**SFB 925**Light induced dynamics and control of correlated quantum systems

# Research Area C

### Project C1

#### Twisted superfluid phase in the extended one-dimensional Bose-Hubbard

* D.-S. Lühmann*

#### Breaking inversion symmetry in a state-dependent honeycomb lattice: Artificial graphene with tunable band gap

* M. Weinberg, C. Staarmann, C. Ölschläger, J. Simonet, K. Sengstock*

Here, we present the application of a novel method for controlling the geometry of a state-dependent honeycomb lattice: The energy offset between the two sublattices of the honeycomb structure can be adjusted by rotating the atomic quantization axis. This enables us to continuously tune between a homogeneous graphene-like honeycomb lattice and a triangular lattice and to open an energy gap at the characteristic Dirac points. We probe the symmetry of the lattice with microwave spectroscopy techniques and investigate the behavior of atoms excited to the second energy band. We find a striking influence of the energy gap at the Dirac cones onto the lifetimes of atoms in the excited band.

#### Symmetry-broken momentum distributions induced by matter-wave diffraction during time-of-flight expansion of ultracold atoms

* M. Weinberg, O. Jürgensen, C. Ölschläger, D.-S. Lühmann, K. Sengstock, J. Simonet*

We study several effects which lead to symmetry-broken momentum distributions of quantum gases released from optical lattices. In particular, we demonstrate that interaction within the first milliseconds of the time-of-flight expansion can strongly alter the measurement of the initial atomic momentum distribution. For bosonic mixtures in state-dependent lattices, inter-species scattering processes lead to a symmetry breaking in momentum space. The underlying mechanism is identified to be diffraction of the matter wave from the total density lattice, which gives rise to a timedependent interaction potential. Our findings are of fundamental relevance for the interpretation of time-of-flight measurements and for the study of exotic quantum phases such as the twisted superfluid. Beyond that, the observed matter-wave diraction can also be used as an interferometric probe. In addition, we report on diffraction from the state-dependent standing light field, which leads to the same symmetry-broken momentum distributions, even for single component condensates.

#### Twisted complex superfluids in optical lattices

*O. Jürgensen, K. Sengstock, D.-S. Lühmann*

We show that correlated pair tunneling drives a phase transition to a twisted superfluid with a complex order parameter. This unconventional superfluid phase spontaneously breaks the time-reversal symmetry and is characterized by a twisting of the complex phase angle between adjacent lattice sites. We discuss the entire phase diagram of the extended Bose--Hubbard model for a honeycomb optical lattice showing a multitude of quantum phases including twisted superfluids, pair superfluids, supersolids and twisted supersolids. Furthermore, we show that the nearest-neighbor interactions breaks the inversion symmetry of the lattice and gives rise to dimerized density-wave insulators, where particles are delocalized on dimers. For two components, we find twisted superfluid phases with strong correlations between the species already for surprisingly small pair-tunneling amplitudes. Interestingly, this ground state shows an infinite degeneracy ranging continuously from a supersolid to a twisted superfluid.

#### Multiphoton interband excitations of quantum gases in driven optical lattices

* M. Weinberg, C. Ölschläger, C. Sträter, S. Prelle, A. Eckardt, K. Sengstock, J. Simonet*

We report on the observation of multiphoton absorption processes for quantum gases in shaken light crystals. Periodic inertial forcing, induced by a spatial motion of the lattice potential, drives multiphoton interband excitations of up to the 9th order. The occurrence of such excitation features is systematically investigated with respect to the potential depth and the driving amplitude. Ab initio calculations of resonance positions as well as numerical evaluation of their strengths exhibit a good agreement with experimental data. In addition our findings set the stage for reaching novel phases of quantum matter by tailoring appropriate driving schemes.

#### 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.

#### Dimerized Mott insulators in hexagonal optical lattices

*O. Jürgensen, D.-S. Lühmann*

We study bosonic atoms in optical honeycomb lattices with anisotropic tunneling and find dimerized Mott insulator (MI) phases with fractional filling. These incompressible insulating phases are characterized by an interaction-driven localization of particles in respect to the individual dimers and large local particle-number fluctuations within the dimers. We calculate the ground-state phase diagrams and the excitation spectra using an accurate cluster mean-field method. The cluster treatment enables us to probe the fundamental excitations of the dimerized MI where the excitation gap is dominated by the intra-dimer tunneling amplitude. This allows the distinction from normal Mott insulating phases gapped by the on-site interaction. In addition, we present analytical results for the phase diagram derived by a higher-order strong-coupling perturbative expansion approach. By computing finite lattices with large diameters the influence of a harmonic confinement is discussed in detail. It is shown that a large fraction of atoms forms the dimerized MI under experimental conditions. The necessary anisotropic tunneling can be realized either by periodic driving of the optical lattice or by engineering directly a dimerized lattice potential. The dimers can be mapped to their antisymmetric states creating a lattice with coupled p-orbitals.

#### Spin Orbit Coupling in Periodically Driven Optical Lattices

* J. Struck, J. Simonet, K. Sengstock*

We propose a novel experimental scheme for the emulation of spin-orbit coupling for ultracold, neutral atoms trapped in a one-dimensional lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons.

A time dependent magnetic field gradient periodically drives the atoms, which can lead to complex valued tunnel matrix elements, equivalent to a gauge dependent shift of the dispersion relation for a 1D lattice. For opposite spin states, the dispersion relations are shifted in opposite direction due to the inverted drive for both states. An additional radio-frequency coupling between the spin states leads to a mixing of the spin dispersion relations and a spin-orbit gap in the band structure.

Phys. Rev. A 90, 031601(R) (2014)

http://arxiv.org/abs/1407.1953

#### Quantum phases in tunable state-dependent hexagonal optical lattices

* D.-S. Lühmann, O. Jürgensen, M. Weinberg, J. Simonet, P. Soltan-Panahi, K. Sengstock*

We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various geometries accessible with this lattice setup and present a novel scheme to control the energy offset with external magnetic fields. The competition of the on-site interaction with the offset energy leads to Mott phases characterized by population imbalances between the sublattices. For the definition of an optimal Hubbard model, we demonstrate a scheme that allows for the efficient computation of Wannier functions. Using a cluster mean-field method, we compute the phase diagrams and provide a universal representation for arbitrary energy offsets. We find good agreement with the experimental data for the superfluid to Mott insulator transition.

#### Tunable gauge potential for spinless particles in driven lattices

*J. Simonet, J. Struck, M. Weinberg, C. Ölschläger, P. Hauke, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger*

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. A suitable periodic shaking of the lattice allows to engineer a Peierls phase for the hopping parameters. This scheme thus allows one to address the atomic internal degrees of freedom independently. We experimentally demonstrate the realisation of such artificial potentials in a 1D lattice, which generate ground state superfluids at arbitrary non-zero quasimomentum [4].

This scheme offers fascinating possibilities to emulate synthetic magnetic fields in 2D lattices. In a triangular lattice, continuously tunable staggered fluxes are realised. Spontaneous symmetry breaking has recently been observed for a π-flux [23]. With the presented scheme, we are now able to study the influence of a small symmetry breaking perturbation.

#### Engineering Ising-XY spin models in a triangular lattice using tunable artificial gauge fields

*J. Struck, M. Weinberg, C. Ölschläger, P. Windpassinger, J. Simonet, K. Sengstock, R. Höppner, P. Hauke, A. Eckardt, M. Lewenstein, L. Mathey*

#### Cluster Gutzwiller method for bosonic lattice systems

*D.-S. Lühmann*

A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.

#### Non-Abelian gauge fields and topological insulators in shaken optical lattices

*P. Hauke, O. Tielemann, A. Celi, C. Ölschläger, J. Simonet, J. Struck, M. Weinberg, P. Windpassinger, K. Sengstock, M. Lewenstein, A. Eckardt*

Time-periodic driving offers a low-demanding method to generate artificial gauge fields in optical lattices. We demonstrate that it is a powerful and versatile tool for engineering two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagom\'e lattice. We propose the realization of a topological or a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.

Phys. Rev. Lett. 109, 145301 (2012)

http://www.arxiv.org/abs/1205.1398

#### Tunable gauge potential for neutral and spinless particles in driven lattices

* J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, P. Windpassinger*

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics.

#### Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices

* P. Soltan-Panahi, D.-S. Lühmann, J. Struck, P. Windpassinger, K. Sengstock*

Orbital physics plays a significant role for a vast number of important phenomena in complex condensed matter systems such as high-Tc superconductivity and unconventional magnetism. In contrast, phenomena in superfluids - especially in ultracold quantum gases - are commonly well described by the lowest orbital and a real order parameter. Here, we report on the observation of a novel multi-orbital superfluid phase with a complex order parameter in binary spin mixtures. In this unconventional superfluid, the local phase angle of the complex order parameter is continuously twisted between neighboring lattice sites. The nature of this twisted superfluid quantum phase is an interaction-induced admixture of the p-orbital favored by the graphene-like band structure of the hexagonal optical lattice used in the experiment. We observe a second-order quantum phase transition between the normal superfluid (NSF) and the twisted superfluid phase (TSF) which is accompanied by a symmetry breaking in momentum space. The experimental results are consistent with calculated phase diagrams and reveal fundamentally new aspects of orbital superfluidity in quantum gas mixtures. Our studies might bridge the gap between conventional superfluidity and complex phenomena of orbital physics.

Nature Physics 8, 71–75 (2012)

http://arxiv.org/abs/1104.3456v1

#### Quantum Simulation of Frustrated Classical Magnetism in Triangular Optical Lattices

* J. Struck, C. Ölschläger, R. Le Targat, P. Soltan-Panahi, A. Eckardt, M. Lewenstein, P. Windpassinger, K. Sengstock*

Magnetism plays a key role in modern technology and stimulates research in several branches of condensed matter physics. Although the theory of classical magnetism is well developed, the demonstration of a widely tunable experimental system has remained an elusive goal. We present the realization of a large-scale simulator for classical magnetism on a triangular lattice by exploiting the particular properties of a quantum system. We use the motional degrees of freedom of atoms trapped in an optical lattice to simulate a large variety of magnetic phases: ferromagnetic, antiferromagnetic, and even frustrated spin configurations. A rich phase diagram is revealed with different types of phase transitions. Our results provide a route to study highly debated phases like spin-liquids as well as the dynamics of quantum phase transitions.

### Project C2

#### Orbital optical lattices with bosons

*T. Kock, C. Hippler, A. Ewerbeck, and A. Hemmerich*

This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalisation process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th band can be tuned such that two inequivalent energetically degenerate energy minima arise at the X±-points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Gamma-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.

J. Phys. B: At. Mol. Opt. Phys. 49, 042001 (2016)

http://arxiv.org/abs/1601.00500

#### Observation of chiral superfluid order by matter wave interference

* T. Kock, M. Ölschläger, A. Ewerbeck, W.-M. Huang, L. Mathey, A. Hemmerich*

The breaking of time reversal symmetry via the spontaneous formation of chiral order is ubiquitous in nature. Here, we present an unambiguous demonstration of this phenomenon for atoms Bose-Einstein condensed in the second Bloch band of an optical lattice. As a key tool we use a matter wave interference technique, which lets us directly observe the phase properties of the superfluid order parameter and allows us to reconstruct the spatial geometry of certain low energy excitations, associated with the formation of domains of different chirality. Our work marks a new era of optical lattices where orbital degrees of freedom play an essential role for the formation of exotic quantum matter, similarly as in electronic systems.

Physical Review Letters 114, 115301 (2015)

http://arxiv.org/abs/1411.3483

#### Controlling coherence via tuning of the population imbalance in a bipartite optical lattice

* M. Di Liberto, T. Comparin , T. Kock, M. Ölschäger, A. Hemmerich, C. Morais Smith*

The control of transport properties is a key tool at the basis of many technologically relevant effects in condensed matter. The clean and precisely controlled environment of ultracold atoms in optical lattices allows one to prepare simplified but instructive models, which can help to better understand the underlying physical mechanisms. We show that by tuning a structural deformation of the unit cell in a bipartite optical lattice, one can induce a phase transition from a superfluid into various Mott insulating phases forming a shell structure in the superimposed harmonic trap. The Mott shells are identified via characteristic features in the visibility of Bragg maxima in momentum spectra. The experimental findings are explained by Gutzwiller mean-field and quantum Monte Carlo calculations. Our system bears similarities with the loss of coherence in cuprate superconductors, known to be associated with the doping induced buckling of the oxygen octahedra surrounding the copper sites.

#### Proposed formation and dynamical signature of a chiral Bose liquid in an optical lattice

* X. Li, A. Paramekanti, A. Hemmerich, W. Vincent Liu*

Recent experiments on p-orbital atomic bosons have suggested the emergence of a spectacular ultracold superfluid with staggered orbital currents in optical lattices. This raises fundamental questions concerning the effects of thermal fluctuations as well as possible ways of directly observing such chiral order. Here we show via Monte Carlo simulations that thermal fluctuations destroy this superfluid in an unexpected two-step process, unveiling an intermediate normal phase with spontaneously broken time-reversal symmetry, dubbed a ‘chiral Bose liquid’. For integer fillings (n≥2) in the chiral Mott regime, thermal fluctuations are captured by an effective orbital Ising model, and Onsager’s powerful exact solution is adopted to determine the transition from this intermediate liquid to the para- orbital normal phase at high temperature. A lattice quench is designed to convert the staggered angular momentum, previously thought by experts difficult to directly probe, into coherent orbital oscillations, providing a time-resolved dynamical signature of chiral order.

Nature Communications 5, 3205 (2014)

http://arxiv.org/abs/1309.0523

#### Interaction-induced chiral px ± i py superfluid order of bosons in an optical lattice

*M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith, A. Hemmerich*

The study of superconductivity with unconventional order is complicated in condensed matter systems by their immense complexity. Optical lattices with their exceptional precision and control allow one to emulate superfluidity avoiding many of the complications of condensed matter. A promising approach to realize unconventional superfluid order is to employ orbital degrees of freedom in higher Bloch bands. In recent work, indications were found that bosons condensed in the second band of an optical chequerboard lattice might exhibit px ± i py order. Here we present experiments, which provide strong evidence for the emergence of px ± i py order driven by the interaction in the local p-orbitals. We compare our observations with a multi-band Hubbard model and find excellent quantitative agreement.

New Journal of Physics 15, 083041 (2013)

http://arxiv.org/abs/1305.1177

#### Topologically induced avoided band crossing in an optical chequerboard lattice

* M. Ölschläger, G. Wirth, T. Kock, A. Hemmerich*

We report on the condensation of bosons in the 4th band of an optical chequerboard lattice providing a topologically induced avoided band crossing involving the second, third, and fourth bands. When the condensate is slowly tuned through the avoided crossing, accelerated band relaxation arises and the zero momentum approximately C4-invariant condensate wave function acquires finite momentum order and reduced C2 symmetry. For faster tuning Landau-Zener oscillations between different superfluid orders arise, which are used to characterize the avoided crossing.

Physical Review Letters, 108, 075302 (2012)

http://lanl.arxiv.org/abs/1110.3716

#### Topological semimetal in a fermionic optical lattice

* K. Sun, W. V. Liu, A. Hemmerich, S. Das Sarma*

Optical lattices have an important role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal3 optical lattices opens up a new avenue towards discovering novel quantum states of matter that have no prior analogues in solid-state electronic materials. Here, we predict that an exotic topological semimetal emerges as a parity-protected gapless state in the orbital bands of a two-dimensional fermionic optical lattice. This new quantum state is characterized by a parabolic band-degeneracy point with Berry flux 2 Pi, in sharp contrast to the Pi-flux of Dirac points as in graphene.We showthat the appearance of this topological liquid is universal for all latticeswith D4 point-group symmetry, as long as orbitals with opposite parities hybridize strongly with each other and the band degeneracy is protected by odd parity. Turning on inter-particle repulsive interactions, the system undergoes a phase transition to a topological insulator whose experimental signature includes chiral gapless domain-wall modes, reminiscent of quantumHall edge states.

#### Unconventional Superfluid Order in the F Band of a Bipartite Optical Square Lattice

* M. Ölschläger, G. Wirth, A. Hemmerich*

We report on the first observation of bosons condensed into the energy minima of an F band of a bipartite square optical lattice. Momentum spectra indicate that a truly complex-valued staggered angular momentum superfluid order is established. The corresponding wave function is composed of alternating local F_(2x^3-3x)±iF_(2y^3-3y) orbits and local S orbits residing in the deep and shallow wells of the lattice, which are arranged as the black and white areas of a checkerboard. A pattern of staggered vortical currents arises, which breaks time-reversal symmetry and the translational symmetry of the lattice potential. We have measured the populations of higher order Bragg peaks in the momentum spectra for varying relative depths of the shallow and deep lattice wells and find remarkable agreement with band calculations.

#### Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice

*G. Wirth, M. Ölschläger, A. Hemmerich*

The successful emulation of the Hubbard model in optical lattices has stimulated extensive efforts to extend their scope to also capture more complex, incompletely understood scenarios of many-body physics. A promising approach is to consider higher bands, where the orbital degree of freedom gives rise to a structural diversity that is directly relevant, for example, for the physics of strongly correlated electronic matter. Here we report evidence for the formation of a superfluid in the P-band of a bipartite optical square lattice with S-orbits and P-orbits arranged in a chequerboard pattern. The observed momentum spectra feature cross-dimensional coherence with a lifetime of nearly 20 ms. Depending on the value of a small adjustable anisotropy of the lattice, our findings are explained either by real-valued striped superfluid order parameters with different orientations Px±Py, or by a complex-valued Px±iPy order parameter, which breaks time-reversal symmetry.

Nature Physics 7, 147 (2011), featured in News & Views ibid.

#### Competing Superconducting States for Ultracold Atoms in Optical Lattices with Artificial Staggered Magnetic Field

* L.-K. Lim, A. Lazarides, A. Hemmerich, C. Morais Smith*

Abstract: We study superconductivity in an ultracold Bose-Fermi mixture loaded into a square optical lattice subjected to a staggered flux. While the bosons form a superfluid at very low temperature and weak interaction, the interacting fermions experience an additional long-ranged attractive interaction mediated by phonons in the bosonic superfluid. This leads us to consider a generalized Hubbard model with on-site and nearest-neighbor attractive interactions, which give rise to two competing superconducting channels. We use the Bardeen-Cooper-Schrieffer theory to determine the regimes where distinct superconducting ground states are stabilized, and find that the non-local pairing channel favors a superconducting ground state which breaks both the gauge and the lattice symmetries, thus realizing unconventional superconductivity. Furthermore, the particular structure of the single-particle spectrum leads to unexpected consequences, for example, a dome-shaped superconducting region in the temperature versus filing fraction phase diagram, with a normal phase that comprises much richer physics than a Fermi-liquid. Notably, the relevant temperature regime and coupling strength is readily accessible in state of the art experiments with ultracold trapped atoms.

#### Strongly interacting two-dimensional Dirac fermions

* L.-K. Lim, A. Lazarides, A. Hemmerich, C. Morais Smith*

We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s-wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.

### Project C3

#### Dynamics of Ultracold Quantum Gases in the Dissipative Fermi-Hubbard Model

* K. Sponselee, L. Freystatzky, B. Abeln, M. Diem, B. Hundt, A. Kochanke, T. Ponath, B. Santra, L. Mathey, K. Sengstock and C. Becker*

Abstract. We employ metastable ultracold 173-Yb atoms to study dynamics in the 1D dissipative Fermi-Hubbard model experimentally and theoretically, and observe a complete inhibition of two-body losses after initial fast transient dynamics. We attribute the suppression of particle loss to the dynamical generation of a highly entangled Dicke state. For several lattice depths and for two- and six-spin component mixtures we find very similar dynamics, showing that the creation of strongly correlated states is a robust and universal phenomenon. This offers interesting opportunities for precision measurements.

#### Relaxation dynamics of a closed high-spin Fermi system far from equilibrium

* U. Ebling, J. S. Krauser, N. Fläschner, K. Sengstock, C. Becker, M. Lewenstein, A. Eckardt*

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold high-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes, which occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.

Phys. Rev. X 4, 021011 (2014)

http://arxiv.org/abs/1312.6704

#### Detecting quadrupole interactions in ultracold Fermi gases

*M. Lahrz, M. Lemeshko, K. Sengstock, C. Becker, L. Mathey*

#### Creation of Quantum-Degenerate Gases of Ytterbium in a Compact 2D-/3D-MOT Setup

*S. Dörscher, A. Thobe, B. Hundt, A. Kochanke, R. Le Targat, P. Windpassinger, C. Becker, K. Sengstock*

*The following article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://rsi.aip.org*

We report on the first experimental setup based on a 2D-/3D-MOT scheme to create both Bose-Einstein condensates and degenerate Fermi gases of several ytterbium isotopes. Our setup does not require a Zeeman slower and offers the flexibility to simultaneously produce ultracold samples of other atomic species. Furthermore, the extraordinary optical access favors future experiments in optical lattices. A 2D-MOT on the strong 1S0-1P1 transition captures ytterbium directly from a dispenser of atoms and loads a 3D-MOT on the narrow 1S0-3P1 intercombination transition. Subsequently, atoms are transferred to a crossed optical dipole trap and cooled evaporatively to quantum degeneracy.

Review of Scientific Instruments 84, 043109

http://arxiv.org/abs/1303.1105

#### Intrinsic Photoconductivity of Ultracold Fermions in Optical Lattices

* J. Heinze, J. S. Krauser, N. Fläschner, B. Hundt, S. Götze, A. Itin, L. Mathey, K. Sengstock, C. Becker*

We report on the first experimental observation of a persistent alternating photocurrent in an ultracold gas of fermionic atoms in an optical lattice. The dynamics is induced and sustained by an external harmonic confinement. We find a counterintuitively momentum-dependent oscillation frequency for excited particles and a fast decay of holes which we attribute to spatial trapping. Lifetime measurements reveal a significant enhancement of particle-hole recombination with increasing interactions.

Phys. Rev. Lett. 110, 085302 (2013)

http://arxiv.org/abs/1208.4020

### Project C4

#### Detecting Friedel oscillations in ultracold Fermi gases

* Keno Riechers, Klaus Hueck, Niclas Luick, Thomas Lompe, Henning Moritz*

Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which a potential barrier provokes in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.

Eur. Phys. J. D 71, 232 (2017)

http://lanl.arxiv.org/abs/1704.06626

#### Two-Dimensional Homogeneous Fermi Gases

* Klaus Hueck, Niclas Luick, Lennart Sobirey, Jonas Siegl, Thomas Lompe, Henning Moritz*

We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as non-local properties of strongly interacting many-body systems. As a first measurement, we use a local probe to extract the equation of state (EOS) of a non-interacting Fermi gas. We then perform matter wave focusing to extract its momentum distribution and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of strongly interacting homogeneous 2D gases in the crossover between attractively interacting fermions and deeply-bound bosonic molecules.

PRL 120, 060402 (2018).

http://lanl.arxiv.org/abs/1704.06315

#### Calibrating High Intensity Absorption Imaging of Ultracold Atoms

* Klaus Hueck, Niclas Luick, Lennart Sobirey, Jonas Siegl, Thomas Lompe, Henning Moritz, Logan W. Clark, Cheng Chin*

Absorption imaging of ultracold atoms is the foundation for quantitative extraction of information from experiments with ultracold atoms. Due to the limited exposure time available in these systems, the signal-to-noise ratio is largest for high intensity absorption imaging where the intensity of the imaging light is on the order of the saturation intensity. In this case, the absolute value of the intensity of the imaging light enters as an additional parameter making it more sensitive to systematic errors. Here, we present a novel and robust technique to determine the imaging intensity in units of the effective saturation intensity to better than 5%. We do this

by measuring the momentum transferred to the atoms by the imaging light while varying its intensity. We further utilize the method to quantify the purity of the polarization of the imaging light and to determine the correct

imaging detuning.

Opt. Express 25, 8670-8679 (2017)

https://arxiv.org/abs/1702.01943

#### Suppression of kHz-Frequency Switching Noise in Digital Micro-Mirror Devices

* Klaus Hueck, Anton Mazurenko, Niclas Luick, Thomas Lompe, Henning Moritz*

igh resolution digital micro-mirror devices (DMD) make it possible to produce nearly arbitrary light fields with high accuracy, reproducibility and low optical aberrations. However, using these devices to trap and manipulate ultracold atomic systems for e.g. quantum simulation is often complicated by the presence of kHz-frequency switching noise. Here we demonstrate a simple hardware extension that solves this problem and makes it possible to produce truly static light fields. This modification leads to a 47 fold increase in the time that we can hold ultracold 6Li atoms in a dipole potential created with the DMD. Finally, we provide reliable and user friendly APIs written in Matlab and Python to control the DMD.

Rev. Sci. Instrum. 88, 016103 (2017)

https://arxiv.org/abs/1611.03397

#### Sudden and slow quenches into the antiferromagnetic phase of ultracold fermions

*M. Ojekhile, R. Höppner, H. Moritz, L. Mathey*

#### Probing superfluidity of Bose-Einstein condensates via laser stirring

*Vijay Pal Singh, Wolf Weimer, Kai Morgener, Jonas Siegl, Klaus Hueck, Niclas Luick, Henning Moritz, Ludwig Mathey*

We investigate the superfluid behavior of a Bose-Einstein condensate of 6Li molecules. In the experiment by Weimer et al., Phys. Rev. Lett. 114, 095301 (2015) a condensate is stirred by a weak, red-detuned laser beam along a circular path around the trap center. The rate of induced heating increases steeply above a velocity vc, which we define as the critical velocity. Below this velocity, the moving beam creates almost no heating. In this paper, we demonstrate a quantitative understanding of the critical velocity. Using both numerical and analytical methods, we identify the non-zero temperature, the circular motion of the stirrer, and the density profile of the cloud as key factors influencing the magnitude of vc. A direct comparison to the experimental data shows excellent agreement.

Phys. Rev. A 93, 023634 (2016)

http://lanl.arxiv.org/abs/1509.02168

#### The critical velocity in the BEC-BCS crossover

* W. Weimer, K. Morgener, V. P. Singh, J. Siegl, K. Hueck, N. Luick, L. Mathey, H. Moritz*

We map out the critical velocity in the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity with ultracold 6Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity vc. In the same samples, we measure the speed of sound vs by exciting density waves and compare the results to the measured values of vc. We perform numerical simulations in the BEC regime and find very good agreement, validating the approach. In the strongly correlated regime, where theoretical predictions only exist for the speed of sound, our measurements of vc provide a testing ground for theoretical approaches.

Phys. Rev. Lett. 114, 095301 (2015)

http://arxiv.org/abs/1408.5239

#### Interferometric Measurement of Local Spin-Fluctuations in a Quantum Gas

* J. Meineke, J.-P. Brantut, D. Stadler, T. Mueller, H. Moritz, T. Esslinger*

Ultracold gases provide a controlled environment that is ideal for studying many intriguing phenomena associated with quantum correlated systems. Current efforts are directed towards the identification of magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, a mapping of the spin polarization of the atoms to the state of a single-mode light beam has been proposed. Here we introduce a quantum-limited interferometer that realizes such an atom–light interface with high spatial resolution. We measure the probability distribution of the local spin polarization in a trapped Fermi gas, showing a reduction of spin fluctuations by up to 4.6(3) dB below shot noise in weakly interacting Fermi gases, and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.

The subtle interplay between quantum-statistics and interactions is at the origin of many intriguing quantum phenomena connected to superfluidity and quantum magnetism. The controlled setting of ultracold quantum gases is well suited to study such quantum correlated systems. Current efforts are directed towards the identification of their magnetic properties, as well as the creation and detection of exotic quantum phases. In this context, it has been proposed to map the spin-polarization of the atoms to the state of a single-mode light beam. Here we introduce a quantum-limited interferometer realizing such an atom-light interface with high spatial resolution. We measure the probability distribution of the local spin-polarization in a trapped Fermi gas showing a reduction of spin-fluctuations by up to 4.6(3) dB below shot-noise in weakly interacting Fermi gases and by 9.4(8) dB for strong interactions. We deduce the magnetic susceptibility as a function of temperature and discuss our measurements in terms of an entanglement witness.

Nature Physics 8, 454 (2012)

http://xxx.lanl.gov/abs/1202.5250

#### High-resolution imaging and manipulation of ultracold fermions

* B. Zimmermann, T. Mueller, J. Meineke, T. Esslinger, H. Moritz*

We report on the local probing and manipulation of an ultracold Fermi gas on the length scale of one micrometer, i.e. of the order of the Fermi wavelength. The essential tool of our experimental setup is a pair of identical, high-resolution microscope objectives. One of the microscope objectives allows local imaging of the trapped Fermi gas of 6Li atoms with a maximum resolution of 660 nm, while the other enables the generation of arbitrary optical dipole potentials on the same length scale. Employing a 2D acousto-optical deflector, we demonstrate the formation of several trapping geometries including a tightly focussed single optical dipole trap, a 4x4-site two-dimensional optical lattice and a 8-site ring lattice configuration. Furthermore, we show the ability to load and detect a small number of atoms in these trapping potentials. A site separation of down to one micrometer in combination with the low mass of 6Li results in tunneling rates which are sufficiently large for the implementation of Hubbard-models with the designed geometries.

#### Local observation of antibunching in a trapped Fermi gas

* T. Müller, B. Zimmermann, J. Meineke, J.-P. Brantut, T. Esslinger, H. Moritz*

For a viewpoint written by Chris Westbrook for "Physics", follow this link.

Local density fluctuations and density profiles of a Fermi gas are measured in situ and analyzed. In the quantum degenerate regime, the weakly interacting 6Li gas shows a suppression of the density fluctuations compared to the nondegenerate case, where atomic shot noise is observed. This manifestation of antibunching is a direct result of the Pauli principle and constitutes a local probe of quantum degeneracy. We analyze our data using the predictions of the fluctuation-dissipation theorem and the local density approximation, demonstrating a fluctuation-based temperature measurement.

Phys. Rev. Lett. 105, 040401 (2010)

http://lanl.arxiv.prg/abs/1005.0302

#### A Mott insulator of fermionic atoms in an optical lattice

* R. Jördens, N. Strohmaier, K. Günter, H. Moritz, T. Esslinger*

Strong interactions between electrons in a solid material can lead to surprising properties. A prime example is the Mott insulator, in which suppression of conductivity occurs as a result of interactions rather than a filled Bloch band. Proximity to the Mott insulating phase in fermionic systems is the origin of many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. The Hubbard model, which encompasses the essential physics of the Mott insulator, also applies to quantum gases trapped in an optical lattice. It is therefore now possible to access this regime with tools developed in atomic physics. However, an atomic Mott insulator has so far been realized only with a gas of bosons7, which lack the rich and peculiar nature of fermions. Here we report the formation of a Mott insulator of a repulsively interacting two-component Fermi gas in an optical lattice. It is identified by three features: a drastic suppression of doubly occupied lattice sites, a strong reduction of the compressibility inferred from the response of double occupancy to an increase in atom number, and the appearance of a gapped mode in the excitation spectrum. Direct control of the interaction strength allows us to compare the Mott insulating regime and the non-interacting regime without changing tunnel-coupling or confinement. Our results pave the way for further studies of the Mott insulator, including spin-ordering and ultimately the question of d-wave superfluidity.

### Project C5

#### Topological Varma superfluid in optical lattices

* M. Di Liberto, A. Hemmerich, and C. Morais Smith*

Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a ten-fold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.

Physical Review Letters 117, 163001 (2016)

https://arxiv.org/abs/1604.06055

#### In-situ observation of optomechanical Bloch oscillations in an optical cavity

*H. Keßler, J. Klinder, B. Prasanna Venkatesh, Ch. Georges, A. Hemmerich*

It is shown experimentally that a Bose-Einstein condensate inside an optical cavity, operating in the regime of strong cooperative coupling, responds to an external force by an optomechanical Bloch oscillation, which can be directly observed in the light leaking out of the cavity. Previous theoretical work predicts that the frequency of this oscillation matches with that of conventional Bloch oscillations such that its in-situ monitoring may help to increase the data acquisition speed in precision force measurements.

New Journal of Physics 18, 102001 (2016)

https://arxiv.org/abs/1606.08386

#### Observation of a superradiant Mott insulator in the Dicke-Hubbard model

* J. Klinder, H. Keßler, M. Reza Bakhtiari, M. Thorwart, and A. Hemmerich*

It is well known that the bosonic Hubbard model possesses a Mott insulator phase. Likewise, it is known that the Dicke model exhibits a self-organized superradiant phase. By implementing an optical lattice inside of a high finesse optical cavity both models are merged such that an extended Hubbard model with cavity-mediated infinite range interactions arises. In addition to a normal superfluid phase, two superradiant phases are found, one of them coherent and hence superfluid and one incoherent Mott insulating.

Physical Review Letters 115, 230403 (2015)

http://arxiv.org/abs/1511.00850

#### Nonequilibrium phase transition of interacting bosons in an intra-cavity optical lattice

* M. R. Bakhtiari, A. Hemmerich, H. Ritsch, M. Thorwart*

We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity, which is weakly coupled to the vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model, which incorporates a single cavity mode, we include the collective back action of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the non-perturbative bosonic dynamical mean-field theory. With the system parameters adapted to recent experiments, we find a quantum phase transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.

Physical Review Letters 114, 123601 (2015)

http://arxiv.org/abs/1410.5735

#### Steering matter wave superradiance with an ultra-narrowband optical cavity

* H. Keßler, J. Klinder, M. Wolke, A. Hemmerich*

A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerated or decelerated by multiples of two recoil momenta. The instability boundary for the onset of matter wave superradiance is recorded and its main features are explained by a mean field model.

Physical Review Letters 113, 070404 (2014)

http://arxiv.org/abs/1407.4954

#### Optomechanical atom-cavity interaction in the sub-recoil regime

* H. Keßler, J. Klinder, M. Wolke, A. Hemmerich*

We study the optomechanical interaction of a Bose-Einstein condensate with a single longitudinal mode of an ultra-high finesse standing wave optical resonator. As a unique feature the resonator combines three extreme regimes, previously not realized together, i.e., strong cooperative coupling, cavity dominated scattering with a Purcell factor far above unity, and sub-recoil resolution provided by a cavity damping rate smaller than four times the single photon recoil frequency. We present experimental observations in good agreement with a two-mode model predicting highly non-linear dynamics with signatures as bistability, hysteresis, persistent oscillations, and superradiant back-scattering instabilities.

New Journal of Physics 16, 053008 (2014)

http://arxiv.org/abs/1403.3545

#### Cavity cooling below the recoil limit

* M. Wolke, J. Klinner, H. Keßler, A. Hemmerich*

Conventional laser cooling relies on repeated electronic excitations by near-resonant light, which constrains its area of application to a selected number of atomic species prepared at moderate particle densities. Optical cavities with sufficiently large Purcell factors allow for laser cooling schemes avoiding these limitations. Here, we report on an atom-cavity system, combining a Purcell factor above 40 with a cavity bandwidth below the recoil frequency associated with the kinetic energy transfer in a single photon scattering event. This lets us access a yet unexplored regime of atom-cavity interactions, in which the atomic motion can be manipulated by targeted dissipation with sub-recoil resolution. We demonstrate cavity-induced heating of a Bose-Einstein condensate and subsequent cooling at particle densities and temperatures incompatible with conventional laser cooling.

#### Normal-Mode-Splitting and Mechanical Effects of an Optical Lattice in a Ring Cavity

* J. Klinner, M. Lindholdt, B. Nagorny, A. Hemmerich*

A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.

### Project C6

#### Symmetry effects on the spin switching of adatoms

* C. Hübner, B. Baxevanis, A. A. Khajetoorians, D. Pfannkuche*

Highly symmetric magnetic environments have been suggested to stabilize the magnetic information stored in magnetic adatoms on a surface. Utilized as memory devices such systems are subjected to electron tunneling and external magnetic fields. We analyze theoretically how such perturbations affect the switching probability of a single quantum spin for two characteristic symmetries encountered in recent experiments and suggest a third one that exhibits robust protection against surface-induced spin flips. Further we illuminate how the switching of an adatom spin exhibits characteristic behavior with respect to low energy excitations from which the symmetry of the system can be inferred.

#### Isospin correlations in two-partite hexagonal optical lattices

* M. Prada, E.-M. Richter, D. Pfannkuche*

Two-component mixtures in optical lattices reveal a rich variety of different phases. We employ an exact diagonalization method to obtain the relevant correlation functions in hexagonal optical lattices which characterize those phases. We relate the occupation difference of the two species to the magnetic polarization. “Iso” -magnetic correlations disclose the nature of the system, which can be of easy-axis type, bearing phase segregation, or of easy-plane type, corresponding to super-counter-fluidity. In the latter case, the correlations reveal easy-plane segregation, involving a highly entangled state. We identify striking correlated supersolid phases appearing within the superfluid limit.

#### Doublon Relaxation in the Bose-Hubbard Model

*A. L. Chudnovskiy, D. M. Gangardt, A. Kamenev*

### Project C7

#### 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.

#### 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.

#### 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.

#### 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.

#### 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)].

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

*I. Brouzos, P. Schmelcher*

### Project C8

#### Hydration shell effects in the relaxation dynamics of photoexcited Fe-II complexes in water

*P. Nalbach, A. J. A. Achner, M. Frey, M. Grosser, C. Bressler, M. Thorwart*

We study the relaxation dynamics of photoexcited Fe-II complexes dissolved in water and identify the relaxation pathway which the molecular complex follows in presence of a hydration shell of bound water at the interface between the complex and the solvent. Starting from a low-spin state, the photoexcited complex can reach the high-spin state via a cascade of different possible transitions involving electronic as well as vibrational relaxation processes. By numerically exact path integral calculations for the relaxational dynamics of a continuous solvent model, we find that the vibrational life times of the intermittent states are of the order of a few ps. Since the electronic rearrangement in the complex occurs on the time scale of about 100 fs, we find that the complex first rearranges itself in a high-spin and highly excited vibrational state, before it relaxes its energy to the solvent via vibrational relaxation transitions. By this, the relaxation pathway can be clearly identified. We find that the life time of the vibrational states increases with the size of the complex (within a spherical model), but decreases with the thickness of the hydration shell, indicating that the hydration shell acts as an additional source of fluctuations.

#### Photon-assisted confinement-induced resonances for ultracold atoms

*V. Leyton, M. Roghani, V. Peano, M. Thorwart*

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi’s pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The modulation opens additional photon-assisted resonant scattering channels. Applying the Bethe-Peierls boundary condition, we obtain the general scattering solution of the time-dependent Floquet-Schrödinger equation which is universal at low energies. The effective one-dimensional scattering length can be controlled by the external driving.

#### Quantification of non-Markovian effects in the Fenna-Matthews-Olson complex

*C. Mujica-Martinez, P. Nalbach, M. Thorwart*

The excitation energy transfer dynamics in the Fenna-Matthews-Olson complex is quantified in terms of a non-Markovianity measure based on the time evolution of the trace distance of two quantum states. We use a system description derived from experiments and different environmental fluctuation spectral functions, which are obtained either from experimental data or from molecular dynamics simulations. These exhibit, in all cases, a nontrivial structure with several peaks attributed to vibrational modes of the pigment-protein complex. Such a structured environmental spectrum can, in principle, give rise to strong non-Markovian effects. We present numerically exact real-time path-integral calculations for the transfer dynamics and find, in all cases, a monotonic decrease of the trace distance with increasing time which renders a Markovian description valid.

#### Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments

*D. Pagel, P. Nalbach, A. Alvermann, H. Fehske, M. Thorwart*

We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation–dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti–Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.

#### Crossover from coherent to incoherent quantum dynamics due to sub-Ohmic dephasing

*P. Nalbach, M. Thorwart*

We report exact results for the influence of purely sub-Ohmic dephasing on the dynamics of a quantum two-level system. From response functions, we determine a crossover coupling strength between oscillatory coherent and overdamped dynamics. Surprisingly, we find no overdamping even at arbitrary large dephasing for spectra with spectral exponent.

#### Organic pi-conjugated copolymers as molecular charge qubits

*C. A. Mujica-Martinez, P. Nalbach, M. Thorwart*

We propose a design for molecular charge qubits based on π-conjugated block copolymers and determine their electronic structure as well as their vibrational active modes. By tuning the length of the oligomers, the tunnel coupling in the charge qubit and its decoherence properties due to molecular vibrations can be chemically engineered. Coherent oscillations result with quality factors of up to 104 at room temperature. In turn, the molecular vibrational spectrum induces strong non-Markovian electronic effects which support the survival of quantum coherence.

#### Noise-Induced Förster Resonant Energy Transfer between Orthogonal Dipoles in Photoexcited Molecules

* P. Nalbach, I. Pugliesi, H. Langhals, M. Thorwart*

#### Quantum noise properties of multiphoton transitions in driven nonlinear resonators

*V. Leyton, V. Peano, M. Thorwart*

We investigate the quantum noise properties of a weakly nonlinear Duffing resonator in the deep quantum regime, where only a few quanta are excited. This regime is dominated by the appearance of coherent multiphoton resonances in the nonlinear response of the resonator to the modulation. We determine simple expressions for the photon noise spectrum and find that the multiphoton resonances also induce a multiple peak structure in that spectrum. When the corresponding multiphoton Rabi oscillations are underdamped, zero-temperature quantum fluctuations determine comparable populations of all quasienergy states which belong to a resonant multiphoton doublet. Most interestingly, the quantum fluctuations probe the multiphoton transitions by inducing several peaks in the noise spectrum of the resonator observables. In particular, the noise of the photon number contains complete information about the multiphoton states and their stationary populations via pairs of nearly symmetric peaks at opposite frequencies. Their widths are determined by the damping of the Rabi oscillations and their heights are proportional to the stationary nonequilibrium populations. A finite detuning from a multiphoton resonance generates a quasielastic noise peak at zero frequency. In addition, we relate the stationary populations of the quasienergy states with an effective quantum temperature and discuss the role of a finite temperature.

### Project C9

#### Theory of enhanced interlayer tunneling in optically driven high Tc superconductors

*J. Okamoto, A. Cavalleri, L. Mathey*

Motivated by recent pump-probe experiments indicating enhanced coherent c-axis transport in underdoped YBCO, we study Josephson junctions periodically driven by optical pulses. We propose a mechanism for this observation by demonstrating that a parametrically driven Josephson junction shows an enhanced imaginary part of the low-frequency conductivity when the driving frequency is above the plasma frequency, implying an effectively enhanced Josephson coupling. We generalize this analysis to a bilayer system of Josephson junctions modeling YBCO. Again, the Josephson coupling is enhanced when the pump frequency is blue-detuned to either of the two plasma frequencies of the material. We show that the emergent driven state is a genuine, non-equilibrium superconducting state, in which equilibrium relations between the Josephson coupling, current fluctuations, and the critical current no longer hold.

#### Designing exotic many-body states of atomic spin and motion in photonic crystals

*M. T. Manzoni, L. Mathey, D. E. Chang*

Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. Here we investigate the strong coupling between atomic internal ("spin") degrees of freedom and motion, which arises from spin-dependent forces associated with the exchange of guided photons. We show that this system can realize a remarkable and extreme limit of quantum spin-orbital systems, where both the direct spin exchange between neighboring sites and the kinetic energy of the orbital motion vanish. We find that this previously unexplored system has a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Neel ordering, and a fractional magnetization plateau associated with trimer formation.

#### Magnus expansion approach to parametric oscillator systems in a thermal bath

*B. Zhu, T. Rexin, L. Mathey*

We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilization at second order, we find that the higher orders further renormalize the oscillator frequency, and additionally create a weakly renormalized effective temperature. The renormalized oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break-down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.

arXiv:1604.01010

http://arxiv.org/abs/1604.01010

* *

#### Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices

*Marlon Nuske, L. Mathey, Eite Tiesinga*

We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultracold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency ∣∣Uf|/2π in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter Δ. The oscillation frequency of Δ is not reproduced by treating the time evolution in mean-field theory. In our theory, the momentum noise (i.e., density-density) correlation functions oscillate at frequency ∣∣Uf|/2π as well as at its second harmonic. For a very deep lattice, with zero tunneling energy, the oscillations of momentum occupation numbers are undamped. Nonzero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. The damping occurs even for a finite-temperature initial BCS state, but not for a noninteracting Fermi gas. Furthermore, damping is stronger for larger order parameter and may therefore be used as a signature of the BCS state. Finally, our theory shows that the noise correlation functions in a honeycomb lattice will develop strong anticorrelations near the Dirac point.

#### Noise correlations of two-dimensional Bose gases

*V. P. Singh, L. Mathey*

We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.

#### Quantum Phases of quadrupolar Fermi gases in optical lattices

*S. G. Bhongale, L. Mathey, E. Zhao, S. F. Yelin, M. Lemeshko*

We introduce a new platform for quantum simulation of many-body systems based on non-spherical particles with zero dipole moment but possessing a significant value of the electric quadrupole moment. Considering a quadrupolar quantum gas trapped in a 2D optical lattice, we show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interactions results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and paves the way to create topological superfluid ground states of px + i py symmetry. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

Phys. Rev. Lett. 110, 155301 (2013)

http://arxiv.org/abs/1211.3317

#### Unconventional Spin Density Waves in Dipolar Fermi Gases

*S. G. Bhongale, L. Mathey, S. Tsai, C. W. Clark, E. Zhao*

The conventional spin density wave (SDW) phase (Overhauser, 1962), as found in antiferromagnetic metal for example (Fawcett 1988), can be described as a condensate of particle-hole pairs with zero angular momentum, $\ell=0$, analogous to a condensate of particle-particle pairs in conventional superconductors. While many unconventional superconductors with Cooper pairs of finite $\ell$ have been discovered, their counterparts, density waves with non-zero angular momenta, have only been hypothesized in two-dimensional electron systems (Nayak, 2000). Using an unbiased functional renormalization group analysis, we here show that spin-triplet particle-hole condensates with $\ell=1$ emerge generically in dipolar Fermi gases of atoms (Lu, Burdick, and Lev, 2012) or molecules (Ospelkaus et al., 2008; Wu et al.) on optical lattice. The order parameter of these exotic SDWs is a vector quantity in spin space, and, moreover, is defined on lattice bonds rather than on lattice sites. We determine the rich quantum phase diagram of dipolar fermions at half-filling as a function of the dipolar orientation, and discuss how these SDWs arise amidst competition with superfluid and charge density wave phases.

Phys. Rev. A 87, 043604 (2012)

http://arxiv.org/abs/1209.2671

#### Decay of a superfluid current of ultra-cold atoms in a toroidal trap

*Amy C. Mathey, Charles W. Clark, L. Mathey*

Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into rotation via a Gauss-Laguerre beam. A potential barrier is then placed in the trap to study the decay of the superflow. We find that the current decays via thermally activated phase slips, which can also be visualized as vortices crossing the barrier region in radial direction. Adopting the notion of critical velocity used in the experiment, we determine it to be lower than the local speed of sound at the barrier. This result is in agreement with the experimental findings, but in contradiction to the predictions of the Gross-Pitaevskii equation. This emphasizes the importance of thermal fluctuations in the experiment.