# Project C7

## 2023

### Dynamical formation of two-fold fragmented many-body state induced by an impurity in a double-well

*J. Chen, S.I. Mistakidis and P. Schmelcher*

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.

### Correlated dynamics of collective droplet excitations in a one-dimensional harmonic trap

*I. A. Englezos, S. I. Mistakidis, and P. Schmelcher*

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.

## 2022

### Counterflow Dynamics of Two Correlated Impurities Immersed in a Bosonic Gas

*F. Theel, S.I. Mistakidis, K. Keiler and P. Schmelcher*

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.

### Theoretical and numerical evidence for the potential realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates

*A. Romero-Ros, G. C. Katsimiga, S. I. Mistakidis, B. Prinari, G. Biondini, P. Schmelcher, and P. G. Kevrekidis*

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.

### Intra- and interband excitations induced residue decay of the Bose polaron in a one-dimensional double-well

*J. Chen, S.I. Mistakidis and P. Schmelcher*

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.

### On-demand generation of dark-bright soliton trains in Bose-Einstein condensates

*A. Romero-Ros, G. C. Katsimiga, P. G. Kevrekidis, B. Prinari, G. Biondini, and P. Schmelcher*

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.

## 2021

### On-demand generation of dark soliton trains in Bose-Einstein condensates

*A. Romero-Ros, G. C. Katsimiga, P. G. Kevrekidis, B. Prinari, G. Biondini, and P. Schmelcher*

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.

### Radiofrequency spectroscopy of one-dimensional trapped Bose polarons: crossover from the adiabatic to the diabatic regime

*S.I. Mistakidis, G.M. Koutentakis, F. Grusdt, H.R. Sadeghpour and P. Schmelcher*

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.

### Many-Body Collisional Dynamics of Impurities Injected into a Double-Well Trapped Bose-Einstein Condensate

*F. Theel, K. Keiler, S.I. Mistakidis and P. Schmelcher*

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.

### Bosonic Quantum Dynamics Following Two Colliding Potential Wells

*F. Köhler and P. Schmelcher*

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.

### Phase diagram, stability and magnetic properties of nonlinear excitations in spinor Bose–Einstein condensates

*G.C. Katsimiga, S.I. Mistakidis, P. Schmelcher and P.G. Kevrekidis*

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.

### Pattern formation of correlated impurities subjected to an impurity-medium interaction pulse

G. Bougas, S.I. Mistakidis and P. Schmelcher

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.

## 2020

### Asymptotic population imbalance of an ultracold bosonic ensemble in a driven double well

*Jie Chen, Aritra K. Mukhopadhyay, and Peter Schmelcher*

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.

### Induced Correlations Between Impurities in a One-Dimensional Quenched Bose Gas

*S.I. Mistakidis, A.G. Volosniev and P. Schmelcher*

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.

### Many-Body Quantum Dynamics and Induced Correlations of Bose Polarons

*S.I. Mistakidis, G.M. Koutentakis, G.C. Katsimiga, Th. Busch and P. Schmelcher*

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.

### Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons

*F. Theel, K. Keiler, S.I. Mistakidis and P. Schmelcher*

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.

### Pulse- and continuously driven many-body quantum dynamics of bosonic impurities in a Bose-Einstein condensate

*K. Mukherjee, S.I. Mistakidis, S. Majumder and P. Schmelcher*

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.

## 2019

### Interaction-induced single-impurity tunneling in a binary mixture of trapped ultracold bosons

*Kevin Keiler and Peter Schmelcher*

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.

### Analytical treatment of the interaction quench dynamics of two bosons in a two-dimensional harmonic trap

*G. Bougas, S.I. Mistakidis, and P. Schmelcher*

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.

### Dissipative Correlated Dynamics of a Moving Bosonic Impurity Immersed in a Bose-Einstein Condensate

*S.I. Mistakidis, F. Grusdt, G.M. Koutentakis and P. Schmelcher*

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.

### Correlated quantum dynamics of two quenched fermionic impurities immersed in a Bose-Einstein condensate

*S. I. Mistakidis, L. Hilbig, and P. Schmelcher*

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.

### Effective approach to impurity dynamics in one-dimensional trapped Bose gases

*S.I. Mistakidis, A.G. Volosniev, N.T. Zinner and P. Schmelcher*

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.

### Quench dynamics and orthogonality catastrophe of Bose polarons

*G.C. Katsimiga, S.I. Mistakidis, G.M. Koutentakis, Th. Busch, and P. Schmelcher*

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.

### Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion

*L. Budewig, S.I. Mistakidis and P. Schmelcher*

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.

### Phase-separation dynamics induced by an interaction quench of a correlated Fermi-Fermi mixture in a double well

*J. Erdmann, S.I. Mistakidis and P. Schmelcher*

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.

## 2018

### Correlated tunneling dynamics of an ultracold Fermi-Fermi mixture confined in a double well

*J. Erdmann, S.I. Mistakidis and P. Schmelcher*

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.

### State engineering of impurities in a lattice by coupling to a Bose gas

*K. Keiler and P. Schmelcher*

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.

### Quench dynamics of finite bosonic ensembles in optical lattices with spatially modulated interactions

*T. Plaßmann, S.I. Mistakidis and P. Schmelcher*

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.

### Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures

*J. Chen, J. Schurer and P. Schmelcher*

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.

### Many-body dissipative flow of a confined scalar Bose-Einstein condensate driven by a Gaussian impurity

*G.C. Katsimiga, S.I. Mistakidis, G.M. Koutentakis, P.G. Kevrekidis and P. Schmelcher*

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.

### Quantum point spread function for imaging trapped few-body systems with a quantum gas microscope

*S. Krönke, M. Pyzh, C. Weitenberg, P. Schmelcher*

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.

### Spectral properties and breathing dynamics of a few-body Bose–Bose mixture in a 1D harmonic trap

*M. Pyzh, S. Krönke, C. Weitenberg, P. Schmelcher*

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.

### Entanglement Induced Interactions in Binary Mixtures

*J. Chen, J.M. Schurer and P. Schmelcher*

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.

### Bosonic quantum dynamics following a linear interaction quench in finite optical lattices of unit filling

*S.I. Mistakidis, G.M. Koutentakis and P. Schmelcher*

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.

### Many-body expansion dynamics of a Bose-Fermi mixture confined in an optical lattice

*P. Siegl, S.I. Mistakidis and P. Schmelcher*

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.

### Correlation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas

*S.I. Mistakidis, G.C. Katsimiga, P.G. Kevrekidis and P. Schmelcher*

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.

### Correlation induced localization of lattice trapped bosons coupled to a Bose–Einstein condensate

*K. Keiler, S. Krönke and P. Schmelcher*

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.

### Quantum dynamics of two trapped bosons following infinite interaction quenches

*L.M.A. Kehrberger, V.J. Bolsinger and P. Schmelcher*

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.

## 2017

### Quantum dynamical response of ultracold few-boson ensembles in finite optical lattices to multiple interaction quenches

*J. Neuhaus-Steinmetz, S. Mistakidis and P. Schmelcher*

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.

### Collective excitations of dipolar gases based on local tunneling in superlattices

*L. Cao, S.I. Mistakidis, X. Deng and P. Schmelcher*

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.

### Mode coupling of interaction quenched ultracold few-boson ensembles in periodically driven lattices

*S.I. Mistakidis and P. Schmelcher*

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.

### Quench-induced resonant tunneling mechanisms of bosons in an optical lattice with harmonic confinement

*G.M. Koutentakis, S.I. Mistakidis and P. Schmelcher*

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.

## 2015

### Resonant quantum dynamics of few ultracold bosons in periodically driven finite lattices

* S.I. Mistakidis, T. Wulf, A. Negretti and P. Schmelcher*

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.

### Two-body correlations and natural-orbital tomography in ultracold bosonic systems of definite parity

* S. Krönke and P. Schmelcher*

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.

### Magnetic Kink States Emulated with Dipolar Superlattice Gases

* X. Yin, L. Cao. P. Schmelcher*

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.

### Correlated quantum dynamics of a single atom collisionally coupled to an ultracold finite bosonic ensemble

* S. Krönke, J. Knörzer and P. Schmelcher*

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.

### Beyond-mean-field study of a binary bosonic mixture in a state-dependent honeycomb lattice

* L. Cao, S. Krönke, J. Stockhofe, J. Simonet, K. Sengstock, D.-S. Lühmann and P. Schmelcher*

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.

### Negative-quench-induced excitation dynamics for ultracold bosons in one-dimensional lattices

* S.I. Mistakidis, L. Cao and P. Schmelcher*

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.

## 2014

### Interaction quench induced multimode dynamics of finite atomic ensembles

*S. Mistakidis, L. Cao, P. Schmelcher*

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.

## 2013

### Quantum breathing dynamics of ultracold bosons in one-dimensional harmonic traps: Unraveling the pathway from few- to many-body systems

* R. Schmitz, S. Krönke, L. Cao, P. Schmelcher*

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.

### The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications

* L. Cao, S. Krönke, O. Vendrell, P. Schmelcher*

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.

### Non-equilibrium quantum dynamics of ultra-cold atomic mixtures: the multi-layer multi-configuration time-dependent Hartree method for bosons

* S. Krönke, L. Cao, O. Vendrell, P. Schmelcher*

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.

### Two-component few-fermion mixtures in a one-dimensional trap: Numerical versus analytical approach

*I. Brouzos, P. Schmelcher*

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)].

## 2012

### Controlled Excitation and Resonant Acceleration of Ultracold Few-Boson Systems by Driven Interactions in a Harmonic Trap

*I. Brouzos, P. Schmelcher*