The nonequilibrium quantum dynamics of few boson ensembles which experience a spatially modulated interaction strength and are confined in finite optical lattices is investigated. We utilize a cosinusoidal spatially modulated effective interaction strength which is characterized by its wavevector, inhomogeneity amplitude, interaction offset and a phase. Performing quenches either on the wavevector or the phase of the interaction profile an enhanced imbalance of the interatomic repulsion between distinct spatial regions of the lattice is induced. Following both quench protocols triggers various tunneling channels and a rich excitation dynamics consisting of a breathing and a cradle mode. All modes are shown to be amplified for increasing inhomogeneity amplitude of the interaction strength. Especially the phase quench induces a directional transport enabling us to discern energetically, otherwise, degenerate tunneling pathways. Moreover, a periodic population transfer between distinct momenta for quenches of increasing wavevector is observed, while a directed occupation of higher momenta can be achieved following a phase quench. Finally, during the evolution regions of partial coherence are revealed between the predominantly occupied wells.

We explore the nonlinear dynamics of a driven power-law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving period, the phase space allows not only for regular and chaotic bounded motion but in particular also for an unbounded motion which exhibits an exponential net growth of the corresponding energies. Our computational study shows that phases of motion with energy gain and loss as well as approximate energy conservation alternate within a single period of the oscillator and can be assigned to the change of the underlying confinement geometry. We demonstrate how the crossover from a single- to a two-component phase space takes place with varying frequency and amplitude and analyze the corresponding volumes in phase space. In the high-frequency regime an effective potential is derived that combines the different features of the driven power-law oscillator. Possible experimental realizations are discussed.

We study the energy transfer in a classical dipole chain of N interacting rigid rotating dipoles. The underlying high-dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.

We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated ab initio studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can account for the antibunching, only the inclusion of the interspecies correlations can lead to the bunching. We show that these correlations effectively create an induced bosonic interaction, which in turn elucidates the occurrence of the bosonic bunching. Finally, we derive a two-site extended Bose-Hubbard model which reveals the low-energy physics of the bosons for the case of much heavier fermions.

The many-body dissipative flow induced by a mobile Gaussian impurity harmonically oscillating within a cigar-shaped Bose-Einstein condensate is investigated. For very small and large driving frequencies the superfluid phase is preserved. Dissipation is identified, for intermediate driving frequencies, by the nonzero value of the drag force whose abrupt increase signals the spontaneous downstream emission of an array of gray solitons. After each emission event, typically each of the solitary waves formed decays and splits into two daughter gray solitary waves that are found to be robust propagating in the bosonic background for large evolution times. In particular, a smooth transition toward dissipation is observed, with the critical velocity for solitary wave formation depending on both the characteristics of the obstacle, namely its driving frequency and width as well as on the interaction strength. The variance of a sample of single-shot simulations indicates the fragmented nature of the system; here it is found to increase during evolution for driving frequencies where the coherent structure formation becomes significant. Finally, we demonstrate that for fairly large particle numbers in situ single-shot images directly capture the gray soliton's decay and splitting.

We establish a theoretical framework for exploring the quantum dynamics of finite ultracold bosonic ensembles based on the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for equations of motion for few-particle reduced density matrices (RDMs). The theory applies to zero as well as low temperatures and is formulated in a highly efficient way by utilizing dynamically optimized single-particle basis states and representing the RDMs in terms of permanents with respect to those. An energy, RDM compatibility, and symmetry conserving closure approximation is developed on the basis of a recursively formulated cluster expansion for these finite systems. In order to enforce necessary representability conditions, two minimally invasive and energy-conserving correction algorithms are proposed, involving the dynamical purification of the solution of the truncated BBGKY hierarchy and the correction of the equations of motion themselves, respectively. For gaining conceptual insights, the impact of two-particle correlations on the dynamical quantum depletion is studied analytically. We apply this theoretical framework to both a tunneling and an interaction-quench scenario. Due to our efficient formulation of the theory, we can reach truncation orders as large as twelve and thereby systematically study the impact of the truncation order on the results. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer timescale in sufficiently far off-equilibrium situations. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimally invasive correction algorithm of the equation of motion can indeed stabilize the BBGKY hierarchy truncated at the second order.

We establish a conceptual framework for the identification and the characterization of induced interactions in binary mixtures and reveal their intricate relation to entanglement between the components or species of the mixture. Exploiting an expansion in terms of the strength of the entanglement among the two species enables us to deduce an effective single-species description. In this way, we naturally incorporate the mutual feedback of the species and obtain induced interactions for both species which are effectively present among the particles of same type. Importantly, our approach incorporates few-body and inhomogeneous systems extending the scope of induced interactions where two particles interact via a bosonic bath-type environment. Employing the example of a one-dimensional ultracold Bose-Fermi mixture, we obtain induced Bose-Bose and Fermi-Fermi interactions with short-range attraction and long-range repulsion. With this, we show how beyond species mean-field physics visible in the two-body correlation functions can be understood via the induced interactions.

Based on a one-dimensional double-well superlattice with a unit filling of ultracold atoms per site, we propose a scheme to generate scalable entangled states in the superlattice through symmetry-protected resonant lattice shaking. Our scheme utilizes periodic lattice modulations with a specific two-body exchange symmetry to entangle two atoms in each unit cell with respect to their orbital degree of freedom, and the complete atomic system in the superlattice becomes a cluster of bipartite entangled atom pairs. To demonstrate this we perform ab initio quantum dynamical simulations using the multilayer multiconfiguration time-dependent Hartree method for mixtures, which accounts for all correlations among the atoms. The proposed clusters of bipartite entanglements manifest as an essential resource for various quantum applications, such as measurement-based quantum computation. The lattice shaking scheme to generate this cluster possesses advantages such as a high scalability, fast processing speed, rich controllability on the target entangled states, and accessibility within current experimental techniques.

The nonequilibrium ultracold bosonic quantum dynamics in finite optical lattices of unit filling following a linear interaction quench from a superfluid to a Mott insulator state and vice versa is investigated. The resulting dynamical response consists of various inter and intraband tunneling modes. We find that the competition between the quench rate and the interparticle repulsion leads to a resonant dynamical response, at moderate ramp times, being related to avoided crossings in the many-body eigenspectrum with varying interaction strength. Crossing the regime of weak to strong interactions several transport pathways are excited. The higher-band excitation dynamics is shown to obey an exponential decay possessing two distinct time scales with varying ramp time. Studying the crossover from shallow to deep lattices we find that for a diabatic quench the excited band fraction decreases, while approaching the adiabatic limit it exhibits a non-linear behavior for increasing height of the potential barrier. The inverse ramping process from strong to weak interactions leads to a melting of the Mott insulator and possesses negligible higher-band excitations which follow an exponential decay for decreasing quench rate. Finally, independently of the direction that the phase boundary is crossed, we observe a significant enhancement of the excited to higher-band fraction for increasing system size.

We unravel the correlated nonequilibrium dynamics of a mass balanced Bose-Fermi mixture in a one-dimensional optical lattice upon quenching an imposed harmonic trap from strong to weak confinement. Regarding the system's ground state, the competition between the inter- and intraspecies interaction strength gives rise to the immiscible and miscible phases characterized by negligible and complete overlap of the constituting atomic clouds, respectively. The resulting dynamical response depends strongly on the initial phase and consists of an expansion of each cloud and an interwell tunneling dynamics. For varying quench amplitude and referring to a fixed phase, a multitude of response regimes is unveiled, being richer within the immiscible phase, which are described by distinct expansion strengths and tunneling channels.

We show that the direction of directed particle transport in a two-dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.

We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction, or size. The scheme employs a periodically shaken two-dimensional dissipative lattice and hinges on a simultaneous transport of particles in species-specific directions. This selective transport is achieved by controlling the late-time nonlinear particle dynamics, via the attractors embedded in the phase space and their bifurcations. To illustrate the spectrum of possible applications of the scheme, we exemplarily demonstrate the separation of polydisperse colloids and mixtures of cold thermal alkali atoms in optical lattices.

We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in Jachymski et al. [Phys. Rev. Lett. 120, 013401 (2018)], is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic-field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect the transmission. We illustrate our findings with concrete examples of experimental relevance, demonstrating that for large atom fluences N a sensitivity of the order of 1 nT/√N for the field strength and 100 nT/(mm √N) for the gradient can be reached with our scheme.

We explore the quench dynamics of a binary Bose–Einstein condensate crossing the miscibility–immiscibility threshold and vice versa, both within and in particular beyond the mean-field approximation. Increasing the interspecies repulsion leads to the filamentation of the density of each species, involving shorter wavenumbers and longer spatial scales in the many-body (MB) approach. These filaments appear to be strongly correlated and exhibit domain-wall structures. Following the reverse quench process multiple dark–antidark solitary waves are spontaneously generated and subsequently found to decay in the MB scenario. We simulate single-shot images to connect our findings to possible experimental realizations. Finally, the growth rate of the variance of a sample of single-shots probes the degree of entanglement inherent in the system.

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a 87Rb Rydberg atom the outer electron of which interacts via spin-dependent s- and p-wave scattering with a polarizable 87Rb ground-state atom. Our model includes also the hyperfine structure of the ground-state atom as well as spin-orbit couplings of the Rydberg and ground-state atom. We focus on d-Rydberg states and principal quantum numbers n in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauss. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.

The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference ΔE between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using ΔE to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, ΔE changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the nonuniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response ΔE.

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green’s matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su–Schrieffer–Heeger (SSH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue–Morse aperiodic systems. Our study demonstrates that topological edge-modes with characteristic power-law envelope appear in open aperiodic systems and coexist with traditional exponentially localized ones. Our results extend the concept of topological states to the scattering resonances of complex open systems with aperiodic order, thus providing an important step towards the predictive design of topological optical metamaterials and devices beyond tight-binding models.

We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb–Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the multi-configuration time-dependent Hartree method for mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function's structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations.

We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one- and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole–dipole interactions, the local frame transformation method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the local frame transformation approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the local frame transformation method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the local frame transformation method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s-wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p-wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.

We investigate the quantum dynamics of two identical bosons in a one-dimensional harmonic trap following an interaction quench from zero to infinite interaction strength and vice versa. For both quench scenarios, closed analytical expressions for the temporal evolution of the wave function as well as the Loschmidt echo are found and the dynamics of the momentum density as well as the reduced single-particle density matrix are analyzed. We observe a crossover of these quantities between bosonic, “symmetrized” fermionic, and fermionic properties. Furthermore, several combined quenches are analyzed as well.

We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the centre of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.

Feshbach resonances, which allow for tuning the interactions of ultracold atoms with an external magnetic field, have been widely used to control the properties of quantum gases. We propose a scheme for using scattering resonances as a probe for external fields, showing that by carefully tuning the parameters it is possible to reach a 10−5  G (or nT) level of precision with a single pair of atoms. We show that, for our collisional setup, it is possible to saturate the quantum precision bound with a simple measurement protocol.

The beyond mean-field (MF) dynamics of a bent dark soliton (BDS) embedded in a two-dimensional repulsively interacting Bose–Einstein condensate is explored. We examine the case of a single BDS comparing the MF dynamics to a correlated approach, the multi-configuration time-dependent Hartree method for bosons. Dynamical snaking of this bent structure is observed, signaling the onset of fragmentation which becomes significant during the vortex nucleation. In contrast to the MF approximation 'filling' of the vortex core is observed, leading in turn to the formation of filled-core vortices, instead of the MF vortex–antivortex pairs. The resulting smearing effect in the density is a rather generic feature, occurring when solitonic structures are exposed to quantum fluctuations. Here, we show that this filling owes its existence to the dynamical building of an antidark structure developed in the next-to-leading order orbital. We further demonstrate that the aforementioned beyond MF dynamics can be experimentally detected using the variance of single shot measurements. Additionally, a variety of excitations including vortices, oblique dark solitons, and open ring dark soliton-like structures building upon higher-lying orbitals is observed. We demonstrate that signatures of the higher-lying orbital excitations emerge in the total density, and can be clearly captured by inspecting the one-body coherence. In the latter context, the localization of one-body correlations exposes the existence of the multi-orbital vortex-antidark structure.

We explore the electronic structure of ultralong-range penta-atomic Rydberg molecules from a merger of a Rydberg atom and two ground-state heteronuclear diatomic molecules. Our focus is on the interaction of Rb(23s) and Rb(n=20, l≥3) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the penta-atomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and orientation of the polar diatomic molecules.

We develop a quantum simulator architecture that is suitable for the simulation of U(1) Abelian gauge theories such as quantum electrodynamics. Our approach relies on the ability to control the hopping of a particle through a barrier by means of the internal quantum states of a neutral or charged impurity particle sitting at the barrier. This scheme is experimentally feasible, as the correlated hopping does not require fine-tuning of the intra- and interspecies interactions. We investigate the applicability of the scheme in a double-well potential, which is the basic building block of the simulator, both at the single-particle and the many-body mean-field level. Moreover, we evaluate its performance for different particle interactions and trapping and, specifically for atom-ion systems, in the presence of micromotion.

We investigate the nonequilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and intercrystal Coulomb interactions and the asymmetric population of the potential wells, we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular, we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zigzag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.

We develop a formalism relating nonlocal current continuity to spatial symmetries of subparts in discrete Schrödinger systems. Breaking of such local symmetries hereby generates sources or sinks for the associated nonlocal currents. The framework is applied to locally inversion-(time-) and translation-(time-) symmetric one-dimensional photonic waveguide arrays with Hermitian or non-Hermitian effective tight-binding Hamiltonians. For stationary states the nonlocal currents become translationally invariant within symmetric domains, exposing different types of local symmetry. They are further employed to derive a mapping between wave amplitudes of symmetry-related sites, generalizing also the global Bloch and parity mapping to local symmetry in discrete systems. In scattering setups, perfectly transmitting states are characterized by aligned invariant currents in attached symmetry domains, whose vanishing signifies a correspondingly symmetric density. For periodically driven arrays, the invariance of the nonlocal currents is retained on period average for quasi-energy eigenstates. The proposed theory of symmetry-induced continuity and local invariants may contribute to the understanding of wave structure and response in systems with localized spatial order.

We present an in-depth many-body investigation of the so-called mesoscopic molecular ions that can buildup when an ion is immersed into an atomic Bose-Einstein condensate in one dimension. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for mixtures of ultracold bosonic species for solving the underlying many-body Schrödinger equation. This enables us to unravel the actual structure of such massive charged molecules from a microscopic perspective. Laying out their phase diagram with respect to atom number and interatomic interaction strength, we determine the maximal number of atoms bound to the ion and reveal spatial densities and molecular properties. Interestingly, we observe a strong interaction-induced localization, especially for the ion, that we explain by the generation of a large effective mass, similarly to ions in liquid Helium. Finally, we predict the dynamical response of the ion to small perturbations. Our results provide clear evidence for the importance of quantum correlations, as we demonstrate by benchmarking them with wave function ansatz classes employed in the literature.

We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of a mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species correlations. The versatility and efficiency of ML-MCTDHX are demonstrated by applying it to the problem of colliding few-atom mixtures of both Bose-Fermi and Fermi-Fermi types. Thereby, we elucidate the role of correlations in the transmission and reflection properties of the collisional events. In particular, we present examples where the reflection (transmission) at the other atomic species is a correlation-dominated effect, i.e., it is suppressed in the mean-field approximation.

We explore the impact of dimensionality on the scattering of a small bosonic ensemble in an elongated harmonic trap off a centered repulsive barrier, thereby taking particle correlations into account. The loss of coherence as well as the oscillation of the center of mass are studied and we analyze the influence of both particle and spatial correlations. Two different mechanisms of coherence losses in dependence of the aspect ratio are found. For small aspect ratios, loss of coherence between the region close to the barrier and outer regions occurs, due to spatial correlations, and for large aspect ratios, incoherence between the two density fragments of the left and right side of the barrier arises due to particle correlations. Apart from the decay of the center-of-mass motion induced by the reflection and transmission, further effects due to the particle and spatial correlations are explored. For tight transversal traps, the amplitude of the center-of-mass oscillation experiences a weaker damping, which can be traced back to the population of a second natural orbital, and for a weaker transversal confinement, we detect a strong decay due to the possibility of transferring energy to transversal excited modes. These effects are enhanced if the aspect ratio is integer valued.

The dynamics of dark–bright (DB) solitons beyond the mean-field approximation is investigated. We first examine the case of a single DB soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the splitting of each of the parent mean-field DB solitons, placed off-center within the parabolic trap, into a fast and a slow daughter solitary wave. The latter process is in direct contrast to the predictions of the mean-field approximation. A variety of excitations including DB solitons in multiple (concurrently populated) orbitals is observed. Dark–antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics.

We study electronic image states around a metallic nanoring and show that the interplay between the attractive polarization force and a repulsive centrifugal force gives rise to Rydberg-like image states trapped several nanometers away from the surface. The nanoring is modeled as a perfectly conducting isolated torus whose classical electrostatic image potential is derived analytically. The image states are computed via a two-dimensional finite-difference scheme as solutions of the effective Schrödinger equation describing the outer electron subject to this image potential. These findings demonstrate not only the existence of detached image states around nanorings but allow us also to provide general criteria on the ring geometry, i.e., the aspect ratio of the torus, that need to be fulfilled in order to support such states.

The correlated nonequilibrium quantum dynamics following a multiple interaction quench protocol for few-bosonic ensembles confined in finite optical lattices is investigated. The quenches give rise to an interwell tunneling and excite the cradle and a breathing mode. Several tunneling pathways open during the time interval of increased interactions, while only a few occur when the system is quenched back to its original interaction strength. The cradle mode, however, persists during and in between the quenches, while the breathing mode possesses distinct frequencies. The occupation of excited bands is explored in detail revealing a monotonic behavior with increasing quench amplitude and a nonlinear dependence on the duration of the application of the quenched interaction strength. Finally, a periodic population transfer between momenta for quenches of increasing interaction is observed, with a power-law frequency dependence on the quench amplitude. Our results open the possibility to dynamically manipulate various excited modes of the bosonic system.

The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose–Einstein condensates is investigated. Motivated by the tunability of the atomic interactions in recent experiments, we explore in detail the impact that changes in the interaction strengths have on these bound pairs by considering significant deviations from the integrable limit. It is found that dark-bright soliton pairs exist as stable configurations in a wide parametric window spanning both the miscible and the immiscible regime of interactions. Outside this parameter interval, two unstable regions are identified and are associated with a supercritical and a subcritical pitchfork bifurcation, respectively. Dynamical manifestation of these instabilities gives rise to a redistribution of the bright density between the dark solitons, and also to symmetry-broken stationary states that are mass imbalanced (asymmetric) with respect to their bright soliton counterpart. The long-time dynamics of both the stable and the unstable balanced and imbalanced dark-bright soliton pairs is analyzed.

Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates.

We demonstrate how to systematically design wave scattering systems with simultaneous coherent perfect absorbing and lasing operation at multiple and prescribed frequencies. The approach is based on the recursive assembly of non-Hermitian emitter and absorber units into self-dual emitter-absorber trimers at different composition levels, exploiting the simple structure of the corresponding transfer matrices. In particular, lifting the restriction to parity-time-symmetric setups enables the realization of emitter and absorber action at distinct frequencies and provides flexibility with respect to the choice of realistic parameters. We further show how the same assembled scatterers can be rearranged to produce unidirectional and bidirectional transparency at the selected frequencies. With the design procedure being generically applicable to wave scattering in single-channel settings, we demonstrate it with concrete examples of photonic multilayer setups.

The collective dynamics of a dipolar fermionic quantum gas confined in a one-dimensional double-well superlattice is explored. The fermionic gas resides in a paramagnetic-like ground state in the weak interaction regime, upon which a new type of collective dynamics is found when applying a local perturbation. This dynamics is composed of the local tunneling of fermions in separate supercells, and is a pure quantum effect, with no classical counterpart. Due to the presence of the dipolar interactions the local tunneling transports through the entire superlattice, giving rise to a collective dynamics. A well-defined momentum-energy dispersion relation is identified in the ab-initio simulations demonstrating the phonon-like behavior. The phonon-like characteristic is also confirmed by an analytical description of the dynamics within a semiclassical picture.

We explore the nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center of mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behavior signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

Recently [P. A. Kalozoumis et al. Phys. Rev. Lett. 113, 050403 (2014)] the concept of local symmetries in one-dimensional stationary wave propagation has been shown to lead to a class of invariant two-point currents that allow to generalize the parity and Bloch theorem. In the present work, we establish the theoretical framework of local symmetries for higher-dimensional interacting many-body systems. Based on the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we derive the equations of motion of local symmetry correlators which are off-diagonal elements of the reduced one-body density matrix at symmetry related positions. The natural orbital representation yields equations of motion for the convex sum of the local symmetry correlators of the natural orbitals as well as for the local symmetry correlators of the individual orbitals themselves. An alternative integral representation with a unique interpretation is provided. We discuss special cases, such as the bosonic and fermionic mean field theory, and show in particular that the invariance of two-point currents is recovered in the case of the non-interacting one-dimensional stationary wave propagation. Finally we derive the equations of motion for anomalous local symmetry correlators which indicate the breaking of a global into a local symmetry in the stationary non-interacting case. I. INTRODUCTION

The out-of-equilibrium dynamics of interaction quenched finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. It is shown that periodic driving enforces the bosons in the outer wells of the finite lattice to exhibit out-of-phase dipolelike modes, while in the central well the atomic cloud experiences a local breathing mode. The dynamical behavior is investigated with varying driving frequencies, revealing resonantlike behavior of the intrawell dynamics. An interaction quench in the periodically driven lattice gives rise to admixtures of different excitations in the outer wells, enhanced breathing in the center, and amplification of the tunneling dynamics. We then observe multiple resonances between the inter- and the intrawell dynamics at different quench amplitudes, with the position of the resonances being tunable via the driving frequency. Our results pave the way for future investigations of the use of combined driving protocols in order to excite different inter- and intrawell modes and to subsequently control them.

We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the center-of-mass and relative motion, the existence of an external force perpendicular to the helix axis couples the center-of-mass to the relative degree of freedom leading to equilibria with a localized center of mass. By tuning the external field various fixed points are created and/or annihilated through different bifurcation scenarios. We provide a detailed analysis of these bifurcations based on which we demonstrate a robust state transfer between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time dependent.

In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter- and intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the intercomponent interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter gives rise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of the bound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations and monitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.

Exploring the impact of dimensionality on the quantum dynamics of interacting bosons in traps including particle correlations is an interesting but challenging task. Due to the different participating length scales the modelling of the short-range interactions in three dimensions plays a special role. We review different approaches for the latter and elaborate that for multi-configurational computational strategies finite range potentials are adequate resulting in the need of large grids to resolve the relevant length scales. This results in computational challenges which include also the exponential scaling of complexity with the number of atoms. We show that the recently developed ab-initio Multi-Layer Multi-Configurational Time- Dependent Hartee method for Bosons (ML-MCTDHB) [J. Chem. Phys. 139, 134103 (2013)] can face both numerical challenges and present an efficient numerical implementation of ML-MCTDHB in three spatial dimensions, particularly suited to describe the quantum dynamics for elongated traps. The beneficial scaling of our approach is demonstrated by studying the tunnelling dynamics of bosonic ensembles in a double well. Comparing three-dimensional with quasi-one dimensional simulations, we find dimensionality-induced effects in the density. Furthermore, we study the crossover from weak transversal confinement, where a mean-field description of the system is sufficient, towards tight transversal confinement, where particle correlations and beyond mean-field effects are pronounced.

The nonequilibrium dynamics of small boson ensembles in a one-dimensional optical lattice is explored upon a sudden quench of an additional harmonic trap from strong to weak confinement. We find that the competition between the initial localization and the repulsive interaction leads to a resonant response of the system for intermediate quench amplitudes, corresponding to avoided crossings in the many-body eigenspectrum with varying final trap frequency. In particular, we show that these avoided crossings can be utilized to prepare the system in a desired state. The dynamical response is shown to depend on both the interaction strength as well as the number of atoms manifesting the many-body nature of the tunneling dynamics.

We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated by varying both the amount of initial excess kinetic energy of one of them and the strength of the electric field. In the field-free case, and depending on the initial excess energy, an abrupt transition between equipartition and nonequipartition regimes is encountered. The study of the phase space structure of the system as well as the formulation of the Hamiltonian in an appropriate coordinate frame provide a thorough understanding of this sharp transition. When the electric field is turned on, the kinetic energy transfer mechanism is significantly more complex and the system goes through different regimes of equipartition and nonequipartition of the energy including chaotic behavior.

Wannier-Mott excitons in a semiconductor layered superlattice (SL) are investigated analytically for the case that the period of the superlattice is much smaller than the 2D exciton Bohr radius. Additionally we assume the presence of a longitudinal external static electric field directed parallel to the SL axis. The exciton states and the optical absorption coefficient are derived in the tight-binding and adiabatic approximations. Strong and weak electric fields providing spatially localized and extended electron and hole states, respectively, are studied. The dependencies of the exciton states and the exciton absorption spectrum on the SL parameters and the electric field strength are presented in an explicit form. We focus on the fine structure of the ground quasi-2D exciton level formed by the series of closely spaced energy levels adjacent from the high frequencies. These levels are related to the adiabatically slow relative exciton longitudinal motion governed by the potential formed by the in-plane exciton state. It is shown that the external electric fields compress the fine structure energy levels, decrease the intensities of the corresponding optical peaks and increase the exciton binding energy. A possible experimental study of the fine structure of the exciton electroabsorption is discussed.

In this book the coherent quantum transport of electrons through two-dimensional mesoscopic structures is explored in dependence of the interplay between the confining geometry and the impact of applied magnetic fields, aiming at conductance controllability. After a top-down, insightful presentation of the elements of mesoscopic devices and transport theory, a computational technique which treats multiterminal structures of arbitrary geometry and topology is developed. The method relies on the modular assembly of the electronic propagators of subsystems which are inter- or intra-connected providing large flexibility in system setups combined with high computational efficiency. Conductance control is first demonstrated for elongated quantum billiards and arrays thereof where a weak magnetic field tunes the current by phase modulation of interfering lead-coupled states geometrically separated from confined states. Soft-wall potentials are then employed for efficient and robust conductance switching by isolating energy persistent, collimated or magnetically deflected electron paths from Fano resonances. In a multiterminal configuration, the guiding and focusing property of curved boundary sections enables magnetically controlled directional transport with input electron waves flowing exclusively to selected outputs. Together with a comprehensive analysis of characteristic transport features and spatial distributions of scattering states, the results demonstrate the geometrically assisted design of magnetoconductance control elements in the linear response regime.

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of PT-symmetric quantum mechanics and paraxial optics.

Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity. However, this control is still sub-optimal. In many scenarios, achieving a fast transformation is crucial to fight against decoherence and imperfection effects. Optimal control theory is believed to be the ideal candidate to bridge the gap between early stage proof-of-principle demonstrations and experimental protocols suitable for practical applications. Indeed, it can engineer protocols at the quantum speed limit – the fastest achievable timescale of the transformation. Here, we demonstrate such potential by computing theoretically and verifying experimentally the optimal transformations in two very different interacting systems: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We also show that such processes are robust with respect to perturbations, including temperature and atom number fluctuations.

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.

We investigate confinement-induced resonances in a system composed of a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region—from the “long-wavelength” limit to the opposite case when the typical length scale of the atom-ion polarization potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the “long-wavelength and zero-energy” limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semianalytic formula for the resonance position in the long-wavelength and zero-energy limit and we investigate numerically the dependence of the resonance condition on the finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, to determine the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi-one-dimensional atomic quantum gas.

The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s- and p-wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length ${a}_{{\rm{1D}}}$ diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of ${a}_{{\rm{1D}}}$. In the vicinity of broad s-wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency ${\omega }_{\perp }$ of the waveguide. Close to p-wave and narrow s-wave resonances, the resonant magnetic field changes as ${\omega }_{\perp }$ varies.

We investigate polyatomic ultralong-range Rydberg molecules consisting of three ground-state atoms bound to a Rydberg atom via s- and p-wave interactions. By employing the finite basis set representation of the unperturbed Rydberg electron Green's function we reduce the computational effort to solve the electronic problem substantially. This method is subsequently applied to determine the potential energy surfaces of triatomic systems in electronic s- and p-Rydberg states. Their molecular geometry and resulting vibrational structure are analyzed within an adiabatic approach that separates the vibrational bending and stretching dynamics. This procedure yields information on the radial and angular arrangement of the nuclei and indicates in particular that kinetic couplings between bending and stretching modes induce a linear structure in triatomic l=0 ultralong-range Rydberg molecules.

We theoretically investigate trapped ions interacting with atoms that are coupled to Rydberg states. The strong polarizabilities of the Rydberg levels increase the interaction strength between atoms and ions by many orders of magnitude, as compared to the case of ground-state atoms, and may be mediated over micrometers. We calculate that such interactions can be used to generate entanglement between an atom and the motion or internal state of an ion. Furthermore, the ion could be used as a bus for mediating spin-spin interactions between atomic spins in analogy to much employed techniques in ion-trap quantum simulation. The proposed scheme comes with attractive features as it maps the benefits of the trapped-ion quantum system onto the atomic one without obviously impeding its intrinsic scalability. No ground-state cooling of the ion or atom is required and the setup allows for full dynamical control. Moreover, the scheme is to a large extent immune to the micromotion of the ion. Our findings are of interest for developing hybrid quantum information platforms and for implementing quantum simulations of solid-state physics.

We develop an analytical approach to the exciton optical absorption for narrow gap armchair graphene nanoribbons (AGNR). We focus on the regime of dominant size quantization in combination with the attractive electron–hole interaction. An adiabatic separation of slow and fast motions leads via the two-body Dirac equation to the isolated and coupled subband approximations. Discrete and continuous exciton states are in general coupled and form quasi-Rydberg series of purely discrete and resonance type character. The corresponding oscillator strengths and widths are derived. We show that the exciton peaks are blue-shifted, become broader and increase in magnitude upon narrowing the ribbon. At the edge of a subband the singularity related to the 1D density of states is transformed into finite absorption via the presence of the exciton. Our analytical results are in good agreement with those obtained by other methods including numerical approaches. Estimates of the expected experimental values are provided for realistic AGNR.

We consider a periodic waveguide array whose unit cell consists of a PT-symmetric quadrimer with two competing loss-gain parameter pairs which lead to qualitatively different symmetry-broken phases. It is shown that the transitions between the phases are described by a symmetry-adapted nonlocal current which maps the spectral properties to the spatially resolved field, for the lattice as well as for the isolated quadrimer. Its site average acts like a natural order parameter for the general class of one-dimensional PT-symmetric Hamiltonians, vanishing in the unbroken phase and being nonzero in the broken phase. We investigate how the beam dynamics in the array is affected by the presence of competing loss-gain rates in the unit cell, showing that the enriched band structure yields the possibility to control the propagation length before divergence when the system resides in the broken PT phase.

We explore the non-equilibrium dynamics of two coupled zig-zag chains of trapped ions in a double well potential. Following a quench of the potential barrier between both wells, the induced coupling between both chains due to the long-range interaction of the ions leads to the complete loss of order in the radial direction. The resulting dynamics is however not exclusively irregular but leads to phases of motion during which various ordered structures appear with ions arranged in arcs, lines and crosses. We quantify the emerging order by introducing a suitable measure and complement our analysis of the ion dynamics using a normal mode analysis showing a decisive population transfer between only a few distinguished modes.

We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected NNth neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. Based on this argument, we derive analytical estimates of the critical parameters at which the fundamental on-site breather branch of solutions turns unstable. In the limit of large NN, these estimates predict the emergence of an effective threshold behavior, which can be viewed as the result of a dimensional crossover to a two-dimensional square lattice.

We investigate an atomic ensemble of interacting bosons trapped in a symmetric double-well potential in contact with a single tightly trapped ion which has been recently proposed [R. Gerritsma et al., Phys. Rev. Lett. 109, 080402 (2012)] as a source of entanglement between a Bose-Einstein condensate and an ion. Compared to the previous study, the present work aims at performing a detailed and accurate many-body analysis of such a combined atomic quantum system by means of the ab initio multiconfiguration time-dependent Hartree method for bosons, which allows us to take into account all correlations in the system. The analysis elucidates the importance of quantum correlations in the bosonic ensemble and reveals that entanglement generation between an ion and a condensate is indeed possible, as previously predicted. Moreover, we provide an intuitive picture of the impact of the correlations on the out-of-equilibrium dynamics by employing a natural orbital analysis which we show to be indeed experimentally verifiable.

We provide a generic scheme offering real-time control of directed particle transport using superimposed driven lattices. This scheme allows one to accelerate, slow, and freeze the transport on demand by switching one of the lattices subsequently on and off. The underlying physical mechanism hinges on a systematic opening and closing of channels between transporting and nontransporting phase space structures upon switching and exploits cantori structures which generate memory effects in the population of these structures. Our results should allow for real-time control of cold thermal atomic ensembles in optical lattices but might also be useful as a design principle for targeted delivery of molecules or colloids in optical devices.

Time-averaged two-point currents are derived and shown to be spatially invariant within domains of local translation or inversion symmetry for arbitrary time-periodic quantum systems in one dimension. These currents are shown to provide a valuable tool for detecting deformations of a spatial symmetry in static and driven lattices. In the static case the invariance of the two-point currents is related to the presence of time-reversal invariance and/or probability current conservation. The obtained insights into the wave functions are further exploited for a symmetry-based convergence check which is applicable for globally broken but locally retained potential symmetries.

We investigate the electronic structure of a triatomic Rydberg molecule formed by a Rydberg atom and two neutral ground-state atoms. Taking into account the s-wave and p-wave interactions, we perform electronic structure calculations and analyze the adiabatic electronic potentials evolving from the Rb (n = 35, l ≥ 3) Rydberg degenerate manifold. We hereby focus on three different classes of geometries of the Rydberg molecules, including symmetric, asymmetric and planar configurations. The metamorphosis of these potential energy surfaces in the presence of an external electric field is explored.

We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found. We argue how these transients are caused and can be understood by a hierarchy of block decompositions of the quasiperiodic lattice. A comparison to the cases of periodic and fully randomized lattices is performed.

A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmetries. The local symmetry bases enable efficient computation of spatially resolved wave amplitudes in systems with arbitrary combinations of local inversion and translation symmetries. The approach opens the perspective of a flexible analysis and control of wave localization in structurally complex systems.

Symmetrien sind fundamentale Eckpfeiler der modernen Physik, nicht zuletzt wegen ihrer Bedeutung für die Erhaltungssätze oder die zulässige Form der Wechselwirkung bei Elementarteilchen. Doch in komplexen Systemen zeigen sich oft in verschiedenen begrenzten Raumbereichen unterschiedliche Symmetrien. Ist es möglich, die Theorie der globalen Symmetrien auf solche Systeme mit lokalen Symmetrien zu erweitern? Tatsächlich lassen sich mathematische Instrumente finden, die lokale Symmetrien beschreiben können und neue Perspektiven bieten, etwa für Anwendungen in der Wellenpropagation.

We investigate the structure and features of an ultralong-range triatomic Rydberg molecule formed by a Rb Rydberg atom and a KRb diatomic molecule. In our numerical description, we perform a realistic treatment of the internal rotational motion of the diatomic molecule, and take into account the Rb(n, l ≥ 3) Rydberg degenerate manifold and the energetically closest neighboring levels with principal quantum numbers n' > n and orbital quantum number l ≤ 2. We focus here on the adiabatic electronic potentials evolving from the Rb(n,l ≥ 3) and Rb(n = 26, l = 2) manifolds. The directional properties of the KRb diatomic molecule within the Rb-KRb triatomic Rydberg molecule are also analyzed in detail.

We apply the concept of quantum speed limit (QSL)—the minimal time needed to perform a driven evolution—to complex interacting many-body systems where the effects of interactions have to be taken into account. We introduce a general strategy to eliminate the detrimental effects of the interparticle repulsion and drive the system at the QSL by applying a compensating control pulse (CCP). To prove the principles we consider a prototypical many-body system, a bosonic Josephson junction, and investigate a transfer of atoms from the ground state of one well to the ground state of the neighboring well, at increasing levels of complexity—from a textbook two-level approximation to full many-body treatment. By tracing the efficiency of the CCP protocol we show that the driven dynamics does follow the geodetic pathway and, therefore, it is optimal. The CCP strategy, applicable for a general interacting quantum many-body system with strong driving, can be of a practical relevance for the experimental implementation of quantum technology protocols, as quantum simulations or matter-wave metrology.

Electronic image states around segmented carbon nanotubes can be confined and shaped along the nanotube axis by engineering the image potential. We show how several such image states can be prepared simultaneously along the same nanotube. The inter-electronic distance can be controlled a priori by engineering tubes of specific geometries. High sensitivity to external electric and magnetic fields can be exploited to manipulate these states and their mutual long-range interactions. These building blocks provide access to a new kind of tailored interacting quantum systems.

The out-of-equilibrium dynamics of finite ultracold bosonic ensembles in periodically driven one-dimensional optical lattices is investigated. Our study reveals that the driving enforces the bosons in different wells to oscillate in-phase and to exhibit a dipole-like mode. A wide range from weak-to-strong driving frequencies is covered and a resonance-like behavior of the intra-well dynamics is discussed. In the proximity of the resonance a rich intraband excitation spectrum is observed. The single particle excitation mechanisms are studied in the framework of Floquet theory elucidating the role of the driving frequency. The impact of the interatomic repulsive interactions is examined in detail yielding a strong influence on the tunneling period and the excitation probabilities. Finally, the dependence of the resonance upon a variation of the tunable parameters of the optical lattice is examined. Our analysis is based on the ab initio multi-configuration time-dependent Hartree method for bosons.

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behavior of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behavior using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breatherlike excitations.

We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of spatially invariant nonlocal currents, emerging when the corresponding generalized potential exhibits symmetries in arbitrary spatial domains. These invariants characterize the wave propagation and provide a spatial mapping of the wave function between any symmetry related domains. This generalizes the Bloch and parity theorems for broken reflection and translational symmetries, respectively. Their nonvanishing values indicate the symmetry breaking, whereas a zero value denotes the restoration of the global symmetry where the well-known forms of the two theorems are recovered. These invariants allow for a systematic treatment of systems with any local symmetry combination, providing a tool for the investigation of the scattering properties of aperiodic but locally symmetric systems. To this aim we express the transfer matrix of a locally symmetric potential unit via the corresponding invariants and derive quantities characterizing the complete scattering device which serve as key elements for the investigation of transmission spectra and particularly of perfect transmission resonances.

The relationship between natural orbitals, one-body coherences, and two-body correlations is explored for bosonic many-body systems of definite parity with two occupied single-particle states. We show that the strength of local two-body correlations at the parity-symmetry center characterizes the number-state distribution and controls the structure of nonlocal two-body correlations. A recipe for the experimental reconstruction of the natural-orbital densities and quantum depletion is derived. These insights into the structure of the many-body wave function are applied to the predicted quantum-fluctuation-induced decay of dark solitons.

We perform an analytical investigation in the framework of generalized K-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for d waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.

We explore the quantum dynamics of a one-dimensional trapped ultracold ensemble of bosonic atoms triggered by the sudden creation of a single ion. The numerical simulations are performed by means of the ab initio multiconfiguration time-dependent Hartree method for bosons which takes into account all correlations. The dynamics is analyzed via a cluster expansion approach, adapted to bosonic systems of fixed particle number, which provides a comprehensive understanding of the occurring many-body processes. After a transient during which the atomic ensemble separates into fractions which are unbound and bound with respect to the ion, we observe an oscillation in the atomic density which we attribute to the additional length and energy scale induced by the attractive long-range atom–ion interaction. This oscillation is shown to be the main source of spatial coherence and population transfer between the bound and the unbound atomic fraction. Moreover, the dynamics exhibits collapse and revival behavior caused by the dynamical build-up of two-particle correlations demonstrating that a beyond mean-field description is indispensable.

We theoretically analyze a discrete Schrödinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, second-neighbor hopping has a strong impact on the band structure, leading to the emergence of a new extremum located inside the band, accompanied by a van Hove singularity in the density of states. The energy band is then divided into a subcritical regime, with the usual unique correspondence between wave number and energy of the traveling waves, and a supercritical regime, in which waves of different wave number are degenerate in energy. We study the consequences of these features in a scattering setup, introducing a defect that locally breaks the translational invariance. The notion of a local probability current is generalized beyond the nearest-neighbor approximation and bound states with energies outside the band are discussed. At subcritical energies inside the band, an evanescent mode coexists with the traveling plane wave, giving rise to resonance phenomena in scattering. At weak coupling to the defect, we identify a prototypical Fano-Feshbach resonance of tunable shape and provide analytical expressions for its profile parameters. At supercritical energies, we observe coupling of the degenerate traveling waves, leading to an intricate wave-packet fragmentation dynamics. The corresponding branching ratios are analyzed.

We demonstrate that repulsive power law interactions can induce deterministic directed transport of particles in dissipative ac-driven periodic potentials, in regimes where the underlying noninteracting system exhibits localized oscillations. Contrasting the well-established single particle ratchet mechanism, this interaction induced transport is based on the collective behaviour of the interacting particles yielding a spatiotemporal nonequilibrium pattern comprising persistent travelling excitations.

We theoretically analyze quasi-one-dimensional Bose-Einstein condensates under the influence of a harmonic trap and a narrow potential defect that moves through the atomic cloud. Performing simulations on the mean-field level, we explore a robust mechanism in which a single dark soliton is nucleated and immediately pinned by the moving defect, making it possible to drag it to a desired position and release it there. We argue on a perturbative level that a defect potential which is attractive to the atoms is suitable for holding and moving dark solitons. The soliton generation protocol is investigated over a wide range of model parameters and its success is systematically quantified by a suitable fidelity measure, demonstrating its robustness against parameter variations, but also the need for tight focusing of the defect potential. Holding the soliton at a stationary defect for long times may give rise to dynamical instabilities, whose origin we explore within a Bogoliubov–de Gennes linearization analysis. We show that iterating the generation process with multiple defects offers a perspective for initializing multiple soliton dynamics with freely chosen initial conditions.

We define auto- and cross-correlation functions capable of capturing dynamical characteristics induced by local phase-space structures in a general dynamical system. These correlation functions are calculated in the standard map for a range of values of the nonlinearity parameter k. Using a model of noninteracting particles, each evolving according to the same standard map dynamics and located initially at specific phase-space regions, we show that for 0.6 Physical Review E 92, 012914 (2015)

We implement the concept of complete local symmetry in lossy acoustic waveguides. Despite the presence of losses, the existence of a spatially invariant current is shown theoretically and observed experimentally. We demonstrate how this invariant current leads to the generalization of the Bloch and parity theorems for lossy systems defining a mapping of the pressure field between symmetry-related spatial domains. Using experimental data, we verify this mapping with remarkable accuracy. For the performed experiment, we employ a construction technique based on local symmetries that allows the design of setups with prescribed perfect transmission resonances in the lossless case. Our results reveal the fundamental role of symmetries in restricted spatial domains, and they clearly indicate that completely locally symmetric devices constitute a promising class of setups with regard to the manipulation of wave propagation.

We develop and analyze a theoretical model to study p-wave Feshbach resonances of identical fermions in atomic waveguides by extending the two-channel model of Lange et al (2009 Phys. Rev. A 79 013622) and Saeidian et al (2012 Phys. Rev. A 86 062713). The experimentally known parameters of Feshbach resonances in free space are used as input of the model. We calculate the shifts and widths of p-wave magnetic Feshbach resonance of 40K atoms emerging in harmonic waveguides as p-wave confinement induced resonance (CIR). Particularly, we show a possibility to control the width and shift of the p-wave CIR by the trap frequency and the applied magnetic field which could be used in corresponding experiments. Our analysis also demonstrates the importance of the inclusion of the effective range in the computational schemes for the description of the p-wave CIRs contrary to the case of s-wave CIRs where the influence of this term is negligible.

We perform a comparative beyond-mean-field study of black and gray solitonic excitations in a finite ensemble of ultracold bosons confined to a one-dimensional box. An optimized density-engineering potential is developed and employed together with phase imprinting to cleanly initialize gray solitons. By means of ab initio simulations with the multiconfiguration time-dependent Hartree method for bosons, we demonstrate that quantum fluctuations limit the lifetime of the soliton contrast, which increases with increasing soliton velocity. A natural orbital analysis reveals a two-stage process underlying the decay of the soliton contrast. The broken parity symmetry of gray solitons results in a local asymmetry of the orbital mainly responsible for the decay, which leads to a characteristic asymmetry of remarkably localized two-body correlations. The emergence and decay of these correlations as well as their displacement from the instantaneous soliton position are analyzed in detail. Finally, the role of phase imprinting for the many-body dynamics is illuminated and additional nonlocal correlations in pairs of counterpropagating gray solitons are observed.

We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degree of freedom of a single particle in the lattice onto a pseudo-spin results in an effective Ising type chain dressed with transverse and longitudinal magnetic fields. The ground state of this effective Ising chain changes from a paramagnetic to a single-kink state as the dipolar interaction increases. Particularly in the single-kink state this effective chain permits emulations of magnetic kink effects. Being realizable with current experimental techniques, this effective Ising chain presents a unique platform for emulations of Ising physics and enriches the toolbox for quantum emulation of spin models by ultracold quantum gases.

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an s-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically explained.

We explore the correlated quantum dynamics of a single atom, regarded as an open system, with a spatio-temporally localized coupling to a finite bosonic environment. The single atom, initially prepared in a coherent state of low energy, oscillates in a one-dimensional harmonic trap and thereby periodically penetrates an interacting ensemble of NA bosons held in a displaced trap. We show that the inter-species energy transfer accelerates with increasing NA and becomes less complete at the same time. System-environment correlations prove to be significant except for times when the excess energy distribution among the subsystems is highly imbalanced. These correlations result in incoherent energy transfer processes, which accelerate the early energy donation of the single atom and stochastically favour certain energy transfer channels, depending on the instantaneous direction of transfer. Concerning the subsystem states, the energy transfer is mediated by non-coherent states of the single atom and manifests itself in singlet and doublet excitations in the finite bosonic environment. These comprehensive insights into the non-equilibrium quantum dynamics of an open system are gained by ab initio simulations of the total system with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons.

We investigate a binary mixture of bosonic atoms loaded into a state-dependent honeycomb lattice. For this system, the emergence of a so-called twisted-superfluid ground state was experimentally observed in Soltan-Panahi et al. [Nat. Phys. 8, 71 (2012)]. Theoretically, the origin of this effect is not understood. We perform numerical simulations of an extended single-band Bose-Hubbard model adapted to the experimental parameters employing the multilayer multiconfiguration time-dependent Hartree method for Bosons. Our results confirm the overall applicability of mean-field theory in the relevant parameter range, within the extended single-band Bose-Hubbard model. Beyond this, we provide a detailed analysis of correlation effects correcting the mean-field result. These have the potential to induce asymmetries in single shot time-of-flight measurements, but we find no indication of the patterns characteristic of the twisted superfluid. We comment on the restrictions of our model and possible extensions.

We consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.

We demonstrate that a site-dependent driving of a periodic potential allows for the controlled manipulation of a quantum particle on length scales of the lattice spacing. Specifically we observe for distinct driving frequencies a near depletion of certain sites which is explained by a resonant mixing of the involved Floquet-Bloch modes occurring at these frequencies. Our results could be exploited as a scheme for a site-selective loading of, e.g., ultracold atoms into an optical lattice.

We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schr¨odinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOC-BEC. Numerical results are found to be in excellent agreement with our analytical predictions.

The nonequilibrium dynamics following a quench of strongly repulsive bosonic ensembles in one-dimensional finite lattices is investigated by employing interaction quenches and/or a ramp of the lattice potential. Both sudden and time-dependent quenches are analyzed in detail. For the case of interaction quenches we address the transition from the strong repulsive to the weakly interacting regime, suppressing in this manner the heating of the system. The excitation modes such as the cradle process and the local breathing mode are examined via local density observables. In particular, the cradle mode is inherently related to the initial delocalization and, following a negative interaction quench, can be excited only for incommensurate setups with filling larger than unity. Alternatively, a negative quench of the lattice depth which favors the spatial delocalization is used to access the cradle mode for setups with filling smaller than unity. Our results shed light on possible schemes to control the cradle and the breathing modes. Finally, employing the notion of fidelity we study the dynamical response of the system after a diabatic or adiabatic parameter modulation for short and long evolution times. The evolution of the system is obtained numerically using the ab initio multilayer multiconfiguration time-dependent Hartree method for bosons, which permits us to follow nonequilibrium dynamics including the corresponding investigation of higher-band effects.

Constraining long-range interacting particles to move on a curved manifold can drastically alter their effective interactions. As a prototype we explore the structure and vibrational dynamics of crystalline configurations formed on a closed helix. We show that the ground state undergoes a pitchfork bifurcation from a symmetric polygonic to a zigzag-like configuration with increasing radius of the helix. Remarkably, we find that, for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and, consequently, localized excitations can propagate in time without significant spreading. Upon increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center-of-mass motion.

We study a discrete Schrödinger equation with arbitrary long-range hopping terms under the influence of an external force. The impact of long-range hoppings on the single-particle Bloch dynamics in the lattice is investigated. A closed expression for the propagator is given, based on which we analyze the dynamics of initially Gaussian wave packets. Our findings capture the anharmonic oscillations recently observed in zigzag lattices and furthermore provide a detailed quantitative description of the crossover between center-of-mass Bloch oscillations for wide wave packets and left-right symmetric width oscillations for narrow single-site excitations. The analytical results are shown to be in agreement with numerical simulations. A helix lattice setup for ultracold atoms is proposed where such hopping terms to far neighbors can be experimentally tuned to sizable values.

We explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on the interaction of a Rb() Rydberg atom with a KRb(N = 0) diatomic polar molecule. There is significant electronic hybridization with the Rb(n = 24, ) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born–Oppenheimer potential curves, essential for the binding of the molecule, with varying electric field and analyze the resulting properties such as the vibrational structure and the alignment and orientation of the polar diatomic molecule.

We study the Rydberg excitation dynamics of laser-driven atoms confined in a one-dimensional three-site lattice with open boundary conditions. Different regular excitation patterns are obtained within various parameter regimes. In the case of a weak Rydberg–Rydberg interaction, the excitation probability possesses a nodal structure which is characterized by an envelope with a period inversely proportional to the interaction. For strong Rydberg interaction we observe dipole blockade and antiblockade effects and an appropriate detuning leads to an overall oscillatory behavior of the Rydberg probability density which is modulated only by small oscillations. Besides an exact diagonalization procedure we study the system by performing first and second order perturbation theory as well as a spectral analysis.

We explore the classical dynamics of atoms in an optical dipole trap formed by two identical Gaussian beams propagating in perpendicular directions. The phase space is a mixture of regular and chaotic orbits, the latter becoming dominant as the energy of the atoms increases. The trapping capabilities of these perpendicular Gaussian beams are investigated by considering an atomic ensemble in free motion. After a sudden turn on of the dipole trap, a certain fraction of atoms in the ensemble remains trapped. The majority of these trapped atoms has energies larger than the escape channels, which can be explained by the existence of regular and chaotic orbits with very long escape times.

The correlated non-equilibrium dynamics of few-boson systems in one-dimensional finite lattices is investigated. Starting from weak interactions we perform a sudden interaction quench and employ the numerically exact multi-layer multi-configuration time-dependent Hartree method for bosons to obtain the resulting quantum dynamics. Focusing on the low-lying modes of the finite lattice we observe the emergence of density-wave tunneling, breathing and cradle-like processes. In particular, the tunneling induced by the quench leads to a 'global' density-wave oscillation. The resulting breathing and cradle modes are inherent to the local intrawell dynamics and connected to excited-band states. Moreover, the interaction quenches couple the density-wave and the cradle modes allowing for resonance phenomena. These are associated with an avoided-crossing in the respective frequency spectrum and lead to a beating dynamics for the cradle. Finally, complementing the numerical studies, an effective Hamiltonian in terms of the relevant Fock states is derived for the description of the spectral properties and the related resonant dynamics.

We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the widths of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a certain parameter range.

We study the properties of a quantum particle interacting with a one-dimensional structure of equidistant scattering centers. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalizes the well-known solid-state physics textbook result known as the Kronig-Penney model. Our generalized model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our attention on the specific atom-ion system and compare our findings with quantum defect theory. Excellent agreement is obtained within the regime of validity of the pseudopotential approximation. This enables us to derive a Bose-Hubbard Hamiltonian for a degenerate quantum Bose gas in a linear chain of ions.

Recently [Phys. Rev. Lett. 106, 093902 (2011)] it has been shown that PT−symmetric scattering systems with balanced gain and loss undergo a transition from PT−symmetric scattering eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification and loss. In the present work we derive the existence of an invariant nonlocal current which can be directly associated with the observed transition playing the role of an “order parameter.” The use of this current for the description of the PT−symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.

A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry possess characteristic distributional and dynamical properties, determined here numerically for certain lattice types. A striking aspect of such a property is given by the return maps of sequential spacings of local symmetry axes, which typically traverse few-point symmetry orbits. This local symmetry dynamics allows for a description of inherently different aperiodic lattices according to fundamental symmetry principles. Illustrating the local symmetry distributional and dynamical properties for several representative binary lattices, we further show that the renormalized axis-spacing sequences follow precisely the particular type of underlying aperiodic order, revealing the presence of dynamical self-similarity. Our analysis thus provides evidence that the long-range order of aperiodic lattices can be characterized in a compellingly simple way by its local symmetry dynamics.

We present an analytical investigation of the quasi-Coulomb impurity states in a narrow gapped armchair graphene nanoribbon (GNR) in the presence of a uniform external electric field directed parallel to the ribbon axis. The effect of the ribbon confinement is taken to be much greater than that of the impurity electric field, which in turn considerably exceeds the external electric field. Under these conditions we employ the adiabatic approximation assuming that the motion parallel (“slow”) and perpendicular (“fast”) to the ribbon axis are separated adiabatically. In the approximation of the isolated size-quantized subbands induced by the “fast” motion, the complex energies of the impurity electron are calculated in explicit form. The real and imaginary parts of these energies determine the binding energy and width of the quasidiscrete state, respectively. The energy width increases with increasing the electric field and ribbon width. The latter forms the background of the mechanism of dimensional ionization. The S matrix—the basic tool of study of the transport problems—can be trivially derived from the phases of the wave functions of the continuous spectrum presented in explicit form. In the double-subband approximation, we calculate the complete widths of the impurity states caused by the combined effect of the electric field and the Fano resonant coupling between the impurity states of the discrete and continuous spectra associated with the ground and first excited size-quantized subbands. Our analytical results are shown to be in agreement with those obtained by other theoretical approaches. Estimates of the expected experimental values for the typically employed GNRs show that for weak electric field the impurity quasidiscrete states remain sufficiently stable to be observed in the corresponding experiment, while a relatively strong field unlocks the captured electrons to further restore their contribution to the transport.

We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi-one-dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are able to numerically obtain the exact many-body ground state of the atomic ensemble in the presence of an ion. We analyze the influence of the atom number and the atom-atom interaction on the ground-state properties. Interestingly, for weakly interacting atoms, we find that the ion impedes the transition from the ideal gas behavior to the Thomas-Fermi limit. Furthermore, we show that this effect can be exploited to infer the presence of the ion both in the momentum distribution of the atomic cloud and by observing the interference fringes occurring during an expansion of the quantum gas. In the strong interacting regime, the ion modifies the fragmentation process in dependence of the atom number parity which allows a clear identification of the latter in expansion experiments. Hence, we propose in both regimes experimentally viable strategies to assess the impact of the ion on the many-body state of the atomic gas. This study serves as the first building block for systematically investigating the many-body physics of such hybrid system.

The isolation of energetically persistent scattering pathways from the resonant manifold of an open electron billiard in the deep quantum regime is demonstrated. This enables efficient conductance switching at varying temperature and Fermi velocity, using a weak magnetic field. The effect relies on the interplay between magnetic focusing and soft-wall confinement, which rescale the scattering pathways and decouple quasibound states from the attached leads, the field-free motion being forwardly collimated. The mechanism proves robust against billiard shape variations and qualifies as a nanoelectronic current control element.

We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p-wave interaction on the ultralong-range molecular states for a pure B-field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2–250 MHz. Both properties are analyzed with varying field strengths. (featured by J. Phys. B in their LabTalk: iopscience.iop.org/0953-4075/labtalk-article/58389)

The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.

Fern des thermodynamischen Gleichgewichts kann ungerichtete Bewegung sogar auf atomaren Skalen in gerichtete Bewegung umgewandelt werden. Dieses Phänomen nutzen biologische Organismen seit Urzeiten. Angesichts der beachtlichen Fortschritte der Nanotechnologie und der Miniaturisierung elektronischer Bauteile rücken gerichtete Teilchenströme aber auch zunehmend in den Fokus von Wissenschaft und Technik. Neue Wege zur Kontrolle von Teilchen und gerichteten Teilchenströmen bieten raumzeitlich getriebene Gitter. Insbesondere ermöglichen sie das Sortieren von Teilchen in Mustern und den Transport ganzer Dichtewellen. Teilchen, die untereinander wechselwirken, wie etwa Ionen, zeigen eine nahezu kollektive Konversion von Chaos zu Ordnung. Diese äußert sich in einer überraschenden, selbstständigen Umkehr der Richtung von Teilchenströmen.

We analyze theoretically the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunneling rate between the wells depends both on the spin of the ion via the short-range spin-dependent atom-ion scattering length and on its motional state with tunneling rates reaching hundreds of hertz. A protocol is presented that could transport an atom from one well to the other, depending on the motional (Fock) state of the ion within a few milliseconds. This phonon-atom coupling is of interest for creating atom-ion entangled states and may form a building block in constructing a hybrid atom-ion quantum simulator. We also analyze the effect of imperfect ground-state cooling of the ion and the role of micromotion when the ion is trapped in a Paul trap. Due to the strong nonlinearities in the atom-ion interaction, the micromotion can cause couplings to high-energy atom-ion scattering states, preventing accurate state preparation and complicating the double-well dynamics. We conclude that the effects of micromotion can be reduced by choosing ion-atom combinations with a large mass ratio and by choosing large interwell distances. The proposed double-well system may be realized in an experiment by combining either optical traps or magnetic microtraps for atoms with ion trapping technology.

The Ramsey interferometer is a prime example of precise control at the quantum level. It is usually implemented using internal states of atoms, molecules or ions, for which powerful manipulation procedures are now available. Whether it is possible to control external degrees of freedom of more complex, interacting many-body systems at this level remained an open question. Here we demonstrate a two-pulse Ramsey-type interferometer for non-classical motional states of a Bose–Einstein condensate in an anharmonic trap. The control sequences used to manipulate the condensate wavefunction are obtained from optimal control theory and are directly optimized to maximize the interferometric contrast. They permit a fast manipulation of the atomic ensemble compared to the intrinsic decay processes and many-body dephasing effects. This allows us to reach an interferometric contrast of 92% in the experimental implementation.

The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIRs) which are attributed to different angular momentum states ℓ, and we explicitly show that in alkaline collisions only four universal ℓ-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of ℓ-wave CIRs is studied. In particular we show that all the ℓ-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized K-matrix theory, and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.

We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using a Fermi pseudopotential approach including s- and p-wave scattering terms, reproduces the measured binding energies. The calculated molecular wave functions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or antialignment with respect to the magnetic field axis.

We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative, and finite chain of interacting particles in a periodic potential towards its many particle equilibrium configuration. Specifically, we observe a transition from an in phase correlated motion via phase randomized oscillations towards oscillations with a phase difference π between adjacent particles thereby yielding the growth of long time transient spatiotemporal oscillation patterns. Parameter modifications allow for designing these patterns, including steady states and even states that combine in phase and correlated out of phase oscillations along the chain. The complex relaxation dynamics is based on finite size effects together with an evolution running from the nonlinear to the linear regime, thereby providing a highly unbalanced population of the center-of-mass and relative motion.

We investigate the quantum mechanics of a single particle constrained to move along an arbitrary smooth reference curve by a confinement that is allowed to vary along the waveguide. The Schrödinger equation is evaluated in the adapted coordinate frame and a transverse-mode decomposition is performed, taking into account both curvature and torsion effects and the possibility of a cross-section potential that changes along the curve in an arbitrary way. We discuss the adiabatic structure of the problem, and examine nonadiabatic couplings that arise due to the curved geometry, the varying transverse profile, and their interplay. The exact multimode matrix Hamiltonian is taken as the natural starting point for few-mode approximations. Such approximate equations are provided, and it is worked out how these recover known results for twisting waveguides and can be applied to other types of waveguide designs. The quantum waveguide Hamiltonian is recast into a form that clearly illustrates how it generalizes the Born-Oppenheimer Hamiltonian encountered in molecular physics. In analogy to the latter, we explore the local gauge structure inherent to the quantum waveguide problem and suggest the usefulness of diabatic states, giving an explicit construction of the adiabatic-to-diabatic basis transformation.

We explore an analogue of optical frequency combs in driven nonlinear phononic systems, and present a mechanism for generating phononic frequency combs through nonlinear resonances. In the underlying process, a set of phonon modes is simultaneously excited by the external driving which yields frequency combs with an array of discrete and equidistant spectral lines of each nonlinearly excited phonon mode. Frequency combs through nonlinear resonance of different orders are investigated, and in particular the possibility of correlation tailoring in higher-order cases is revealed. We suggest that our results can be applied in various nonlinear acoustic processes, such as phonon harvesting, and can also be generalized to other nonlinear systems.

Cross-correlations are thought to emerge through interaction between particles. Here we present a universal dynamical mechanism capable of generating power-law cross-correlations between non-interacting particles exposed to an external potential. This phenomenon can occur as an ensemble property when the external potential induces intermittent dynamics of Pomeau-Manneville type, providing laminar and stochastic phases of motion in a system with a large number of particles. In this case, the ensemble of particle-trajectories forms a random fractal in time. The underlying statistical self-similarity is the origin of the observed power-law cross-correlations. Furthermore, we have strong indications that a sufficient condition for the emergence of these long-range cross-correlations is the divergence of the mean residence time in the laminar phase of the single particle motion (sporadic dynamics). We argue that the proposed mechanism may be relevant for the occurrence of collective behaviour in critical systems.

We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion; i.e., we observe the counterintuitive phenomenon that disorder leads to regular behavior. If the disorder is localized in a finite-sized part of the lattice, the described hopping causes initially diffusive particles to even accumulate in regular structures of the corresponding phase space. A hallmark of this accumulation is the emergence of pronounced peaks in the velocity distribution of particles that should be detectable in state of the art experiments, e.g., with cold atoms in optical lattices.

We discuss how continuous probing of a quantum system allows estimation of unknown classical parameters embodied in the Hamiltonian of the system. We generalize the stochastic master equation associated with continuous observation processes to a Bayesian filter equation for the probability distribution of the desired parameters, and we illustrate its application by estimating the direction of a magnetic field. In our example, the field causes a ground state spin precession in a two-level atom which is detected by the polarization rotation of off-resonant optical probes, interacting with the atomic spin components.

We study experimentally and theoretically the dynamics of apparent dark soliton stripes in an elongated Bose-Einstein condensate. We show that for the trapping strengths corresponding to our experimental setup, the transverse confinement along one of the tight directions is not strong enough to arrest the formation of solitonic vortices or vortex rings. These solitonic vortices and vortex rings, when integrated along the transverse direction, appear as dark soliton stripes along the longitudinal direction thereby hiding their true character. The latter significantly modifies the interaction dynamics during collision events and can lead to apparent examples of inelasticity and what may appear experimentally even as a merger of two dark soliton stripes. We explain this feature by means of the interaction of two solitonic vortices leading to a sling shot event with one of the solitonic vortices being ejected at a relatively large speed. Furthermore we observe expanding collision bubbles which consist of repeated inelastic collisions of a dark soliton stripe pair with an increasing time interval between collisions.

We develop a nonperturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory and allows us to include accurately long-range anisotropic interactions. For ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization of, e.g., Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases.

Following a “bottom-up approach” in understanding many-particle effects and dynamics we provide a systematic ab initio study of the dependence of the breathing dynamics of ultracold bosons in a one-dimensional (1D) harmonic trap on the number of bosons ranging from few to many. To this end, we employ the multilayer multiconfiguration time-dependent Hartree method for bosons (ML-MCTDHB) which has been developed very recently [ Krönke, Cao, Vendrell and Schmelcher New J. Phys. 15 063018 (2013)]. The beating behavior for two bosons is found numerically and consequently explained by an analytical approach. Drawing on this, we show how to compute the complete breathing mode spectrum in this case. We examine how the two-mode breathing behavior of two bosons evolves to the single-frequency behavior of the many-particle limit when adding more particles. In the limit of many particles, we numerically study the dependence of the breathing mode frequency on both the interaction strength as well as on the particle number. We provide an estimate for the parameter region where the mean-field description provides a valid approximation.

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case, bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincaré surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.

We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.

We develop a classification of perfectly transmitting resonances occurring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield piecewise translation-invariant quantities, which are used to distinguish resonances with arbitrary field profile from resonances following the medium symmetries. Focusing on light scattering in aperiodic multilayer structures, we demonstrate this classification for representative setups, providing insight into the origin of perfect transmission. We further show how local symmetries can be utilized for the design of optical devices with perfect transmission at prescribed energies. Providing a link between resonant scattering and local symmetries of the underlying medium, the proposed approach may contribute to the understanding of optical response in complex systems.

We propose and theoretically investigate a hybrid system composed of a crystal of trapped ions coupled to a cloud of ultracold fermions. The ions form a periodic lattice and induce a band structure in the atoms. This system combines the advantages of high fidelity operations and detection offered by trapped ion systems with ultracold atomic systems. It also features close analogies to natural solid-state systems, as the atomic degrees of freedom couple to phonons of the ion lattice, thereby emulating a solid-state system. Starting from the microscopic many-body Hamiltonian, we derive the low energy Hamiltonian, including the atomic band structure, and give an expression for the atom-phonon coupling. We discuss possible experimental implementations such as a Peierls-like transition into a period-doubled dimerized state.

We present three types of dark solitons in quasi–one-dimensional spin-orbit coupled repulsive Bose-Einstein condensates. Among these families, two are always stable, while the third one is only stable sufficiently close to the linear regime. The solitons' excitation spectra reveal the potential existence of a second anomalous mode. While the first such mode describes the soliton oscillatory motion in a parabolic trap, the second, when present, reflects the double-well structure of the underlying single-particle spectrum. This novel mode results in moving density stripes in the vicinity of the soliton core, or in an out-of-phase oscillation of the constituent components, with little effect on the nearly stationary striped total density of the composite soliton.

We investigate the impact of an electric field on the structure of ultra-long-range polar diatomic rubidium Rydberg molecules. Both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground-state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows shifting of the corresponding potential wells in such a manner that the importance of the p-wave interaction can be controlled and the individual wells are energetically lowered at different rates. As a consequence the equilibrium configuration and corresponding energetically lowest well move to larger internuclear distances for increasing field strength. For strong fields the admixture of nonpolar molecular Rydberg states leads to the possibility of exciting the large angular momentum polar states via two-photon processes from the ground state of the atom. The resulting properties of the electric dipole moment and the vibrational spectra are analyzed with varying field strength.

Dynamical focusing of ensembles of neutral particles in energy and configuration space has been demonstrated recently (Petri et al. in Phys. Rev. E (R) 82:035204, 2010) using time-dependent elliptical billiards. The interplay of nonlinearity, dissipation, and driving yields the occurrence of attractors in the phase space of the billiard. Here, we show that dissipative oval billiards with slowly oscillating elliptical scatterers in the interior allow for a dynamical focusing on simple periodic trajectories with close to perfect efficiency. This setup should be more amenable to corresponding experiments of certain type which are briefly discussed.

We develop and apply the multi-layer multi-configuration time-dependent Hartree method for bosons, which represents an ab initio method for investigating the non-equilibrium quantum dynamics of multi-species bosonic systems. Its multi-layer feature allows for tailoring the wave function ansatz to describe intra- and inter-species correlations accurately and efficiently. To demonstrate the beneficial scaling and efficiency of the method, we explored the correlated tunneling dynamics of two species with repulsive intra- and inter-species interactions, to which a third species with vanishing intra-species interaction was weakly coupled. The population imbalances of the first two species can feature a temporal equilibration and their time evolution significantly depends on the coupling to the third species. Bosons of the first and second species exhibit a bunching tendency, whose strength can be influenced by their coupling to the third species.

We present a theoretical study of the impact of an electric field combined with a magnetic field on the rotational dynamics of open-shell diatomic molecules. Within the rigid rotor approximation, we solve the time-independent Schrödinger equation including the fine-structure interactions and the Λ-doubling effects. We consider three sets of molecule-specific parameters and several field regimes and investigate the interplay between the different interactions identifying the dominant one. The possibility of inducing couplings between the spin and rotational degrees of freedom is demonstrated.

Employing Monte Carlo simulation techniques we investigate the statistical properties of equally charged particles confined in a one-dimensional box trap and detect a crossover from a crystalline to a cluster phase with increasing temperature. The corresponding transition temperature depends separately on the number of particles N and the box size L, implying nonextensivity due to the long-range character of the interactions. The probability density of the spacing between the particles exhibits at low temperatures an accumulation of discrete peaks with an overall asymmetric shape. In the vicinity of the transition temperature it is of a Gaussian form, whereas in the high-temperature regime an exponential decay is observed. The high-temperature behavior shows a cluster phase with a mean cluster size that first increases with the temperature and then saturates. The crossover is clearly identifiable also in the nonlinear behavior of the heat capacity with varying temperature. The influence of the trapping potential on the observed results as well as possible experimental realizations are briefly addressed.

We investigate the ground state properties and tunnelling dynamics of ultracold dipolar bosons in a one-dimensional triple-well trap from a few-body ab initio perspective. Our focus is primarily on the distinctive features of dipolar bosons compared to the contact interacting bosons. The formation of intra-well localization is observed for a very strong dipolar interaction. General population rearrangement as well as fragmentation and localization effects has been found, depending strongly on the particle number. The energy spectrum for two particles exhibits avoided crossings that lead to several distinct resonances involving different bands, i.e. to an inter-band resonant tunnelling dynamics. The corresponding mechanisms are investigated by studying the pair probability and performing an eigenstate analysis.

We introduce the concept of parity symmetry in restricted spatial domains—local parity—and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown that, in each domain of local parity symmetry of the potential, there exists an invariant quantity in the form of a nonlocal current, in addition to the globally invariant probability current. For symmetrically incoming states, both invariant currents vanish if weak commutation of the total local parity operator with the Hamiltonian is established, leading to local parity eigenstates. For asymmetrically incoming states which resonate within locally symmetric potential units, the complete local parity symmetry of the probability density is shown to be necessary and sufficient for the occurrence of perfect transmission. We connect the presence of local parity symmetries on different spatial scales to the occurrence of multiple perfectly transmitting resonances, and we propose a construction scheme for the design of resonant transparent aperiodic potentials. Our findings are illustrated through application to the analytically tractable case of piecewise constant potentials.

We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [ I. Brouzos and P. Schmelcher Phys. Rev. Lett. 108 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [ G. Zürn et al. Phys. Rev. Lett. 108 075303 (2012)].

We study the crossover of a finite one-dimensional bosonic ensemble from weak to strong interactions in harmonic traps and multi-well potentials. We perform diffusion quantum Monte Carlo calculations which we show to be in good agreement with results from analytical functions that we construct to describe these systems. For the harmonic trap, we use the correlated-pair wavefunction which we introduced in Brouzos and Schmelcher (2012 Phys. Rev. Lett. 108 045301) considering here much larger atom numbers, going beyond the few body ensembles studied in our previous work. We also investigate double and triple wells, changing correspondingly the uncorrelated part of the ansatz to describe efficiently the single-particle behaviour. On-site effects beyond mean-field and standard Bose–Hubbard calculations that appear in densities being captured by our analytical functions are explored.

A Fermi golden rule for population transfer between instantaneous eigenstates of elliptical quantum billiards with oscillating boundaries is derived. Thereby the occurrence of both the recently observed resonant population transfer between instantaneous eigenstates and the empirical criterion stating that these transitions occur when the driving frequency matches the mean difference of the latter [ Lenz et al. New J. Phys. 13 103019 (2011)] is explained. As a second main result a criterion judging which resonances are resolvable in a corresponding experiment of certain duration is provided. Our analysis is complemented by numerical simulations for three different driving laws. The corresponding resonance spectra are in agreement with the predictions of both criteria.

We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [ Phys. Rev. A 79 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of s-, d-, and g-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of s-wave resonant scattering.

An analytical study of discrete and resonant impurity quasi-Coulomb states in a narrow gapped armchair graphene nanoribbon (GNR) is performed. We employ the adiabatic approximation assuming that the motions parallel (“slow”) and perpendicular (“fast”) to the boundaries of the ribbon are separated adiabatically. The energy spectrum comprises a sequence of series of quasi-Rydberg levels relevant to the slow motion adjacent from the low energies to the size-quantized levels associated with the fast motion. Only the series attributed to the ground size-quantized subband is really discrete, while others corresponding to the excited subbands consist of quasidiscrete (Fano resonant) levels of nonzero energetic widths, caused by the coupling with the states of the continuous spectrum branching from the low lying subbands. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron is derived in an explicit form. Narrowing the GNR leads to an increase of the binding energy and the resonant width both induced by the finite width of the ribbon. Displacing the impurity center from the midpoint of the GNR causes the binding energy to decrease, while the resonant width of the first excited Rydberg series increases. As for the second excited series, their widths become narrower with the shift of the impurity. A successful comparison of our analytical results with those obtained by other theoretical and experimental methods is presented. Estimates of the binding energies and the resonant widths taken for the parameters of typical GNRs show that not only the strictly discrete but also some resonant states are quite stable and could be studied experimentally in doped GNRs.

The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wave function between the two vortex “wells.” We interpret this phenomenon by virtue of a vortex-induced double-well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition to the symmetric and antisymmetric ones. The theoretical prediction of these states is corroborated by detailed numerical computations.

Long-range interactions are shown to cause, as time evolves, consecutive reversals of directed currents for dilute ensembles of particles in driven lattices. These current reversals are based on a general mechanism that leads to an interaction-induced accumulation of particles in the regular regions of the underlying single-particle phase space and to a synchronized single-particle motion as well as enhanced efficiency of Hamiltonian ratchets. Suggestions for experimental implementations using ionized mesoscopic clusters in micromechanical lattices or dipolarly interacting colloidal particles in ac-driven optical lattices are provided.

A semianalytical approach to atomic waveguide scattering for harmonic confinement is developed, taking into account all partial waves. As a consequence ℓ-wave confinement-induced resonances are formed, being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the K-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.

We demonstrate the emergence of criticality due to power-law cross correlations in an ensemble of noninteracting particles propagating in an infinite Lorentz channel. The origin of these interparticle long-range correlations is the intermittent dynamics associated with the ballistic corridors in the single particle phase space. This behavior persists dynamically, even in the presence of external driving, provided that the billiard’s horizon becomes infinite at certain times. For the driven system, we show that Fermi acceleration permits the synchronization of the particle motion with the periodic appearance of the ballistic corridors. The particle ensemble then acquires characteristics of self-organization as the weight of the phase space regions leading to critical behavior increases with time.

We investigate the tunneling properties of a two-species few-boson mixture in a one-dimensional triple well and harmonic trap. The mixture is prepared in an initial state with a strong spatial correlation for one species and complete localization of the other species. We observe a correlation-induced tunneling process in the weak interspecies interaction regime. The onset of the interspecies interaction disturbs the spatial correlations of one species and induces a tunneling process between the correlated wells. The corresponding tunneling properties can be controlled by the spatial correlations with an underlying mechanism that is inherently different from the well-known resonant tunneling process. We also observe and analyze the correlated tunneling of both species in the intermediate interspecies interaction regime and the tunneling via higher band states for strong interactions.

Strong electric and magnetic fields tend to have opposite effects on the formation and structure of molecules. Strong electric fields always tend to separate the oppositely charged particles (electrons and nuclei), which causes molecules to ionize and dissociate. However, for strong homogeneous and static magnetic fields, binding can be strengthened. For hydrogen, the simplest atom, a certain class of its quantum states, including the ground state, becomes increasingly bound with increasing magnetic field strength (1–3). The electronic cloud shrinks transverse to the magnetic field, and because of the immediate proximity of the attractive nucleus, the overall energy decreases. This feature transfers to diatomic and linear-chain molecules, where the chemical binding energy increases and the corresponding bond distances decrease. The field strengths needed are far beyond the strongest available in the laboratory (30 to 40 T) but can be encountered in the atmospheres of magnetic white dwarfs (102 to 105 T) and neutron stars (>107 T). On page 327 of this issue, Lange et al. (4) show that, in addition to this diamagnetic enhanced binding, there exists an elementary paramagnetic bonding mechanism that occurs for the perpendicular orientation of a diatomic molecule with respect to the external magnetic field.

We explore the nonequilibrium dynamics of noninteracting classical particles in a one-dimensional driven superlattice which is composed of domains exposed to different time-dependent forces. It is shown how the combination of directed transport and conversion processes from diffusive to ballistic motion causes strong correlations between velocity and phase for particles passing through a superlattice. A detailed understanding of the underlying mechanism allows us to tune the resulting velocity distributions at distinguished points in the superlattice by means of local variations of the applied driving force. As an intriguing application we present a scheme how initially diffusive particles can be transformed into a monoenergetic pulsed particle beam whose parameters such as its energy can be varied.

A field-theoretical approach to the scattering off an oscillating quantum system is developed. As a key ingredient it employs the adiabatic eigenstate basis and consists of a perturbative scheme for the calculation of the geometric phases influencing the transmission through the time-dependent potential landscape. The main advantage is the identification of basic diagrams which allow for an immediate interpretation of the underlying elementary physical processes contributing to the scattering and transmission behavior. We apply our method to the simple, but prototypical, problem of transmission through an one-dimensional oscillating δ potential and demonstrate how it enables a deeper understanding of the relevant physical processes.

We investigate static properties of laser-driven ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains, and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser-detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and are discussed.

We theoretically explore the external electric field control of a species of ultralong-range molecules that emerge from the interaction of a ground-state polar molecule with a Rydberg atom. The external field mixes the Rydberg electronic states and, therefore, strongly alters the electric field seen by the polar diatomic molecule due to the Rydberg electron. As a consequence, the adiabatic potential energy curves responsible for the molecular binding can be tuned in such a way that an intersection with neighboring curves occurs. The latter leads to admixture of s-wave character in the Rydberg wave function and will substantially facilitate the experimental preparation and realization of this particular class of Rydberg molecule species.

We analyze d-wave resonances in atom-atom scattering in the presence of harmonic confinement by employing a higher-partial-wave pseudopotential. Analytical results for the scattering amplitude and transmission are obtained and compared to corresponding numerical ones, which employ the Lennard-Jones potential. Qualitative agreement is observed for weak confinement. For strong confinement the pseudopotential does not capture the s- and d-wave interference phenomena, yielding an asymmetric Fano profile for the transmission resonance.

We investigate the excitation properties of finite ultracold bosonic systems in a one-dimensional harmonic trap with a time-dependent interaction strength. The driving of the interatomic coupling induces excitations of the relative motion exclusively with specific and controllable contributions of momentarily excited many-body states. Mechanisms for selective excitation to few-body analogs of collective modes and acceleration occur in the vicinity of resonances. Via the few-body spectrum and a Floquet analysis, we study the excitation mechanisms and the corresponding impact of the driving frequency and strength as well as the initial correlation of the bosonic state. The fundamental case of two atoms is analyzed in detail and forms a key ingredient for the bottom-up understanding of cases with higher atom numbers, thereby examining finite-size corrections to macroscopic collective modes of oscillation.

We study vortex excitations in one-component Bose-Einstein condensates, with a special emphasis on the role of anisotropic confinement for the existence, stability and dynamical properties of vortices and particularly few-vortex clusters. Symmetry breaking features are pervasive within this system even in its isotropic installment, where cascades of symmetry breaking bifurcations give rise to the multi-vortex clusters, but also within the anisotropic realm which naturally breaks the rotational symmetry of the multi-vortex states. Our first main tool for analyzing the system consists of a weakly nonlinear (bifurcation) approach which starts from the linear states of the problem and examines their continuation and bifurcation into novel symmetry-broken configurations in the nonlinear case. This is first done in the isotropic limit and the modifications introduced by the anisotropy are subsequently presented. The second main tool concerns the highly nonlinear regime where the vortices can be considered as individual topologically charged "particles" which precess within the parabolic trap and interact with each other, similarly to fluid vortices. The conclusions stemming from both the bifurcation and the interacting particle picture are corroborated by numerical computations which are also used to bridge the gap between these two opposite-end regimes.

We show the existence of ultra-long-range giant dipole molecules formed by a neutral alkali ground state atom that is bound to the decentered electronic wave function of a giant dipole atom. The adiabatic potential surfaces emerging from the interaction of the ground state atom with the giant dipole electron possess a rich topology depending on the degree of electronic excitation. Binding energies and the vibrational motion in the energetically lowest surfaces are analyzed by means of perturbation theory and exact diagonalization techniques. The resulting molecules are truly giant with internuclear distances up to several μm. Finally, we demonstrate the existence of intersection manifolds of excited electronic states that potentially lead to a vibrational decay of the ground state atom dynamics.

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.

Riesige homonukleare Moleküle können ein permanentes elektrisches Dipolmoment tragen.

We explore the tunneling dynamics of strongly correlated bosonic mixtures in a one-dimensional double well. The roles of the inter- and intraspecies interactions and their interplay are investigated using the numerically exact multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is studied for three initial configurations: complete and partial population imbalance and a species-separated state. Increasing the interspecies interaction leads to a strong increase of the tunneling time period analogous to the quantum self-trapping for condensates. The intraspecies repulsion can suppress or enhance the tunneling period depending on the strength of the interspecies correlations as well as the initial configuration. Completely correlated tunneling between the two species and within the same species as well as mechanisms of species separation and counterflow are revealed. These effects are explained by studying the few-body energy spectra as well as the properties of the contributing stationary states.

We analyze the spectrum of the three-site Bose-Hubbard model with periodic boundary conditions using a semiclassical method. The Bohr-Sommerfeld quantization is applied to an effective classical Hamiltonian which we derive using resonance normal form theory. The derivation takes into account the 1:1 resonance between frequencies of a linearized classical system and brings nonlinear terms into a corresponding normal form. The obtained expressions reproduce the exact low-energy spectrum of the system remarkably well even for a small number of particles N corresponding to fillings of just two particles per site. Such small fillings are often used in current experiments, and it is inspiring to get insight into this quantum regime using essentially classical calculations.

We discuss a candidate solution for the controlled trapping and manipulation of two individual Rydberg atoms by means of a magnetic Ioffe-Pritchard trap that is superimposed by a constant electric field. In such a trap Rydberg atoms experience a permanent electric dipole moment that can be of the order of several hundred debye. The interplay of electric dipolar repulsion and three-dimensional magnetic confinement leads to a well controllable equilibrium configuration with tunable trap frequency and atomic distance. We thoroughly investigate the trapping potentials and analyze the interaction-induced stabilization of two such trapped Rydberg atoms. Possible limitations and collapse scenarios are discussed.

Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton “molecules,” composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.

We analyze the impact of multichannel scattering in harmonic waveguides on the positions and widths of confinement-induced resonances for both isotropic and anisotropic transversal confinement. Multichannel scattering amplitudes and transmission coefficients are calculated and used to characterize the resonant behavior of atomic collisions with varying anisotropy. A mechanism is established which leads to a splitting of the confinement-induced resonance in the presence of anisotropy.

We analyze the quantum dynamics of the time-dependent elliptical billiard using the example of a certain breathing mode. A numerical method for the time propagation of an arbitrary initial state is developed based on a series of transformations, thereby removing the time dependence of the boundary conditions. The time evolution of the energies of different initial states is studied. The maximal and minimal energies that are reached during the time evolution show a series of resonances as a function of the applied driving frequency. At these resonances, higher (or lower) lying states are periodically populated, leading to the observed change in energy. The resonances occur when the driving frequency or a multiple of it matches the mean energetic difference between the two involved states exactly. This picture is confirmed by a few-level Rabi-like model with periodic couplings, reproducing the key results of our numerical study.

Recently, the occurrence of exponential Fermi acceleration (FA) has been reported in a rectangular billiard with an oscillating bar inside (Shah et al 2010 Phys. Rev. E 81 056205). In this paper, we analyze the underlying physical mechanism and show that the phenomenon can be understood as a sequence of highly correlated motions, consisting of alternating phases of free propagation and motion along the invariant spanning curves of the well-known one-dimensional Fermi–Ulam model. The key mechanism for the occurrence of exponential FA can be captured in a random walk model in velocity space with step width proportional to the velocity itself. The model reproduces the occurrence of exponential FA and provides a good ab initio prediction of the value of the growth rate, including its full parameter dependence. Our analysis clearly points out the requirements for exponential FA, thereby opening the prospect of finding other systems exhibiting this unusual behavior.

he internal electric field of a Rydberg atom electron can bind a polar molecule to form a giant ultralong-range stable polyatomic molecule. Such molecules not only share their properties with Rydberg atoms (such as long lifetimes and large sizes) but they also possess huge permanent electric dipole moments and in addition allow for coherent control of the polar molecule orientation. In this work, we include additional Rydberg manifolds which couple to the nearly degenerate set of Rydberg states employed in the previous work (S T Rittenhouse and H R Sadeghpour 2010 Phys. Rev. Lett. 104 243002). The coupling of a set of (n + 3)s Rydberg states with the n(l > 2) nearly degenerate Rydberg manifolds in alkali metal atoms leads to pronounced avoided crossings in the Born–Oppenheimer potentials. Ultimately, these avoided crossings enable the formation of the giant polyatomic Rydberg molecules with standard two-photon laser photoassociation techniques.

We investigate the spectral properties of a finite laser-driven lattice of ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with variable spacings are considered. In the case of a weak laser coupling, we find a multitude of many-body Rydberg states with well-defined excitation properties which are adiabatically accessible starting from the ground state. A comprehensive analysis of the degeneracies of the spectrum as well as of the single- and pair-excitation numbers of the eigenstates is performed. In the strong laser regime, analytical solutions for the pseudo-fermionic eigenmodes are derived. Perturbative energy corrections for this approximative approach are provided.

We study dark–bright (DB) ring solitons in two-component Bose–Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, 'filling' species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of DB soliton stripes and vortex-bright soliton clusters from the DB ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that the stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like DB soliton configuration.

We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience a force which is oscillating with the distance between the particles. This leads to stable equilibrium configurations and correspondingly induced bound states whose number is tunable with the parameters of the helix. We demonstrate the existence of a plethora of equilibria of few-body chains with different symmetry character that are allowed to freely move. An outline concerning the implications on many-body helical chains is provided.

We examine the impact of the combination of a static electric field and a non-resonant linearly polarized laser field on an asymmetric top molecule. Within the rigid rotor approximation, we analyze the symmetries of the Hamiltonian for all possible field configurations. For each irreducible representation, the Schrödinger equation is solved by a basis set expansion in terms of a linear combination of symmetric top eigenfunctions respecting the corresponding symmetries, which allows us to distinguish avoided crossings from genuine ones. Using the fluorobenzene and pyridazine molecules as prototypes, the rotational spectra and properties are analyzed for experimentally accessible static field strengths and laser intensities. Results for energy shifts, orientation, alignment, and hybridization of the angular motion are presented as the field parameters are varied. We demonstrate that a proper selection of the fields gives rise to a constrained rotational motion in three Euler angles, the wave function being oriented along the electrostatic field direction, and aligned in other two angles.

We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a possibility for studying strongly correlated atomic systems beyond s-wave physics.

Motivated by recent experiments studying the dynamics of configurations bearing a small number of vortices in atomic Bose-Einstein condensates (BECs), we illustrate that such systems can be accurately described by ordinary differential equations (ODEs) incorporating the precession and interaction dynamics of vortices in harmonic traps. This dynamics is tackled in detail at the ODE level, both for the simpler case of equal charge vortices, and for the more complicated (yet also experimentally relevant) case of opposite charge vortices. In the former case, we identify the dynamics as being chiefly quasi-periodic (although potentially periodic), while in the latter, irregular dynamics may ensue when suitable external drive of the BEC cloud is also considered. Our analytical findings are corroborated by numerical computations of the reduced ODE system.

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose–Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.

We propose a method for the determination of the interaction potential of Rydberg atoms. Specifically, we consider a laser-driven Rydberg gas confined in a one-dimensional lattice and demonstrate that the Rydberg atom number after a laser excitation cycle as a function of the laser detuning provides a measure for the Rydberg interaction coefficient. With the lattice spacing precisely known, the proposed scheme only relies on the measurement of the number of Rydberg atoms and thus circumvents the necessity to map the interaction potential by varying the interparticle separation.

We explore the photodissociation of polar diatomic molecules in static electric fields in the rotationally cold regime using the example of the LiCs molecule. A giant enhancement of the differential cross section is found for laboratory electric field strengths, and analyzed with varying rovibrational bound states, continuum energies as well as field strengths.

A quantized vortex dipole is the simplest vortex molecule, comprising two countercirculating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasiperiodic behavior, in which the vortex lines undergo stable epicyclic orbits.

We develop a mechanism for the controlled conversion of ballistic to diffusive motion and vice versa. This process takes place at the interfaces of domains with different time-dependent forces in lattices of laterally oscillating barrier potentials. As a consequence, long-time transient oscillations of the particle density are formed, which can be converted to permanent density waves by an appropriate tuning of the driving forces. The proposed mechanism opens the perspective of an engineering of the nonequilibrium dynamics of particles in inhomogeneously driven lattices.

We present a theoretical study of recent laser-alignment and mixed-field-orientation experiments of asymmetric top molecules. In these experiments, pendular states were created using linearly polarized strong ac electric fields from pulsed lasers in combination with weak electrostatic fields. We compare the outcome of our calculations with experimental results obtained for the prototypical large molecule benzonitrile (C7H5N) [J. L. Hansen et al., Phys. Rev. A, 2011, 83, 023406.] and explore the directional properties of the molecular ensemble for several field configurations, i.e., for various field strengths and angles between ac and dc fields. For perpendicular fields one obtains pure alignment, which is well reproduced by the simulations. For tilted fields, we show that a fully adiabatic description of the process does not reproduce the experimentally observed orientation, and it is mandatory to use a diabatic model for population transfer between rotational states. We develop such a model and compare its outcome to the experimental data confirming the importance of non-adiabatic processes in the field-dressed molecular dynamics.

We study the existence and stability properties of clusters of alternating charge vortices in repulsive Bose–Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well. We also explore the evolution of unstable states and their transient dynamics exploring configurations of nearby bifurcation branches.

By exploring the four-terminal transmission of a semielliptic open quantum billiard in dependence of its geometry and an applied magnetic field, it is shown that a controllable switching of currents between the four terminals can be obtained. Depending on the eccentricity of the semiellipse and the width and placement of the leads, high transmittivity at zero magnetic field is reached either through states guided along the curved boundary or focused onto the straight boundary of the billiard. For small eccentricity, attachment of leads at the ellipse foci can yield optimized corresponding transmission, while departures from this behavior demonstrate the inapplicability of solely classical considerations in the deep quantum regime. The geometrically determined transmission is altered by the phase-modulating and deflecting effect of the magnetic field, which switches the pairs of leads connected by high transmittivity. It is shown that the elliptic boundary is responsible for these very special transport properties. At higher field strengths edge states form and the multiterminal transmission coefficients are determined by the topology of the billiard. The combination of magnetotransport with geometrically optimized transmission behavior leads to an efficient control of the current through the multiterminal structure.

We present and analyze mechanisms for the patterned deposition of particles in a spatio-temporally driven lattice. The working principle is based on the breaking of the spatio-temporal translation symmetry, which is responsible for the equivalence of all lattice sites, by applying modulated phase shifts to the lattice sites. The patterned trapping of the particles occurs in confined chaotic seas, created via the ramping of the height of the lattice potential. Complex density profiles on the length scale of the complete lattice can be obtained by a quasi-continuous, spatial deformation of the chaotic sea in a frequency modulated lattice.

We study the tunneling of a small ensemble of strongly repulsive bosons in a one-dimensional (1D) triple-well potential. The usual treatment within the single-band approximation suggests a suppression of tunneling in the strong-interaction regime. However, we show that several windows of enhanced tunneling are opened in this regime. This enhanced tunneling results from higher band contributions, and has the character of interband tunneling. It can give rise to various tunneling processes, such as single-boson tunneling and two-boson correlated tunneling of the ensemble of bosons, and is robust against deformations of the triple-well potential. We introduce a basis of generalized number states, including all contributing bands, to explain the interband tunneling, and demonstrate various processes of interband tunneling and its robustness by numerically exact calculation.

We investigate the effects of anisotropy on the stability and dynamics of vortex cluster states which arise in Bose-Einstein condensates. Sufficiently strong anisotropies are shown to stabilize states with arbitrary numbers of vortices that are highly unstable in the isotropic limit. Conversely, anisotropy can be used to destabilize states which are stable in the isotropic limit. Near the linear limit, we identify the bifurcations of vortex states including their emergence from linear eigenstates, while in the strongly nonlinear limit, a particle-like description of the dynamics of the vortices in the anisotropic trap is developed. Both are in very good agreement with numerical results. Collective modes of stabilized many vortex cluster states are demonstrated.

We explore the non-equilibrium escape dynamics of long-range interacting ions in one-dimensional traps. The phase space of the few ion setup and its impact on the escape properties are studied. As the main result, we show that an instantaneous reduction of the trap's potential depth leads to the synchronized emission of a sequence of ion pairs if the initial configurations are close to the crystalline ionic configuration. The corresponding time intervals of the consecutive pair emission as well as the number of emitted pairs can be tuned by changing the final trap depth. Correlations between the escape times and kinetic energies of the ions are observed and analyzed.

We explore the stability and dynamics of dark-bright solitons in two-component elongated Bose-Einstein condensates by developing effective 1D vector equations as well as solving the corresponding 3D Gross-Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the dark-bright (DB) soliton on the atom number of its components is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom for a large occupation of the component supporting the dark soliton. Moreover, the interactions of two DB solitons are investigated with special emphasis on the importance of their relative phases. Experimental results showcasing dark-bright soliton dynamics and collisions in a BEC consisting of two hyperfine states of $^{87}$Rb confined in an elongated optical dipole trap are presented.

An analytical approach to the problem of the fundamental and exciton magnetoelectroabsorption in a narrow quantum well (QW) is developed. The external magnetic and electric fields are parallel and both tilted with respect to the QW growth axis. The width of the QW is taken to be much less than the magnetic length and the exciton Bohr radius. The effect of the electric field on size quantized states reduces to the size-quantized Stark shift of the well subbands. Analytical dependencies of the coefficient of the optical absorption and the exciton binding energy on the strengths of the external fields, width of the QW, exciton parameters and tilt angle are obtained and discussed. Novel effects forbidden in bulk material are found to occur. These are based on the interplay between the parallel magnetic and electric fields which in turn is caused by the splitting of the tilted fields into transverse and longitudinal components. In particular, an inversion effect is revealed. Estimates of the expected experimental values are provided for GaAs/AlGaAs QW.

We study few-boson tunneling in a one-dimensional double well with a spatially modulated interaction. The dynamics changes from Rabi oscillations in the noninteracting case to a highly suppressed tunneling for intermediate coupling strengths followed by a reappearance near the fermionization limit. With extreme interaction inhomogeneity in the regime of strong correlations, we observe tunneling between the higher bands. The dynamics is explained on the basis of the few-body spectrum and stationary eigenstates. For a higher number of particles N⩾3, it is shown that the inhomogeneity of the interaction can be tuned to generate tunneling resonances. Finally, a tilted double well and its interplay with the interaction asymmetry are discussed.

We develop and analyze a scheme to achieve both spatial and energetic focusing of an ensemble of neutral particles which is based on an oscillating billiard with frictional forces. The interplay of two competing mechanisms, acceleration due to collisions with the oscillating billiard walls and deceleration caused by friction, leads to the emergence of attractors in phase space. Their specific properties, i.e., spatial localization and energy spread, can be controlled and tuned by varying, e.g., the frequency of the time-dependent billiard.

In the present work, we offer a unifying perspective between the dark soliton stripe and the vortex multipole (dipole, tripole, aligned quadrupole, quintopole, etc.) states that emerge in the context of quasi-two-dimensional Bose-Einstein condensates. In particular, we illustrate that the multivortex states with the vortices aligned along the (former) dark soliton stripe sequentially bifurcate from the latter state in a supercritical pitchfork manner. Each additional bifurcation adds an extra mode to the dark soliton instability and an extra vortex to the configuration; moreover, the bifurcating states inherit the stability properties of the soliton prior to the bifurcation. The critical points of this bifurcation are computed analytically via a few-mode truncation of the system, which clearly showcases the symmetry-breaking nature of the corresponding bifurcation. We complement this small(-er) amplitude, few mode bifurcation picture, with a larger amplitude, particle-based description of the ensuing vortices. The latter enables us to characterize the equilibrium position of the vortices, as well as their intrinsic dynamics and anomalous modes, thus providing a qualitative description of the nonequilibrium multivortex dynamics.

In this work, the spectral properties of a singly charged vortex in a Bose–Einstein condensate confined in a highly anisotropic (disc-shaped) harmonic trap are investigated. Special emphasis is placed on the analysis of the so-called anomalous (negative energy) mode of the Bogoliubov spectrum. We use analytical and numerical techniques to illustrate the connection of the anomalous mode to the precession dynamics of the vortex in the trap. Effects due to inhomogeneous interatomic interactions and dissipative perturbations motivated by finite-temperature considerations are explored. We find that both of these effects may give rise to oscillatory instabilities of the vortex, which are suitably diagnosed through the perturbation-induced evolution of the anomalous mode, and monitored by direct numerical simulations.

We demonstrated very recently [Lenz et al., New J. Phys. 11, 083035 (2009)] that an ensemble of particles in the driven elliptical billiard shows a surprising crossover from subdiffusion to normal diffusion in momentum space. This crossover is not parameter induced, but rather occurs dynamically in the evolution of the ensemble. In this work, we consider three different driving modes of the elliptical billiard and perform a comprehensive analysis of the corresponding four-dimensional phase space. The composition of this phase space is different in the high-velocity regime compared to the low-velocity regime. We will show, among others, by investigating periodic orbits and probability distributions of laminar phases that the stickiness properties, which eventually determine the diffusion, are intimately connected with this change in the composition of the phase space with respect to velocity. In the course of the evolution, the accelerating ensemble thus explores regions of varying stickiness, leading to the mentioned crossover in the diffusion.

We explore how the extraordinary properties of Rydberg atoms can be employed to impact the motion of ultracold ground state atoms. Specifically, we use an off-resonant two-photon laser dressing to map features of the Rydberg states on ground state atoms. It is demonstrated that the interplay between the spatially varying quantization axis of the considered Ioffe–Pritchard field and the fixed polarizations of the laser transitions provides the possibility of substantially manipulating the ground state trapping potential.

We present all-electron relativistic studies of the polarizability properties of the Xe dimer. The studies rely on finite-field calculations of the dimer energies obtained by ab initio methods including electron correlations. An extended set of basis functions is designed in order to ensure a high accuracy of the calculations. Particular attention is paid to the analysis of the nonadditivity and anisotropy of the polarizability of the dimer. It is found that the polarizability of the dimer relative to that of the atoms can be accurately described analytically, at least for internuclear distances around and larger than the equilibrium distance of the dimer.

We investigate the quantum transmission through laterally driven single- and double-barrier systems in the nonlinear regime of strong driving. A broad parameter range is explored, distinguishing in particular between different frequency regimes. The applicability of an effective, time independent, potential description in the high-frequency regime is explored. Moreover, we analyze in detail the inelastic processes and their dependence on parameters, resonant tunneling, and photon assisted tunneling. For the single-barrier problem we address driving laws that differ from the purely sinusoidal one. In this context, we encounter reduced spatial and temporal symmetries and demonstrate the corresponding effects on quantum pumping. For the double barrier, the focus of our studies lies on the impact of the variation in the relative phase of the barriers on the transmission.

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a noncubic nonlinearity, appropriate to describe the dimensionality crossover regime from one- to three-dimensional, we obtain branches of solutions in the form of single and multiple dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons’ equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double-well setting, which may lead to instabilities or decouple multiple dark soliton states.

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a noncubic nonlinearity, appropriate to describe the dimensionality crossover regime from one- to three-dimensional, we obtain branches of solutions in the form of single and multiple dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons’ equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double-well setting, which may lead to instabilities or decouple multiple dark soliton states.

We utilize the combination of two standard trapping techniques, a magnetic trap and an optical trap in a Raman setup, to propose a versatile and tunable trap for cold atoms. The created potential provides several advantages over conventional trapping potentials. One can easily convert the type of the trap, for example, from a single-well to a double-well trap. Atoms in different internal states can be trapped in different trap types, thereby enabling the realization of experiments with multicomponent Bose-Einstein condensates. Moreover, one can achieve variations of the trapping potential on small length scales without the need of microstructures. We present the potential surfaces for different setups, demonstrate their tunability, give a semianalytical expression for the potential, and propose experiments which can be realized within such a trap.

We explore the dynamics of noninteracting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed.

We report on the observation of confinement-induced resonances in strongly interacting quantum-gas systems with tunable interactions for one- and two-dimensional geometry. Atom-atom scattering is substantially modified when the s-wave scattering length approaches the length scale associated with the tight transversal confinement, leading to characteristic loss and heating signatures. Upon introducing an anisotropy for the transversal confinement we observe a splitting of the confinement-induced resonance. With increasing anisotropy additional resonances appear. In the limit of a two-dimensional system we find that one resonance persists.

We study the ground-state properties and quantum dynamics of few-boson mixtures with strong interspecies repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter, and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intraspecies repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the back action of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: by varying the degree of localization of the “barrier” atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons), this leads to the tunneling of attractively bound pairs.

We study the quantum dynamics of strongly interacting few-boson mixtures in one-dimensional traps. If one species is strongly localized compared to the other (e.g., much heavier), it can serve as an effective potential barrier for that mobile component. Near the limit of infinite localization, we map this to a system of identical bosons in a double well. For realistic localization, the backaction of the light species on the 'barrier' atoms is explained—to lowest order—in terms of an induced attraction between these. Even in equilibrium, this may outweigh the bare intra-species interaction, leading to unexpected correlated states. Remarkably, the backaction drastically affects the inter-species dynamics, such as the tunnelling of an attractively bound pair of fermionized atoms

We theoretically investigate the quantum properties of nS, nP, and nD Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to pointlike particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schrödinger equation. In addition to the electronic properties, the center-of-mass dynamics of trapped Rydberg atoms is studied. In particular, we analyze the influence of a short-time Rydberg excitation, as required by certain quantum-information protocols, on the center-of-mass dynamics of trapped ground-state atoms. A corresponding heating rate is derived and the implications for the purity of the density matrix of an encoded qubit are investigated.

We study the classical dynamics of a polar diatomic molecule in the presence of a strong static homogeneous electric field. Our full rovibrational investigation includes the interaction with the field due to the permanent electric dipole moment and the polarizability of the molecule. Using the LiCs molecule as a prototype, we explore the stability of the equilibrium points and their bifurcations as the field strength is increased. The phase space structure and its dependence on the energy and field strength are analyzed in detail. We demonstrate that depending on the field strength and on the energy, the phase space is characterized either by regular features or by small stochastic layers of chaotic motion.

Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases, consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms, such as giant dipole states, are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence the electronic structure of Rydberg atoms, and we describe the utility of corresponding effects for achieving tightly trapped ultracold Rydberg atoms. We review recent work on large, extended cold Rydberg gases in magnetic fields and their formation in strongly magnetized ultracold plasmas through collisional recombination. Implications of these results for current antihydrogen production experiments are pointed out, and techniques for the trapping and cooling of such atoms are investigated.

We perform the first long-time exploration of the classical dynamics of a driven billiard with a four-dimensional phase space. With increasing velocity of the ensemble, we observe an evolution from a large chaotic sea with stickiness due to regular islands to thin chaotic channels with diffusive motion leading to Fermi acceleration. As a surprising consequence, we encounter a crossover, which is not parameter induced but rather occurs dynamically, from amplitude-dependent tunable subdiffusion to universal normal diffusion in momentum space.

In this work, we consider quasi-one-dimensional Bose–Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double-well potentials. In particular, we study a setup in which such a “collisionally inhomogeneous” BEC has the same (attractive–attractive or repulsive–repulsive) or different (attractive–repulsive) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle–node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle–node tends to infinity and eventually only the two original branches remain, which is completely different from the standard double-well phenomenology. Finally, one of these branches changes its monotonicity as a function of the chemical potential, a feature especially prominent, when the sign of the nonlinearity changes between the two wells. Our theoretical predictions, are in excellent agreement with the numerical results.

We explore the quantum dynamics of heteronuclear atomic collisions in waveguides and demonstrate the existence of a novel mechanism for the resonant formation of polar molecules. The molecular formation probabilities can be tuned by changing the trap frequencies that characterize the transverse modes of the atomic species. The origin of this effect is the confinement-induced mixing of the relative and center of mass motions in the atomic collision process leading to a coupling of the diatomic continuum to the center of mass excited molecular states in closed transverse channels

We investigate the ground state of one-dimensional few-atom Bose–Bose mixtures under harmonic confinement throughout the crossover from weak to strong inter-species attraction. The calculations are based on the numerically exact multi-configurational time-dependent Hartree method. For repulsive components, we detail the condition for the formation of a molecular Tonks–Girardeau gas in the regime of intermediate inter-species interactions, and the formation of a molecular condensate for stronger coupling. Beyond a critical inter-species attraction, the system collapses to an overall bound state. Different pathways emerge for unequal particle numbers and intra-species interactions. In particular, for mixtures with one attractive component, this species can be viewed as an effective potential dimple in the trap center for the other, repulsive component

Employing oval-shaped quantum billiards connected by quantum wires as the building blocks of a linear quantum-dot array, we calculate the ballistic magnetoconductance in the linear-response regime. Optimizing the geometry of the billiards, we aim at a maximal finite over zero-field ratio of the magnetoconductance. This switching effect arises from a relative phase change in scattering states in the oval quantum dot through the applied magnetic field, which lifts a suppression of the transmission characteristic for a certain range of geometry parameters. It is shown that a sustainable switching ratio is reached for a very low-field strength, which is multiplied by connecting only a second dot to the single one. The impact of disorder is addressed in the form of remote impurity scattering, which poses a temperature-dependent lower bound for the switching ratio, showing that this effect should be readily observable in experiments.

We study the effect of a strong static homogeneous electric field on the highly excited rovibrational levels of the 7Li133Cs dimer in its electronic ground state. Our full rovibrational investigation of the system includes the interaction with the field due to the permanent electric dipole moment and the polarizability of the molecule. We explore the evolution of the states next to the dissociation threshold as the field strength is increased. The rotational and vibrational dynamics are influenced by the field; effects such as orientation, angular motion hybridization and squeezing of the vibrational motion are demonstrated and analyzed. The field also induces avoided crossings causing a strong mixing of the electrically dressed rovibrational states. Importantly, we show how some of these highly excited levels can be shifted to the continuum as the field strength is increased, and conversely how two atoms in the continuum can be brought into a bound state by lowering the electric field strength

By investigating the quantum properties of magnetically trapped nS1/2 Rydberg atoms, it is demonstrated that the composite nature of Rydberg atoms significantly alters their trapping properties opposed to pointlike particles with the same magnetic moment. We show how the specific signatures of the Rydberg trapping potential can be probed by means of ground-state atoms that are off-resonantly coupled to the Rydberg state via a two photon laser transition. In addition, it is demonstrated how this approach provides an alternative possibility of generating traps for ground-state atoms. Simulated time-of-flight pictures mirroring the experimental situation are provided.

We present an analytical investigation of quasi-one-dimensional excitons in thin uniform (single) and double nanoscaled cylindrical quantum wires (UQWR and DQWR) surrounded by a barrier of infinite height and exposed to external electric and strong magnetic fields. The DQWR is formed by inserting an impenetrable longitudinal barrier in a single-quantum wire. Both external fields are directed parallel to the quantum wire (QWR) axis. The radius of the QWRs and the magnetic length are taken to be much less than the exciton Bohr radius. For the dependencies of the positions and widths of the complex quasidiscrete energy levels of the indirect exciton in the DQWR, in which the carriers are separated by the insertion on the confinement, electric field strength and width of the interwire barrier are derived. The confinement (insertion) leads to an increase (decrease) of the exciton binding energy. The impact of the electric field ionization of the exciton is less pronounced for strongly confined and weakly separated carriers. The coefficient of the exciton absorption in the UQWR as a function of the confinement and electric field is calculated in an explicit form. The effect of the confinement and electric field on the exciton peak closely resembles that on the quasidiscrete level of the indirect exciton in the DQWR. Electron-hole attraction increases remarkably the optical Franz-Keldysh electroabsorption in the frequency region below the edge and distant from the exciton peaks. The coefficient of absorption reflecting the electric field ionization and autoionization caused by the coupling between the discrete and continuous exciton states adjacent to the different size-quantized or Landau levels is obtained analytically. A comparison of our analytical results with numerical data is performed. Estimates of the expected experimental values for the parameters of GaAs/GaAlAs QWR show that the autoionized exciton magnetostates in thin biased QWRs are sufficiently stable to be observed.

We study the flow of a spinor (F=1) Bose-Einstein condensate in the presence of an obstacle. We consider the cases of ferromagnetic and polar spin-dependent interactions, and find that the system demonstrates two speeds of sound that are identified analytically. Numerical simulations reveal the nucleation of macroscopic nonlinear structures, such as dark solitons and vortex-antivortex pairs, as well as vortex rings in one- and higher-dimensional settings, respectively, when a localized defect (e.g., a blue-detuned laser beam) is dragged through the spinor condensate at a speed larger than the second critical speed.

We examine ground state correlations for repulsive, quasi one-dimensional bosons in a harmonic trap. In particular, we focus on the few particle limit N=2, 3, 4, ..., where exact numerical solutions of the many particle Schrödinger equation are available, by employing the multi-configuration time-dependent Hartree method. Our numerical results for the inhomogeneous system are modeled with the analytical solution of the homogeneous problem using the Bethe ansatz and the local density approximation. Tuning the interaction strength from the weakly correlated Gross–Pitaevskii to the strongly correlated Tonks–Girardeau regime reveals finite particle number effects in the second-order correlation function beyond the local density approximation

We consider the statics and dynamics of F = 1 spinor Bose–Einstein condensates (BECs) confined in double-well potentials. We use a two-mode Galerkin-type quasi-analytical approximation to describe the stationary states of the system. This way, we are able to obtain not only earlier results based on the single-mode approximation (SMA) frequently used in studies of spinor BECs, but also additional modes that involve either two or all three spinor components of the F = 1 spinor BEC. The results based on this Galerkin-type decomposition are in good agreement with the analysis of the full system. We subsequently analyze the stability of these multi-component states, as well as their dynamics when we find them to be unstable. The instabilities of the symmetric or anti-symmetric states exhibit symmetry-breaking and recurrent asymmetric patterns. Our results yield qualitatively similar bifurcation diagrams both for polar (such as 23Na) and ferromagnetic (such as 87Rb) spinor BECs

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.

We demonstrate that atoms in magnetically insensitive hyperfine states (m=0) can be trapped efficiently by a Bose-Einstein Condensate of the same atomic species occupying a different hyperfine state. The latter is trapped magnetically. Hyperfine-state–changing collisions, and therefore loss of the trapped (m=0) atoms, are shown to be strongly inhibited in case of a low density of the confined atomic cloud. We monitor the transition from a "soft" to a "hard" effective potential by studying the backaction of the trapped (m=0) atoms onto the condensate which provides their confinement. The controlled outcoupling of the trapped atoms by shaping the condensate wave function is explored. We observe a pulsed emission of atoms from the trapping region reminiscent of an atom laser

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of noninteracting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.

A detailed analysis of the classical nonlinear dynamics of a single driven square potential barrier with harmonically oscillating position is performed. The system exhibits dynamical trapping which is associated with the existence of a stable island in phase space. Due to the unstable periodic orbits of the KAM structure, the driven barrier is a chaotic scatterer and shows stickiness of scattering trajectories in the vicinity of the stable island. The transmission function of a suitably prepared ensemble yields results which are very similar to tunneling resonances in the quantum mechanical regime. However, the origin of these resonances is different in the classical regime.

A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards

The stationary states of a few bosons in a one-dimensional harmonic trap are investigated throughout the crossover from weak to strongly attractive interactions. For sufficient attraction, three different classes of states emerge: (i) N-body bound states, (ii) bound states of smaller fragments and (iii) gas-like states that fermionize, that is, map to ideal fermions in the limit of infinite attraction. The two-body correlations and momentum spectra characteristic of the three classes are discussed, and the results are illustrated using the soluble two-particle model.

A comparative study of the effect of a static homogeneous electric field on the rovibrational spectra of several polar dimers in their X1Σ+ electronic ground state is performed. Focusing upon the rotational ground state within each vibrational band, results for energies and various expectation values are presented. For moderate field strengths the electric-field–induced energy shifts, orientation, alignment, and angular-motion hybridization are analyzed up to high vibrational excitations close to the dissociation threshold.

We study the ground states of one-dimensional Bose-Bose mixtures under harmonic confinement. As we vary the interspecies coupling strength up to the limit of infinite repulsion, we observe a generalized, composite-fermionization crossover. The initially coexisting phases demix as a whole for weak intraspecies interactions, whereas the atoms localize individually for strong intraspecies repulsion. By symmetry, the two components end up with strongly overlapping profiles, albeit sensitive to symmetry-breaking perturbations. Different pathways emerge if the two components have different atom numbers, different intraspecies interactions, or different masses and/or trap frequencies.

We study few-boson tunneling in a one-dimensional double well. As we pass from weak interactions to the fermionization limit, the Rabi oscillations first give way to highly delayed pair tunneling (for medium coupling), whereas for very strong correlations multiband Rabi oscillations emerge. All this is explained on the basis of the exact few-body spectrum and without recourse to the conventional two-mode approximation. Two-body correlations are found essential to the understanding of the different tunnel mechanisms. The investigation is complemented by discussing the effect of skewing the double well, which offers the possibility to access specific tunnel resonances.

Motivated by recent proposals of “collisionally inhomogeneous” Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a “stitching” approach to analytically approximate the pertinent solutions of the underlying nonlinear Schrödinger equation by matching the wave function and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that stationary solitons must be centered in one of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.

We develop a grid method for multichannel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency ω permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic, and heteronuclear collisions. In the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.

We explore the dynamical evolution of an ensemble of noninteracting particles propagating freely in an elliptical billiard with harmonically driven boundaries. The existence of Fermi acceleration is shown thereby refuting the established assumption that smoothly driven billiards whose static counterparts are integrable do not exhibit acceleration dynamics. The underlying mechanism based on intermittent phases of laminar and stochastic behavior of the strongly correlated angular momentum and velocity motion is identified and studied with varying parameters. The diffusion process in velocity space is shown to be anomalous and we find that the corresponding characteristic exponent depends monotonically on the breathing amplitude of the billiard boundaries. Thus it is possible to tune the acceleration law in a straightforwardly controllable manner.

In this work we study the nonlinear dynamics of the static and the driven ellipse. In the static case, we find numerically an asymptotical algebraic decay for the escape of an ensemble of noninteracting particles through a small hole due to the integrable structure of the phase space of the system. Furthermore, for a certain hole position, a saturation value in the decay that can be tuned arbitrarily by varying the eccentricity of the ellipse is observed and explained. When harmonic boundary oscillations are applied, this saturation value, caused by librator-type orbits, is gradually destroyed via two fundamental processes which are discussed in detail. As a result, an amplitude-dependent emission rate is obtained in the long-time behavior of the decay, suggesting that the driven elliptical billiard can be used as a controllable source of particles.

We explore the quantum transmission through open oval-shaped quantum dots. The transmission spectra show periodic resonances and, depending on the geometry parameter, a strong suppression of the transmission for low energies. Applying a weak perpendicular magnetic field changes this situation drastically and introduces a large conductance. We identify the underlying mechanisms being partially due to the specific shape of the oval that causes a systematic decoupling of a substantial number of states from the leads. Importantly, a pairwise destructive interference of the transmitting states is encountered thereby leading to the complete conductance suppression. Coupling properties and interferences can be tuned via a weak magnetic field. These properties are robust with respect to the presence of disorder in the quantum dot.

We discuss the properties of ultracold Rydberg atoms in a Ioffe-Pritchard magnetic field configuration. The derived two-body Hamiltonian unveils how the large size of Rydberg atoms affects their coupling to the inhomogeneous magnetic field. The properties of the compound electronic and center of mass quantum states are thoroughly analyzed. We find very tight confinement of the center of mass motion in two dimensions to be achievable while barely changing the electronic structure compared to the field free case. This paves the way for generating a one-dimensional ultracold Rydberg gas.

We investigate the rotational dynamics of heteronuclear diatomic molecules possessing a 1Σ+ electronic ground state exposed to a strong external time-dependent homogeneous electric field. An exponential switching on and off is employed for the electric field. We analyze the orientation and hybridization of the angular motion, together with the population of pendular and rotational states in the constant-field and field-free regimes, as the switching times are modified. Exact results are compared with those of an N-mode approach to the rotational dynamics derived within the effective rotor approximation. It is demonstrated that robust predictions are possible with respect to the number of pendular states and partial waves involved in the constant and postpulse regimes, respectively. The final wave packet shows a wide variety of localization and orientation phenomena arranged in characteristic patterns, which alternate between two angular hemispheres and are periodic in time.

A wave-packet propagation method is developed and applied to investigate the quantum dynamics of scattering processes of identical and distinguishable atoms in harmonic waveguides. The quantum dynamics of the confinement-induced resonances (CIRs) for ultracold collisions of identical particles, s-wave CIRs for bosons and p-wave CIRs for fermions, is explored in detail. Our multigrid approach allows us to fully take into account the coupling between the center-of-mass (c.m.) and relative motions in the case of distinguishable atoms. The latter includes, in particular, s- and p-partial-wave mixing, caused by the confining trap, which acts differently on the different atomic species. Specifically, we explore in detail the recently discovered [J. I. Kim, V. S. Melezhik, and P. Schmelcher, Phys. Rev. Lett. 97, 193203 (2006)] dual CIR, which is based on a destructive interference mechanism leading to complete transmission in the waveguide, although the corresponding scattering in free space exhibits strong s- and p-wave scattering.

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and “cigar-shaped” condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis. Numerical results are shown to be in very good agreement with the corresponding analytical predictions.

The quantum resonances of an atom possessing a single valence electron which shows hyperfine interaction with the nucleus is investigated in the presence of a three-dimensional magnetic quadrupole field. Particular emphasis is put on the study of the interplay of the hyperfine and quadrupole forces. By analyzing the underlying Hamiltonian, a variety of symmetries are revealed, which give rise to a twofold degeneracy of the resonance energies. Our numerical approach employs the complex scaling method and a Sturmian basis set. Several regimes and classes of short- and long-lived resonances are identified. The energies and decay widths of the resonances are characterized by their electronic and nuclear spin properties.

The electronic spectrum of a Rydberg atom immersed in a Bose-Einstein condensate is investigated. The Heisenberg equations of motions for the condensate and the Rydberg atom are derived. Neglecting the back action of the Rydberg atom onto the condensate decouples the equations describing the condensate and Rydberg atom. In this case the spectral structure of the Rydberg atom is completely determined by an effective potential which depends on the density distribution of the condensate. We study the spectral properties for the situation of an isotropic harmonic and anharmonic as well as axially symmetric confinement. In the latter case an intriguing analogy with Rydberg atoms in magnetic fields is encountered.

We deal with the effects of an anharmonic trap on an interacting two-boson system in one dimension. Our primary focus is on the role of the induced coupling between the center of mass and the relative motion as both anharmonicity and the (repulsive) interaction strength are varied. The ground state reveals a strong localization in the relative coordinate, counteracting the tendency to fragment for stronger repulsion. To explore the quantum dynamics, we study the system’s response upon (i) exciting the harmonic ground state by continuously switching on an additional anharmonicity and (ii) displacing the center of mass, this way triggering collective oscillations. The interplay between collective and internal dynamics materializes in the collapse of oscillations, which are explained in terms of few-mode models.

The formation of heteronuclear molecules in their electronic ground states from a mixture of two ultracold atomic species via a one-photon stimulated emission process is investigated. The presence of an additional external homogeneous and static electric field is shown to severely influence the induced emission process. Using the LiCs molecule as a prototype, we study the corresponding cross section and its dependence on the continuum energy, final rovibrational state, and static electric field strength. The possibility of controlling the single-photon association process via an additional static electric field is demonstrated.

Fermi acceleration of an ensemble of noninteracting particles evolving in a stochastic two-moving wall variant of the Fermi-Ulam model (FUM) and the phase randomized harmonically driven periodic Lorentz gas is investigated. As shown in [A. K. Karlis, P. K. Papachristou, F. K. Diakonos, V. Constantoudis, and P. Schmelcher, Phys. Rev. Lett. 97, 194102 (2006)], the static wall approximation, which ignores scatterer displacement upon collision, leads to a substantial underestimation of the mean energy gain per collision. In this paper, we clarify the mechanism leading to the increased acceleration. Furthermore, the recently introduced hopping wall approximation is generalized for application in the randomized driven Lorentz gas. Utilizing the hopping approximation the asymptotic probability distribution function of the particle velocity is derived. Moreover, it is shown that, for harmonic driving, scatterer displacement upon collision increases the acceleration in both the driven Lorentz gas and the FUM by the same amount. On the other hand, the investigation of a randomized FUM, comprising one fixed and one moving wall driven by a sawtooth force function, reveals that the presence of a particular asymmetry of the driving function leads to an increase of acceleration that is different from that gained when symmetrical force functions are considered, for all finite number of collisions. This fact helps open up the prospect of designing accelerator devices by combining driving laws with specific symmetries to acquire a desired acceleration behavior for the ensemble of particles.

Quantum transport through an open periodic array of up to five dots is investigated in the presence of a magnetic field. The device spectrum exhibits clear features of the band structure of the corresponding one-dimensional artificial crystal which evolves with varying field. A significant magnetically controlled current flow is induced with changes up to many orders of magnitude depending on temperature and material parameters. We propose a simple design for measuring with current technology the magnetic subband formation of quasi one-dimensional Bloch electrons

We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can be tuned by varying the driving amplitude is established. Pulsed escape rates and decelerated escaping particles are generic properties of the harmonically breathing billiard. This suggests time-dependent billiards as prototype systems to study the nonequilibrium evolution of classical ensembles encountering a multitude of scattering processes off driven targets

An analytical approach to the problem of the multiphoton exciton absorption in biased narrow-well superlattices (SLs) induced by the optical transitions to the localized resonant exciton states is developed. Both the ac electric field of the intense optical wave and the dc electric field are directed parallel to the SL axis. The SL is formed by a periodic sequence of quantum wells (QWs) whose widths are taken to be much less than the exciton Bohr radius. The model of the SL potential employs a limiting form of the Kronig-Penney potential, i.e., a periodic chain of QWs separated by δ-function-type barriers. A sufficiently strong dc electric field provides the localization of the carriers within one period of the SL. Analytical dependencies of the coefficient of the multiphoton exciton absorption on the characteristics of the dc and ac electric fields and on the parameters of the SL in the approximation of both isolated and interacting Wannier-Stark levels are obtained in the nearest-neighbor tight-binding approximations. Our analytical results correlate well with those obtained in numerical investigations. Estimates of the expected experimental values are performed for the parameters of a GaAs∕AlGaAs SL.

We study the quantum properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap which is superimposed by a homogeneous electric field. Trapped Rydberg atoms can be created in long-lived electronic states exhibiting a permanent electric dipole moment of several hundred Debye. The resulting dipole-dipole interaction in conjunction with the radial confinement is demonstrated to give rise to an effectively one-dimensional ultracold Rydberg gas with a macroscopic interparticle distance. We derive analytical expressions for the electric dipole moment and the critical linear density of Rydberg atoms.

A dual confinement induced resonance effect first observed numerically in a paper [J. I. Kim, V. S. Melezhik and P. Schmelcher, Phys. Rev. Lett. 97 (2006), 193203] predicts the possibility of suppressing the effective two-body interaction in a quasi-one dimensional (1D) cylindrical geometry. Here this low dimensionality effect is analytically modeled by applying a previous formalism to treat low energy quantum scattering processes under tight confinement [J. I. Kim, J. Schmiedmayer and P. Schmelcher, Phys. Rev. A 72 (2005), 042711]. This analytic formalism is improved in order to account non-perturbatively for the three dimensional (3D) scattering phase shift l=1 for a given spherically symmetric interaction potential between distinguishable colliding particles. The role of the confinement on the scattering properties can then be systematically calculated up to the p-wave.

A general quantum theory is presented for unconventional anionic states supported by the presence of an external magnetic field. The theory applies to atomic anions and allows for straightforward extensions to anions formed in magnetic fields by other species, e.g., by clusters or small molecules. A special focus of the theory is on the coupling of the anion’s motion across the magnetic field to the motion of the attached electron. Neglecting this coupling, the magnetically induced anionic states are known to constitute an infinite manifold of bound states. In reality, the number of bound anionic states is finite. Typically, the quantized motion of the anion in the field results in sequences of excitations. These might include, depending on properties of the anion and on the magnetic field strengths, a few or a substantial number of states. Explicit results obtained by quantum ab initio calculations are presented and discussed on bound states and radiative transitions for some experimentally relevant atomic anions.

The formation of ultracold molecules via stimulated emission followed by a radiative de-excitation cascade in the presence of a static electric field is investigated. By analyzing the corresponding cross-sections, we demonstrate the possibility to populate the lowest rotational excitations via photoassociation. The modification of the radiative cascade due to the electric field leads to narrow rotational state distributions in the vibrational ground state. External fields might therefore represent an additional valuable tool towards the ultimate goal of quantum state preparation of molecules.

We examine the lowest excitations of one-dimensional few-boson systems trapped in double wells of variable barrier height. Based on a numerically exact multiconfigurational method, we follow the whole pathway from the noninteracting to the fermionization limit. It is shown how, in a purely harmonic trap, the initially equidistant, degenerate levels are split up due to interactions, but merge again for strong enough coupling. In a double well, the low-lying spectrum is largely rearranged in the course of fermionization, exhibiting level adhesion and (anti)crossings. The evolution of the underlying states is explained in analogy to the ground-state behavior. Our discussion is complemented by illuminating the crossover from a single to a double well.

Recently a model Hamiltonian proposed by Benguria et al. has been utilized to treat the H+2 ion in the extreme high field limit by calculating the corresponding Feynman propagator. Here an extended analysis is presented that can be applied to linear configurations of the molecules H2+3 and H3+4, stabilized by the application of an intense magnetic field along the chain axes. Results for the electron density are presented for the high field regime. Numerical results in the literature confirm the main predictions of the largely analytical model given here. Electronic transitions between the bound states of the model are also briefly considered.

We investigate the quantum properties of an ultracold Rydberg atom exposed to a magnetic quadrupole field and a homogeneous electric field. The properly transformed Hamiltonian explicitly depends on the conserved total angular momentum and couples the centre of mass and electronic degrees of freedom. The corresponding Schr¨odinger equation is solved by an adiabatic separation focusing on a fixed n-manifold. The shape of the adiabatic electronic potential energy surfaces is analysed. With increasing electric field strength, avoided crossings among them become ubiquitous and the electric field-dominated regime spreads out within the centre-of-mass coordinate space. A transition from smooth surfaces for weak electric fields to surfaces involving a cusplike behaviour in the strong field regime is observed. The latter involves a characteristic splitting behaviour of the surfaces due to the competition of the Stark and magnetic interactions. In contrast to previous investigations, our setup allows for the trapping of quantum states with a comparatively small electronic angular momentum.

The effects of a static, homogeneous, and strong electric field on the radiative and steric properties of the LiCs molecule in its 1Σ+ electronic ground state are investigated. Combining discretization and basis-set methods, the rovibrational Schrödinger equation is solved and dipole transition rates are calculated. Spontaneous emission decay rates and radiative lifetimes of rovibrationally excited states have been studied extensively and particularly in the presence of the external homogeneous electric field. The intriguing possibility to control the alignment and orientation by applying a sufficiently strong field while switching between different configurations via absorption and emission processes is demonstrated.

We present an investigation of the resonances of a doubly excited helium atom in a strong magnetic field covering the regime B=0–100 a.u. A full-interaction approach which is based on an anisotropic Gaussian basis set of one-particle functions being nonlinearly optimized for each field strength is employed. Accurate results for a total of 17 resonances below the threshold consisting of He+ in the N=2 state are reported in this work. This includes states with total magnetic quantum numbers M=0,−1,−2 and even z parity. The corresponding binding energies are compared to approximate energies of two-particle configurations consisting of two hydrogenlike electrons in the strong-field regime, thereby providing an understanding of the behavior of the energies of the resonances with varying field strength.

A parallel algorithm for the implementation of the recursive Green’s function technique, which is extensively applied in the coherent scattering formalism, is developed. The algorithm performs a domain decomposition of the scattering region among the processors participating in the computation and calculates the Schur’s complement block in the form of distributed blocks among the processors. If the method is applied recursively, thereby eliminating the processors cyclically, it is possible to arrive at a Schur’s complement block of small size and compute the desired block of the Green’s function matrix directly. The numerical complexity due to the longitudinal dimension of the scatterer scales linearly with the number of processors, though, the computational cost due to the processors’ cyclic reduction establishes a bottleneck to achieve efficiency 100%. The proposed algorithm is accompanied by a performance analysis for two numerical benchmarks, in which the dominant sources of computational load and parallel overhead as well as their competitive role in the efficiency of the algorithm will be demonstrated.

We investigate resonances of spin-1 bosons in a three-dimensional magnetic quadrupole field. Complementary to the well-known positive energy resonances it is shown that there exist short-lived, i.e., broad, negative energy resonances. The latter are characterized by an atomic spin that is aligned antiparallel to the local magnetic field direction. In contrast to the positive energy resonances the lifetimes of the negative energy resonances decrease with increasing total magnetic quantum number. We derive a mapping of the two branches of the spectrum.

We study the correlation properties of the ground states of few ultracold bosons, trapped in double wells of varying barrier height in one dimension. Extending previous results on the signature of the transition from a Bose-condensed state via fragmentation to the hard-core limit, we provide a deeper understanding of that transition by relating it to the loss of coherence in the one-body density matrix and to the emerging long-range tail in the momentum spectrum. These are accounted for in detail by discussing the natural orbitals and their occupations. Our discussion is complemented by an analysis of the two-body correlation function.

We discuss the properties of Rydberg atoms in a magnetic Ioffe-Pritchard trap being commonly used in ultracold atomic physics experiments. The Hamiltonian is derived, and it is demonstrated how tight traps alter the coupling of the atom to the magnetic field. We solve the underlying Schrödinger equation of the system within a given n manifold and show that for a sufficiently large Ioffe field strength the 2n2-dimensional system of coupled Schrödinger equations decays into several decoupled multicomponent equations governing the center of mass motion. An analysis of the fully quantized center of mass and electronic states is undertaken. In particular, we discuss the situation of tight center of mass confinement outlining the procedure to generate a low-dimensional ultracold Rydberg gas.

Motivated by recent experimental studies of matter waves and optical beams in double-well potentials, we study the corresponding solutions of the nonlinear Schrödinger equation. Using a Galerkin-type approach, we obtain a detailed handle on the nonlinear solution branches of the problem, starting from the corresponding linear ones, and we predict the relevant bifurcations for both attractive and repulsive nonlinearities. The dynamics of the ensuing unstable solutions is also examined. The results illustrate the differences that arise between the steady states and the bifurcations emerging in symmetric and asymmetric double wells.

We investigate bright matter-wave solitons in the presence of a spatially varying scattering length. It is demonstrated that a soliton can be confined due to the inhomogeneous collisional interactions. Moreover, we observe the enhanced transmission of matter-wave solitons through potential barriers for suitably chosen spatial variations of the scattering length. The results indicate that the manipulation of atomic interactions can become a versatile tool to control matter-wave dynamics.

We investigate the transition of a quasi-one-dimensional few-boson system from a weakly correlated to a fragmented and finally a fermionized ground state. Our numerically exact analysis, based on a multiconfigurational method, explores the interplay between different shapes of external and interparticle forces. Specifically, we demonstrate that the addition of a central barrier to an otherwise harmonic trap may support the system’s fragmentation, with a symmetry-induced distinction between even and odd atom numbers. Moreover, the impact of inhomogeneous interactions is studied, where the effective coupling strength is spatially modulated. It is laid out how the ground state can be displaced in a controlled way depending on the trap and the degree of modulation. We present the one- and two-body densities and, beyond that, highlight the role of correlations on the basis of the natural occupations.

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in “interacting” quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.

Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the displacement of the walls (static wall approximation), leads to a systematic underestimation of particle acceleration. An improved approximative map is introduced, which takes into account the effect of the wall displacement, and in addition allows the analytical estimation of the long term behavior of the particle mean velocity as well as the corresponding probability distribution, in complete agreement with the numerical results of the exact dynamics. This effect accounting for the increased particle acceleration—Fermi hyperacceleration—is also present in higher-dimensional systems, such as the driven Lorentz gas.

We explore properties of atoms whose magnetic hyperfine sublevels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this class of potentials and demonstrate their potential use to build atom optical elements such as double wells, interferometers, and ringtraps. Moreover, we perform simulations of interference experiments carried out in rf induced double-well potentials. We discuss how the nature of the atom-field coupling mechanism gives rise to a decrease of the interference contrast.

We investigate the effects of a strong electric field on the rovibrational dynamics of LiCs in its 1R+ electronic ground state. Using a hybrid computational technique combining discretisation and basis set methods, the rovibrational Schro¨dinger equation is solved. Results for energy levels and various expectation values are presented. The validity of the previous developed effective and adiabatic rotor approaches is investigated. The electric field-induced hybridization is analyzed up to high rotational excitations and for a large range of magnetic quantum numbers.

A harmonic single electron quantum dot in a spatially periodic magnetic field is investigated. The energy spectrum, magnetization, probability, and current density are studied for varying parameters (i.e., amplitude, wavelength, and phase) of the periodic magnetic field. For wavelengths comparable to the oscillator length of the dot, we observe a rich spectral behavior. For higher field amplitudes and depending on the phase of the field, avoided and exact level crossings dominate the spectrum and quasidegenerate low lying states occur systematically. We employ a simple model for the interpretation of the quasidegeneracies and their impact on the probability and current densities. The latter are very sensitive with respect to the phase of the magnetic field. For wavelengths being small compared to the oscillator length, the impact of the field is very minor, thus the obtained spectrum is approximately that of a pure harmonic oscillator. For large values of k the eigenfunctions take up a spatially varying phase and the magnitude of the probability current decreases slowly with increasing k. Different from the dot in a homogeneous magnetic field, the magnetization, as a function of the field amplitude, has a minimum, depending on the phase and wavelength of the field.

We investigate the resonant quantum motion of spin-1 particles in a magnetic guide. A symmetry analysis is undertaken in order to reveal the complex symmetry properties of the system which lead to a twofold degeneracy in the energy-level spectrum. Lifetimes and energies of the resonance states are computed by employing the complex scaling method. By analyzing several hundreds of resonances we are able to make conclusions about the global properties of the resonance spectrum. The effect of an Ioffe field which is applied parallel to the guide is also discussed. We observe a global increase of the lifetimes with increasing Ioffe-field strength. For certain parameter regimes we find the ground-state resonance to exhibit a longer lifetime than the energetically neighbored excited states. The latter could have interesting implications on the time evolution of trapped ultracold atomic ensembles. Applications of our results to calculate the resonance energies andlifetimes of the trapped alkali-metal atoms 7Li and 87Rb are outlined.

We investigate the transmission of electrons through a quantum ring coupled to a quantum dot by applying a finite difference approach augmented by exterior complex scaling for the solution of the corresponding time-independent Schrödinger equation. It is shown that the transmission in the presence of an additional ring- or dot-bound electron is energetically suppressed compared with the transmission for a pure quantum dot–ring system, being reminiscent of the so-called Coulomb blockade effect in quantum dots. The different behaviour for varying parameters as well as in the presence of an attractive impurity in the dot is discussed in some detail.

We investigate the impact of an external magnetic field on ultra-long-range and ultracold Rydberg molecules. The Born–Oppenheimer potential surfaces are analysed and discussed for different values of the magnetic field strength. The magnetic field provides an angular confinement turning a rotational degree of freedom into a vibrational one. We explore the vibrational dynamics and observe a pronounced transition in the level spacing from a linear splitting via an irregular regime to a 2D harmonic oscillator-like behaviour. Scaling arguments for the dependence of the potential energy surfaces on the field strengths are provided. The occurrence of a monotonic lowering of the magnitude of the electric dipole moment with increasing magnetic field strength is shown.

We analyze the quantum properties of atoms in a magnetic quadrupole field. The quantum dynamics of ground state atoms in this field configuration is studied firstly. We formulate the Hamiltonian and perform a symmetry analysis. Due to the particular shape of the quadrupole field in general there exist no stable states. We provide resonance energies, lifetimes and calculate the density of states and investigate under what conditions quasi-bound states occur that possess long lifetimes. An effective scalar Schrödinger equation describing such states is derived. As a next step we explore the influence of a high gradient quadrupole field on the electronic structure of excited atoms. An effective one-body approach together with the fixed nucleus approximation is employed in order to derive the electronic Hamiltonian. We present the energy spectrum and discuss peculiar features such as non-trivial spin densities and magnetic field induced electric dipole moments.

In this work we present an investigation on the quantum dynamics of ultracold electronically excited atoms exposed to an external magnetic quadrupole field. We present a general Hamiltonian which describes the quantum dynamics of an atom in an arbitrary linear magnetic field. This makes our approach applicable to a wide range of atoms and magnetic field configurations. The system is solved by incorporating an adiabatic separation of the electronic and center-of-mass dynamics. We provide the adiabatic energy surfaces and discuss under which conditions trapped center-of-mass states can be achieved. We present energies and wave functions of the corresponding quantum states. By analyzing the properties of the combined center-of-mass and electronic quantum states we demonstrate that the extension of the electronic wave function can exceed that of the center-of-mass motion. Therefore such atoms cannot be considered as being pointlike. A discussion of electromagnetic transitions is also provided.

Finite-size effects not only alter the energy levels of small systems, but can also lead to additional effective interactions within these systems. Here the problem of low-energy quantum scattering by a spherically symmetric short-range potential in the presence of a general cylindrical confinement is investigated. A Green’s function formalism is developed which accounts for the full three-dimensional (3D) nature of the scattering potential by incorporating all phase shifts and their couplings. This quasi-1D geometry gives rise to scattering resonances and weakly localized states, whose binding energies and wave functions can be systematically calculated. Possible applications include, e.g., impurity scattering in ballistic quasi-1D quantum wires in mesoscopic systems and in atomic matter-wave guides. In the particular case of parabolic confinement, the present formalism can also be applied to pair collision processes such as two-body interactions. Weakly bound pairs and quasimolecules induced by the confinement and having zero or higher orbital angular momentum can be predicted, such as p- and d-wave pairings.

We investigate the evolution of the rovibrational spectrum of heteronuclear diatomic molecules exposed to a strong static electric field. The field induces avoided crossings causing a strong mixing of the electrically dressed rovibrational states. At the avoided crossing the molecular configuration is a strongly distorted and asymmetric one showing well-pronounced localization effects of the corresponding probability densities. The potential impact of our findings on the state-selective chemical reaction dynamics is discussed.

Multielectron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode and stability analysis are performed. A classification of the various modes, which are dominated by the magnetic field or the Coulomb interactions, is provided. Based on the MCTDH approach, we carry out a six-dimensional wave-packet dynamical study for the two-electron resonances, yielding in particular lifetimes of more than 0.1 μs for strong electric fields.

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity is found to lead to a gravitational potential, as well as to a renormalization of the parabolic potential coefficient. This feature allows one to influence the motion of fundamental as well as higher-order solitons.

In a magnetic field, an atom (or molecule) can attach an extra electron to form an unconventional anionic state which has no counterparts in field-free space. Assuming the atom to be infinitely heavy, these magnetically induced anionic states are known to constitute an infinite manifold of bound states. In reality, the species can move and its motion across the magnetic field couples to the motion of the attached electron. We treat this coupling, for the first time, quantum mechanically, and show that it makes the number of bound anionic states finite. Explicit numerical quantum results are presented and discussed.

We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field B. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall description of the nonmonotonic behavior of the average magnetoconductance in terms of the corresponding classical trajectories, thus, establishing a basic tool useful in the design and analysis of experiments.

We analyze the dynamics of dark matter-wave solitons on a Thomas-Fermi cloud described by the Gross-Pitaevskii equation with radial symmetry. One-dimensional, ring, and spherical dark solitons are considered, and the evolution of their amplitudes, velocities, and centers is investigated by means of a Lagrangian approach. In the case of large-amplitude oscillations, higher-order corrections to the corresponding equations of motion for the soliton characteristics are shown to be important in order to accurately describe its dynamics. The numerical results are found to be in very good agreement with the analytical predictions.

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.

Multi-electron giant dipole resonances of atoms in crossed electric and magnetic fields are investigated. Stationary configurations corresponding to a highly symmetric arrangement of the electrons on a decentered circle are derived, and a normal-mode stability analysis is performed. A classification of the various modes, which are dominated either by the magnetic or Coulomb interactions, is provided. A six-dimensional wave-packet dynamical study, based on the MCTDH approach, is accomplished for the two-electron resonances, yielding in particular lifetimes of more than 0.1 μs for strong electric fields.

We investigate the rovibrational dynamics of heteronuclear diatomic molecules exposed to a strong external static and homogeneous electric field. We encounter in the presence of the field the effect of induced adiabatic coupling among the vibrational and hybridized rotational motions. Exact results are compared to the predictions of the adiabatic rotor approach as well as to the previously established effective rotor approximation. A detailed analysis of the impact of the electric field is performed: the hybridized and oriented rotational motion, the mixing of angular momenta, and the squeezing of the vibrational motion are observed. It is demonstrated that these effects can well be accounted for by the adiabatic rotor approximation.

We investigate the motion of neutral fermions and bosons in a three-dimensional magnetic quadrupole trap. Inspecting the underlying Hamiltonian a variety of symmetries is revealed which give rise to degeneracies of the resonance energies. Our numerical approach which involves the eigenvalue problem resulting from a Sturmian basis set together with the complex scaling method enables us to calculate several hundred resonance states. The distributions of the energies and decay widths of the resonances are analyzed for both spin-1/2 fermions and spin-1 bosons. We also investigate under what conditions quasibound states with long lifetimes can be achieved. An effective scalar Schrödinger equation describing such states is derived. The results are applied to the cases of the alkali-metal atoms 87Rb and 6Li trapped in a hyperfine ground state.

We investigate the theoretical foundations of neutral two-body systems exposed to an inhomogeneous magnetic field. Various representations for the Hamiltonian describing the coupled centre-of-mass and internal motion are derived. For the specific case of a magnetic quadrupole field we establish the continuous and discrete symmetries and show that the energy levels of the interacting system are two-fold degenerate. We exploit the symmetries in two alternative ways and derive corresponding effective equations of motion. The first approach eliminates two of the six spatial degrees of freedom and leads to an (infinite) set of coupled channel equations for the spin and spatial degrees of freedom. The second approach introduces the projection of the total angular momentum onto the symmetry axis of the quadrupole field as a canonical momentum, thereby eliminating the corresponding cyclic angle.

An analytical investigation of resonant impurity and exciton states in a narrow quantum well (QW) is performed. We employ the adiabatic multisubband approximation assuming that the motions parallel and perpendicular to the heteroplanes separate adiabatically. The coupling between the Coulomb states associated with the different size-quantized subbands (N=1, 2, …) is taken into account. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron and the exciton optical absorption coefficient are derived in an explicit form. The spectrum comprises a sequence of series of quasi-Coulomb levels (n) where only the series belonging to the ground subband N=1 is truly discrete while the excited series N⩾2 consist of quasi-discrete energy levels possessing non-zero widths ΓNn. Narrowing the QW leads to an increase of the binding energy and to a decrease of the resonant energy width ΓNn and the resonant energy shift ΔENn of the impurity electron. Displacing the impurity center from the midpoint of the QW causes the binding energy to decrease while the width ΓNn and the corresponding shift ΔENn both increase. A Lorentzian form is recovered for the exciton absorption profile. The absorption peak is narrowed and blue shifted for a narrowing of the quantum well. A successful comparison with existing numerical data is performed. For GaAs QW’s it is shown that the resonant states analyzed here are sufficiently stable to be observed experimentally.

We study electronically excited atoms exposed to a magnetic quadrupole field. In order to describe the electron dynamics, a one-body approach is employed. Due to the inhomogeneity of the field, the spatial and spin degrees of freedom become coupled in a unique way. The underlying unitary and anti-unitary symmetries are discussed in detail leading to remarkable features such as a two-fold degeneracy of any energy level. We analyse the energy level structure throughout a wide range of field gradients. An investigation of the electronic spin properties is performed by studying the spatially dependent spin-polarization which exhibits a rich nodal structure. We compute wavelengths and strengths for electromagnetic transitions and provide the selection rules. A discussion of the so-called ellipsoidal states which exhibit unique properties such as large mean orbital angular momenta and spatial compactness is provided. The property of magnetic field-induced permanent electric dipole moments is analysed in detail. Wherever reasonable, the results obtained for the quadrupole field are compared to the homogeneous field case.

We investigate the resonant motion of neutral spin-1/2-fermions in a magnetic guide. A wealth of unitary and antiunitary symmetries is revealed in particular giving rise to a twofold degeneracy of the energy levels. To compute the energies and decay widths of a large number of resonances the complex scaling method is employed. We discuss the dependence of the lifetimes on the angular momentum of the resonance states. In this context the existence of so-called quasibound states is shown. In order to approximately calculate the resonance energies of such states a radial Schrödinger equation is derived which improves the well-known adiabatic approximation. The effects of an additionally applied homogeneous Ioffe field on the resonance energies and decay widths are also considered. The results are applied to the case of the 6Li atom in the F=1/2 hyperfine ground state.

The problem of an impurity electron in a quantum ring (QR) in the presence of a radially directed strong external electric field is investigated in detail. Both an analytical and a numerical approach to the problem are developed. The analytical investigation focuses on the regime of a strong wire-electric field compared to the electric field due to the impurity. An adiabatic and quasiclassical approximation is employed. The explicit dependences of the binding energy of the impurity electron on the electric field strength, parameters of the QR, and position of the impurity within the QR are obtained. Numerical calculations of the binding energy based on a finite-difference method in two and three dimensions are performed for arbitrary strengths of the electric field. It is shown that the binding energy of the impurity electron exhibits a maximum as a function of the radial position of the impurity that can be shifted arbitrarily by applying a corresponding wire-electric field. The maximal binding energy monotonically increases with increasing electric field strength. The inversion effect of the electric field is found to occur. An increase of the longitudinal displacement of the impurity typically leads to a decrease of the binding energy. Results for both low- and high-quantum rings are derived and discussed. Suggestions for an experimentally accessible setup associated with the GaAs∕GaAlAs QR are provided.

We investigate the role of the unstable periodic orbits and their manifolds in the dynamics of a time-dependent two-dimensional scattering system. As a prototype we use two oscillating disks on the plane with the oscillation axes forming an angle θ. The phase space of the system is five dimensional and it possesses a variety of families of unstable periodic orbits (UPOs) with intersecting manifolds. We perform numerical experiments to probe the structure of distinct scattering functions, in one and two dimensions, near the location of the UPOs. We find that the corresponding manifolds occur only in a very particular and localized way in the high-dimensional phase space. As a consequence the underlying fractal structure is ubiquitous only in higher-dimensional, e.g., two-dimensional, scattering functions. Both two-dimensional and one-dimensional scattering functions are dominated by seemingly infinite sequences of discontinuities characterized by small values of the magnitude of the projectile’s outgoing velocity. These peaks accumulate toward the phase-space locations of the UPOs, with a rate which monotonically depends on the corresponding instability exponent. They represent the intersections of the set of the initial conditions with invariant sets of larger dimensionality embedded in the phase space of the system, which are not directly related with the UPOs. We adopt the term “dilute chaos” to characterize these phenomenological aspects of the scattering dynamics.

We investigate electronically excited atoms in a magnetic guide. It turns out that the Hamiltonian describing this system possesses a wealth of both unitary as well as antiunitary symmetries that constitute an uncommon extensive symmetry group. One consequence is the twofold degeneracy of any energy level. The spectral properties are investigated for a wide range of field gradients and the spatial distributions of the spin polarization are analyzed. Wavelengths, oscillator strengths, and selection rules are provided for the corresponding electromagnetic transitions. The effects due to an additional homogeneous bias field constituting a Ioffe-Pritchard trap are explored equally.

We present an analysis of the properties as well as the diverse applications and extensions of the method of stabilisation transformation. This method was originally invented to detect unstable periodic orbits in chaotic dynamical systems. Its working principle is to change the stability characteristics of the periodic orbits by applying an appropriate global transformation of the dynamical system. The theoretical foundations and the associated algorithms for the numerical implementation of the method are discussed. This includes a geometrical classification of the periodic orbits according to their behaviour when the stabilisation transformations are applied. Several refinements concerning the implementation of the method in order to increase the numerical efficiency allow the detection of complete sets of unstable periodic orbits in a large class of dynamical systems. The selective detection of unstable periodic orbits according to certain stability properties and the extension of the method to time series are discussed. Unstable periodic orbits in continuous-time dynamical systems are detected via introduction of appropriate Poincaré surfaces of section. Applications are given for a number of examples including the classical Hamiltonian systems of the hydrogen and helium atom, respectively, in electromagnetic fields. The universal potential of the method is demonstrated by extensions to several other nonlinear problems that can be traced back to the detection of fixed points. Examples include the integration of nonlinear partial differential equations and the numerical determination of Markov-partitions of one-parametric maps.

The electronic structure of the lithium atom in a strong magnetic field 0⩽γ⩽10 is investigated. Our computational approach is a full configuration interaction method based on a set of anisotropic Gaussian orbitals that is nonlinearly optimized for each field strength. Accurate results for the total energies and one-electron ionization energies for the ground and several excited states for each of the symmetries 20+, 2(−1)+, 4(−1)+, 4(−1)−, 2(−2)+, 4(−2)+, and 4(−3)+ are presented. The behavior of these energies as a function of the field strength is discussed and classified. Transition wavelengths for linear and circular polarized transitions are presented as well.

We investigate the electronic struc