Session J03: Dynamics of Cold Atoms in Optical Lattices

Real time correlations in the Fermi-Hubbard model

Quantum simulations with ultracold fermionic atoms in optical lattices have provided us with new insights into low-temperature properties of quantum lattice models of strongly-correlated electrons. Recent advances in creating and manipulating box traps have resulted in homogeneous systems and have paved the way for studying their transport properties. I will argue that dynamical properties of the Fermi-Hubbard model, such as conductivity, can be obtained more accurately through real time, as opposed to imaginary time, correlation functions at temperatures relevant to current experiments. I will present results for conductivity and other transport properties from the numerical linked-cluster expansions.   

Spin dynamics with bosons in tilted optical lattices

In recent years, several experiments have realised interesting many-body phenomena with bosonic atoms in tilted optical lattices. This especially includes resonant tunneling dynamics when the on-site interaction shift for two atoms is approximately an integer multiple of the energy offset between neigbouring sites. We show that near the two-site resonance in such experiments, the dynamics can be described by a spin model that maps onto coupled Ising chains. This system exhibits unusual behaviour both out of equilibrium, and in its critical behaviour near the tunnelling resonance point. We discuss the resulting many-body physics, and possibilities to observe the corresponding phenomena in experiments. One of the special properties of such systems is that very sensitive phenomena are often more accessible than in homogeneous systems, because entropy in the initial atomic state maps to small amounts of localised disorder in the spin model, leaving the initial state in that system much closer to zero-temperature.   

FFLO Superfluidity in the 1D-3D Crossover of a Spin-imbalanced Fermi Gas

The FFLO polarized superfluid is characterized by finite center of mass pairs. This novel superfluid has yet to be conclusively observed in either condensed matter or ultracold atomic gases. Ultracold atomic gases provide an ideal platform to realize novel quantum many-body states due to their tunability and versatility. We create a pseudo-spin-1/2 system using the lowest two hyperfine states of $^{6}$Li. By engineering a spin imbalance, we produce an effective magnetic field. The atoms are confined in an array of 1D tubes with variable tunneling, produced using a 2D optical lattice. Interactions are tuned via a Feshbach resonance. Previous work identified the crossover from 3D to 1D as the most likely region to stabilize the FFLO superfluid\footnote{Meera M. Parish et al., Phys. Rev. Lett. 99, 250403 (2007)}\footnote{M. C. Revelle et al., Phys. Rev. Lett. 117, 235301 (2016)}. We present our progress towards direct observation of the domain walls containing the excess unpaired fermions. The periodicity of these domain walls is a definitive signature of the FFLO phase.   

Effective SU($N$) multi-body interactions in ultracold fermionic atoms on a lattice

Ultracold fermionic alkaline-earth atoms featuring SU($N$) symmetric interactions and two long-lived electronic states are a promising platform for performing quantum simulation and quantum information processing tasks. A crucial ingredient for realizing this goal is the characterization of interaction parameters which govern low energy atomic collisions. We report recent measurements enabled by the exquisite spectroscopic sensitivity of the 3-D $^{87}$Sr optical lattice clock at JILA, resolving interaction-induced density-dependent shifts in the energy spectra of multiply-occupied lattice sites. In order to account for these shifts, we develop a low-energy effective field theory exhibiting SU($N$)-symmetric multi-body interactions mediated by virtual occupation of high-energy motional states. Though effective multi-body interactions have previously been observed in ultracold bosonic gasses prepared in a single hyperfine state, our work deals for the first time with collisions between $N$ fermionic atoms in $N$ different nuclear spin states, each with two electronic degrees of freedom. Nonetheless, due to the SU($N$) symmetry of collisions we are able to find a simple way to express multi-body Hamiltonians and fully characterize the corresponding many-body eigenstates.   

Phasonic spectroscopy of tunable quantum quasicrystals

We report on experiments studying excitations in a tunable quantum quasicrystal consisting of cold strontium atoms in a bichromatic optical lattice. The phasonic degree(s) of freedom of solid-state quasicrystals (analogues of phonon modes in a regular crystal) are typically not dynamically accessible, and yet are believed to have significant effects on thermal and electronic transport. We directly drive this phason mode and observe the excitation of the lattice-bound atoms, which are analogous to the electrons in a real quasicrystal. We discuss both the familiar phononically driven excitations of ground band atoms and the results of this novel coherent phasonic spectroscopy. We identify fundamental resonances and higher-order processes, study their dependence on tunneling and modulation strength, and compare spectroscopic results for phasonic and phononic modes of excitation.   

Pair Production with Ultracold Atoms

Electron-positron pair production in quantum electrodynamics (QED) is predicted to occur at electric field strengths beyond Schwinger’s limit of approximately E=10$^{18}$ V/m. However, fields on this scale are not experimentally accessible, and direct observation of pair production is currently out of reach. The versatility of ultra-cold atomic experiments makes it possible to simulate these quantum phenomena. Here, we exploit the mapping between the Dirac dispersion relation that underlies pair production and the dispersion relation of a 1-D optical lattice at the edge of the Brillouin zone. A linear force applied to the atoms models an electric field, and atoms excited to the second band of the lattice simulate pair production. We load a cloud of $^{87}$Rb into the lowest band of such a lattice and study the number of 'pairs' produced as a function of the force applied or the "rest mass", allowing us to probe Schwinger's limit.   

Experimental Realization of a Relativistic Harmonic Oscillator

We report the experimental study of a harmonic oscillator in the relativistic regime [1]. The oscillator is composed of ultracold lithium atoms in the third band of an optical lattice, which have an energy-momentum relation nearly identical to that of a massive relativistic particle, with a reduced effective mass and speed of light. Imaging the shape of oscillator worldlines at velocities up to 98{\%} of the effective speed of light reveals a crossover from sinusoidal to nearly photon-like propagation. Effective time dilation causes the measured period of oscillations to increase with energy; our measurements reveal beyond-leading-order contributions to this relativistic anharmonicity. Preparing oscillator ensembles, we observe an intrinsic relativistic dephasing and a breathing mode with exactly the opposite phase of that predicted for non-relativistic harmonic motion. All observed dynamics are in quantitative agreement with longstanding relativistic predictions [2,3]. [1] K. M. Fujiwara et al., arXiv:1712.09501 [cond-mat.quant-gas] (2017). [2] E. H. Hutten, Nature 205, 892 (1965). [3] W. Moreau, R. Easther, and R. Neutze, American Journal of Physics 62, 531 (1994).   

Fast long-range coherent transport in hybridized Floquet-Bloch bands

Floquet band engineering uses driving in a lattice to hybridize and tune the properties of the original static Bloch bands. Here we discuss the experimental exploration and characterization of hybridized Floquet-Bloch bands using ultracold lithium atoms in an amplitude-modulated 1D optical lattice. In the absence of driving, we report the first experimental observation of position-space center-of-mass Bloch oscillations, which allow direct imaging of the band structure. Strikingly, when a drive is applied, we observe that the interplay of momentum-space and real-space evolution in a Floquet-Bloch band leads to large-scale rapid coherent atomic transport across thousands of lattice sites. This ``giant Floquet-Bloch oscillation'' can be understood as a consequence of reversible Landau-Zener tunneling to and from higher bands with relativistic dispersion. Transport can be precisely regulated via the drive frequency and strength, offering a simple and powerful tool for atomic control and opening up the possibility of more complex band hybridization schemes.   

Experimental realisation of a two-dimensional optical quasicrystal for ultracold atoms

Quasicrystals are long-range ordered structures which lack translational symmetry. They exhibit a wealth of fascinating properties, including phasonic degrees of freedom, fractal-like band structure, and a direct link to higher dimensions via cut-and-project techniques. In this work we introduce optical quasicrystals as novel tools for quantum simulation with ultracold atoms. We report on the first experimental realisation of an optical quasicrystal for ultracold atoms in two dimensions, which is implemented using an eightfold optical lattice. In a matter-wave diffraction experiment we expose a Bose-Einstein condensate of $^{87}$Rb atoms to transient pulses of lattice light and record the resulting momentum distribution. This procedure can be seen as a continuous quantum walk in reciprocal space and demonstrates the fundamental differences between periodic and quasiperiodic lattices. Furthermore, it allows us to visualise the striking self-similarity of the fractal momentum-space structure in the quasicrystalline case, in very good agreement with theory. Finally, we show that our system provides a novel route to synthetic dimensions as we experimentally simulate a continuous-time quantum walk in a tight-binding model in one, two, three, and four dimensions.   

Helical spacetime density waves in a trimmerized kagome lattice

The theoretical discovery and experimental preparation of Floquet/discrete time crystals have triggered heated discussions for ordered phases in a highly non-equilibrium scenario. In previous works, the interesting phenomena chiefly occur in the temporal direction, while the effects of the underlying lattice geometry play little roles. Here, motivated by an ongoing experiment at Berkeley concerning trimerized kagome optical lattice, we show that a helical spacetime density wave breaking spatiotemporal translation symmetry can emerge with rigid periodicity for soft-core bosons, when the lattice is under periodic quenches. Our work paves the way for finding a wide range of spatiotemporally ordered phases in various lattices far away from equilibrium.