Session D09: Quantum Phases in Optical Lattices

Live

We discuss our recent measurements of the dynamics of global mass currents of ultracold $^{40}$K in a cubic optical lattice using a quantum gas microscope [1]. A periodic force is applied by sinusoidally displacing a harmonic optical potential. In the linear response regime, the ratio between current and force gives the conductivity, through Ohm's law. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both the real and imaginary conductivity, up to a frequency sufficient to capture transport dynamics within the lowest band, and well below the band gap. The spectral width of the real conductivity reveals the current dissipation rate, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. We observe that a finite lattice depth causes relaxation of current due to the breaking of Galilean invariance, which enables damping through collisions between fermions. We also discuss measurements in progress on applying this experimental technique to a strongly correlated regime of large on-site interactions, one-dimensional systems, and disordered systems. \\ $^1$R. Anderson \textit{et al.}, Phys. Rev. Lett. {\bf 122}, 153602 (2019).   

Live

Quantum gases loaded into optical lattices with single site resolution have emerged as one of the most powerful quantum simulators for investigating exotic many-body physics related to condensed matter systems. Here, we demonstrate the ability to extract the full information of a single-band Fermi-Hubbard model in the charge base without parity projection. By harnessing the power of Feshbach enhanced interactions between two atoms in a single well, we coherently load doubly occupied lattice sites into a double-well trap, preventing light assisted atom loss during the imaging process. With the full charge occupation, we measure the compressibility of the cloud and show that the temperature can be measured from the density-density correlations according to a fluctuation-dissipation theorem. Furthermore, we observe the strong correlation between doublons and holons, a signature of spin-ordering due to super-exchange interactions. This work establishes the possibility to extract both the spin and charge information of a two-component Fermi gas, and provides a route to studying Hubbard physics beyond two dimensions by enabling transverse dynamics.   

Live

Quasicrystals are long-range ordered but not periodic and represent an interesting middle ground between order and disorder. I will present how we experimentally realise a two-dimensional quasicrystaline optical lattice for ultracold atoms with eightfold rotationally symmetric. [1] By studying the diverging timescale required for adiabatically loading, we probe the disorder-induced localised phase and demonstrate its resilience against to interactions. [2] Our experimental results are consistent with a mean-field shift of the localisation transition. Quasiperiodic potentials, lacking conventional rare regions, provide the ideal testing ground to realise many-body localisation in 2D. [1] Konrad Viebahn, Matteo Sbroscia, Edward Carter, Jr-Chiun Yu, Ulrich Schneider. ``Matter-wave diffraction from a quasicrystalline optical lattice''. Phys. Rev. Lett. 122, 110404 (2019). [2] Matteo Sbroscia, Konrad Viebahn, Edward Carter, Jr-Chiun Yu, Alexander Gaunt, Ulrich Schneider. ``Observing localisation in a 2D quasicrystalline optical lattice''. arXiv:2001.10912 (2020).   

Live

In lattice systems with particle-number conservation the von Neumann entanglement entropy $S_{\textrm{ent}}$ is the sum of number entropy $S_{\textrm{n}}$ and configurational entropy $S_\textrm{conf}$. As shown recently both quantities can be obtained in an experiment from the full counting statistics. We numerically investigate the particle-number entropy $S_n$ following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to be many-body localized and where the von-Neumann entanglement entropy is known to grow as $S_{\textrm{ent}}\sim \ln t$ as function of time $t$, also the number entropy increases as function of time as $S_n\sim\ln\ln t$. If this growth continues in the thermodynamic limit for infinite times, it would signal (ultra-slow) ergodic behavior rather than localization of particles. We show furthermore that for free systems $S_{\textrm{ent}}$ is completely fixed by $S_{\textrm{n}}$.   

Live

We discuss experiments on quantum gases in tunable quasiperiodic optical potentials. Use of a bichromatic lattice with tunable period ratio between the two sublattices enables at least two new measurements. First, studying the frequency-dependent response of a quasiperiodically-trapped gas to lattice modulation offers a direct probe of the multifractal Hofstadter butterfly energy spectrum which also characterizes 2D electron gases in the integer quantum Hall regime. This extends previous experiments at fixed period ratio which have measured 1D slices of this 2D spectrum [1]. Second, observing time evolution of an initially narrow density distribution in a bichromatic lattice at rational and irrational period ratios allows a detailed probe of localization physics and may reveal signatures of a change in eigenvalue statistics across a localization transition.   

Live

Ultracold clouds of atoms placed into carefully designed optical lattice potentials form an excellent tool for probing the dynamics of interacting, quantum mechanical particles. In this work, we investigate the properties of non-linear Bloch bands of Bose-Einstein condensates that come into existence for sufficiently strong interactions between the atoms. In our experiments, we analyze the properties of non-linear Bloch bands by applying optical lattices and performing well-controlled lattice accelerations. The experiments reveal non-exponential tunneling of atoms which is conceptually connected to predicted loop structures. Our observation of non-exponential tunneling provides a clear demonstration of the power of ultracold atoms for investigating complex quantum mechanical dynamics.   

On Demand

We study the superfluid (SF) - Mott insulator (MI) transition of spin-1 bosons with antiferromagnetic interaction in an optical lattice based on the spin-1 Bose-Hubbard model [1]. It has been shown that in contrast to the spineless case the SF-MI phase transition is of first order [2]. We derive the time-dependent Ginzburg-Landau (TDGL) equation expanding up to the 6th order of the SF order parameter in the vicinity of the first-order SF-MI phase transition. We employ the TDGL equation to study the stability of superfluid mass current and spin current. Mass current induces dynamical instability involving the U(1) phase mode [3]. We find that the critical velocity of mass current is finite at the SF-MI phase boundary due to the existence of the metastable SF state and it vanishes at the point where the metastable SF state disappears. Spin current also induces dynamical instability that involves spin wave excitations. We find a parameter region where the superfluid polar state is unstable against infinitesimal spin current. This implies emergence of an unknown magnetic phase in this parameter region that cannot be described by the mean-filed theory.\\ $^{1}$S.\,Tsuchiya, {\it et al.,} PRA {\bf 70}, 043628 (2004). \\ $^{2}$T.\,Kimura, {\it et al.,} PRL {\bf 84}, 110403 (2005).   

Topological Phases of Interacting Fermions in Optical Lattices

Recent experiments have placed cold atoms into optical lattices in the presence of synthetic fields. This talk will review studies of Hubbard-Hofstadter models in regimes revealing topological phases of ultracold fermions arising from the interplay of inter-particle interactions and synthetic fields in kagome and square optical lattices. Focusing on one regime in particular, attractive interactions in a square optical lattice, we find that attractive s-wave interactions lead to a higher-order topological superfluid [1]. Higher-order topological superconductors hosting Majorana-Kramers pairs as corner modes have recently been proposed in two-dimensional materials. Here, we show that such Majorana-Kramers pairs can be realized using a conventional s-wave superfluid in an optical lattice but with a soliton. The Majorana-Kramers pairs emerge at the “corners” defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme sets the stage for observing possible higher-order topological superfluidity with conventional s-wave superfluids of cold atoms. 1. C. Zeng et al., Phys. Rev. Lett. 123, 060402 (2019)   

Experimental observation of non-ergodic behavior in the tilted Fermi-Hubbard model

Using ultracold fermionic $^{\mathrm{40}}$K atoms in an optical lattice we study the dynamics of the one-dimensional Fermi-Hubbard model subject to an external linear potential (``tilt''), which has recently attracted considerable theoretical and experimental interest in the context of ergodicity-breaking and constrained dynamics. Starting from a charge-density wave initial state (quarter filling) we measure the spin-resolved time evolution of the occupation imbalance between even and odd lattice sites as a local probe of localization. We identify two fundamentally different regimes: At short times we measure parity-projected real-space Bloch oscillations which, depending on the strength of the tilt, exhibit interaction induced damping and frequency modulation. At long times the dynamics reveal a robust steady state imbalance up to about 300 tunneling times, whose value depends on the interaction strength. We compare our experimental results to numerical calculations employing tDMRG on short time scales and exact diagonalization on long timescales and find excellent agreement throughout. Finally, we couple adjacent 1D systems to probe the crossover from a non-ergodic 1D to an ergodic 2D system and find a spin-dependent decay of the imbalance depending on the transverse coupling strength.   

Not Participating

Bose-Einstein condensates in higher Bloch bands of optical lattices immensely extend the possibilities for quantum simulation of solid state models. Unconventional superfluids and new topological states of matter are expected to emerge from the interplay of spin and orbital degrees of freedom as well as the lattice symmetry. We report on Bose-Einstein condensation in the second and fourth band of a bipartite honeycomb lattice. Tuning the energy offset between the two sublattices allows a controlled transfer to higher bands. We have investigated the emergence of coherence for these metastable states as well as the interplay of band relaxation dynamics and condensation by tracing the dynamics in the Brillouin zones. Understanding these non-equilibrium processes constitutes an essential requirement for the stabilization of unconventional spinor condensates in higher bands.