Shaken Optical Lattice Research Articles

Reinforcement-learning-based matter-wave interferometer in a shaken optical lattice

We demonstrate the design of a matterwave interferometer to measure acceleration in one dimension with high precision. The system we base this on consists of ultracold atoms in an optical lattice potential created by interfering laser beams. Our approach uses reinforcement learning, a branch of machine learning, that generates the protocols needed to realize lattice-based analogs of optical components including a beam splitter, a mirror, and a recombiner. The performance of these components is evaluated by comparison with their optical analogs. The interferometer's sensitivity to acceleration is quantitatively evaluated using a Bayesian statistical approach. We find the sensitivity to surpass that of standard Bragg interferometry, demonstrating the future potential for this design methodology.

Optimal frequency window for Floquet engineering in optical lattices

The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $\tau$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $\tau$. As a main result, we find that, when increasing the lattice depth, $\tau$ increases faster than the experimentally relevant time scale given by the tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.

Exotic domain walls in Bose-Einstein condensates with double-well dispersion

We study the domain walls which form when Bose condensates acquire a double-well dispersion. Experiments have observed such domain walls in condensates driven across a ${\mathbb{Z}}_{2}$ symmetry-breaking phase transition in a shaken optical lattice. We derive a generic model to describe the dispersion and to compute the wave functions and energies of the domain walls. We find two distinct regimes which demand different physical pictures. In the weak-coupling regime, where interactions are weak compared to the kinetic-energy barrier, ``density-wave domain walls'' form that support an extended density wave and a series of phase steps. These features can be understood as the quantum interference between domains with distinct momenta. In the strong-coupling regime where interaction dominates, the system forms ``phase domain walls'' which have the minimum width allowed by the uncertainty principle and suppressed density modulation. Analytic results for the domain-wall wave functions are obtained in the two regimes. The energy of domain walls behaves similarly to that of topological defects in paradigmatic field theories.

Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition.

The dynamics of many-body systems spanning condensed matter, cosmology, and beyond are hypothesized to be universal when the systems cross continuous phase transitions. The universal dynamics are expected to satisfy a scaling symmetry of space and time with the crossing rate, inspired by the Kibble-Zurek mechanism. We test this symmetry based on Bose condensates in a shaken optical lattice. Shaking the lattice drives condensates across an effectively ferromagnetic quantum phase transition. After crossing the critical point, the condensates manifest delayed growth of spin fluctuations and develop antiferromagnetic spatial correlations resulting from the sub-Poisson distribution of the spacing between topological defects. The fluctuations and correlations are invariant in scaled space-time coordinates, in support of the scaling symmetry of quantum critical dynamics.

Extended Bose-Hubbard model in a shaken optical lattice

We study an extended Bose-Hubbard model with next-nearest-neighbor (NNN) hopping in a shaken optical lattice. We show how mean-field phase diagram evolves with the change of NNN hopping amplitude $t_{2}$, which can be easily tuned via shaking amplitude. As $t_{2}$ increases, a $Z_{2}$-symmetry-breaking superfluid ($Z_{2}$SF) phase emerges at the bottom of the Mott lobs. The tricritical points between normal superfluid, $Z_{2}$SF, and Mott insulator (MI) phases are identified. We further demonstrate the tricritical point can be tuned to the tip of the Mott lobe, in which case a new critical behavior has been predicted. Within random-phase approximation, excitation spectra in the three phases are obtained, which indicate how the phase transitions occur.

Quantum phase transition of bosons in a shaken optical lattice

Recently, the lattice shaking technique has been used to couple different Bloch bands resonantly. For the one-dimensional (1D) case, in which shaking is along only one direction, experimental observation of domain-wall formation has been explained by superfluid Ising transition. Inspired by these, we generalize to a 2D case in which shaking is along two orthogonal directions. Analogous to the 1D case, we find three different phases, the normal superfluid (NSF) phase, the $D_4$ symmetry-breaking superfluid ($D_4$SF) phase and the Mott insulator (MI) phase. Furthermore, we demonstrate that the interaction effect induced by inhomogeneous band mixing can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. Unlike in the 1D case, shaking types also can modify the critical shaking amplitude. We also construct a low-energy effective field theory to study the quantum criticality of bosons near the tricritical point of NSF, $D_4$SF and MI phases. Moreover, we find a Bose liquid with anisotropically algebraic order and propose to change the Bose-Einstein condensation (BEC) into a non-condensed Bose liquid by tuning the shaking amplitude approaching the critical value.

Shaping topological properties of the band structures in a shaken optical lattice

To realize band structures with non-trivial topological properties in an optical lattice is an exciting topic in current studies on ultra cold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking an optical lattice, which is directly applicable in current experiments. The photon-assistant band hybridization leads to the production of an effective spin-orbit coupling, in which the band index represents the pseudospin. When this spin-orbit coupling has finite strengths along multiple directions, non-trivial topological structures emerge in the Brillouin zone, such as topological defects with a winding number 1 or 2 in a shaken square lattice. The shaken lattice also allows one to study the transition between two band structures with distinct topological properties.

Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice

Solid state systems derive their richness from the interplay between interparticle interactions and novel band structures that deviate from those of free particles. Strongly interacting systems, where both of these phenomena are of equal importance, exhibit a variety of theoretically interesting and practically useful phases. Systems of ultracold atoms are rapidly emerging as precise and controllable simulators, and it is precisely in this strongly interacting regime where simulation is the most useful. Here we demonstrate how to hybridize Bloch bands in optical lattices to introduce long-range ferromagnetic order in an itinerant atomic system. We find spontaneously broken symmetry for bosons with a double-well dispersion condensing into one of two distinct minima, which we identify with spin-up and spin-down. The density dynamics following a rapid quench to the ferromagnetic state confirm quantum interference between the two states as the mechanism for symmetry breaking. Unlike spinor condensates, where interaction is driven by small spin-dependent differences in scattering length, our interactions scale with the scattering length itself, leading to domains which equilibrate rapidly and develop sharp boundaries characteristic of a strongly interacting ferromagnet.

Exploring dynamic localization with a Bose-Einstein condensate

We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering.