Session F02: Artificial Gauge Fields, Spin-Orbit Coupling, and Optical Lattices

Vortices in Rotating Bose-Einstein Condensate Shells

We present a study of superfluid vortices in rotating shell-shaped Bose-Einstein condensates (BECs). Hollow spherical BECs are of interest in connection to ongoing experimental efforts on the International Space Station and they naturally occur in optical lattice systems of ultracold bosons and interiors of neutron stars. Fundamentally, they have interesting geometry (non-zero curvature) and topology (hollow center). When BECs are rotated, discrete vortices are generated in pairs, as a consequence of the quantum coherence and the closed shape of the system. Using a mean-field approach, numerical solutions of the Gross-Pitaevskii equation and insights from classical fluid dynamics, we find that hollow condensates have a lower energy barrier to emergence of vortices than fully filled BECs. Further, we show that the rotation frequency at which nucleation of vortex lines is energetically favorable increases with BEC shell thickness. At this frequency the first vortex line is generated as straight and extends along the rotation axis. We consider the possibility of bent vortex lines (off-axis vortex pairs of opposite circulations in the two-dimensional shell limit) and determine that they are unstable except at fast rotation.   

Dynamics of Quantum Gas in Non-Abelian Gauge Field

We experimentally realize SU(2)-symmetric artificial gauge field with the tripod laser scheme. First, the non-Abelian nature of the artificial gauge field is revealed by performing loop operations, at different orders, in the parameter space [1]. It was found that the dynamics of internal states leads to a new thermometric scheme that exploits the interferometric-displacement of atoms [1]. Afterwards, the coupling dynamics of internal( i.e., spin)- and external(i.e., momentum)-degrees of freedoms, in a two-dimensional non-Abelian gauge field, is shown to exhibit an asymmetric expansion of the atomic cloud [2]. This spin-orbit-coupled gas breaks the Galilean invariance and modifies the usual reflection-laws, owing to its inherent peculiar dispersion relation. The density distribution of external dynamics markedly carries the signature of the non-Abelian nature of the underlying gauge field.

[1] F. Leroux, K. Pandey, R. Rebhi, F. Chevy, C. Miniatura, B. Gremaud, and D. Wilkowski, Non-Abelian and adiabatic geometric transformation in a cold atomic gas, Nat. Commun. 9, 3580 (2018).
[2] M. Hasan, C. S. Madasu, C. C. Kwong, F. Chevy, D. Wilkowski (under preparation).   

Quantum simulation of Dynamical gauge field for ultra-cold atoms in a cavity

Quantum simulation of synthetic gauge field in ultra-cold atoms provides opportunity to realize the analogues of Landau levels of electrons and Quantum Hall Physics, Hofstadter-Harper Hamiltonian, and topological phases in a much more controlled environment. Where the initial studies were mostly on synthetic gauge fields that do not have dynamics of their own, a number of current studies aimed to create dynamical gauge field for neutral ultra -cold atoms to extend the scope of such analogue quantum simulations for condensed matter and high-energy physics related phenomena.
In this work, we propose that ultra cold atoms in high finesse ring cavity of suitable geometry to create a non-uniform dynamical gauge field for neutral ultracold atom. The resulting energy spectrum is similar to the energy dispersion for an electron in a similar magnetic modulation that can effectively create one dimensional flow of such ultra-cold atoms. Starting with single atoms dynamics in such synthetically created dynamical non-uniform gauge field we extend this idea to the ultra-cold atomic Bose-Einstein condensates and study the corresponding dynamics.
  

Superfluidity and Bogoliubov excitations of a striped spin-orbit coupled BEC induced by a weak optical lattice

We investigate the ground-state superfluidity and Bogoliubov excitations of a striped spin-orbit coupled Bose-Einstein condensate (BEC) with the momentum-space hopping induced by a weak optical lattice. The ground-state phase diagram and corresponding superfluid fraction are calculated for different system parameters. The Bogoliubov spectrum is studied and an exotic avoided band crossing between roton and Goldstone modes is revealed, which is very different from traditional spin-orbit coupled Bose-Einstein condensate with double-gapless Goldstone modes. We study the quantum depletion, which can be used to characterize the phase transitions.   

Optical Vortex Braiding in Composite Bessels

We theoretically propose and experimentally demonstrate the braiding of optical vortices in a laser beam with more than 2π rotation by superposing Bessel modes with a plane wave. Laser beams containing a single, centered vortex with integer-valued orbital angular momentum (OAM) have been extensively studied and engineered, but beams with two or more optical vortices have received less attention. Optical vortex braiding refers to the periodic rotation of two or more vortices around the central axis of propagation in a laser beam. Braiding is a topological feature in knot theory, but no physically-realizable scheme for optical vortex braiding beyond a ¼ - rotation has been identified, much less experimentally demonstrated. In this work, we present a theoretical proposition for braiding optical vortices in Bessel beams, along with analytical expressions for the braiding trajectories and braiding period. We accompany this work with the experimental realization of vortex braiding in physical laser beams, using Bessel-Gaussian beams. We show two vortices braiding completely three times, the most observed to our knowledge.   

Spin Angular Momentum in Acoustic Field Theory

We construct a Lagrangian representation of acoustic field theory that accounts for the local radiation forces and torques experienced by subwavelength probe particles, analogous to those experienced by Rayleigh particles in optical fields. The traditional acoustic Lagrangian representation with a scalar potential is unable to reproduce these measured effects. By introducing a displacement vector potential, analogous to the electromagnetic vector potential, we derive the appropriate local momentum and spin densities directly as conserved Noether currents. The results agree with those proposed in recent analyses of intrinsic acoustic spin and are consistent with recent experiments.   

Bose-Einstein condensation in effective Harper-Hofstadter bands: simulations of synthetic magnetic fields by optical lattice shaking

The cold atom field has been focused on generating topological and other exotic phases of quantum matter by, for example, creating strong
synthetic magnetic fields. In the present work we use time-dependent Gross-Pitaevskii simulations to investigate the feasibility of these
schemes. There are several key questions we numerically address: 1. Can one implement shaking so that a BEC will emerge, consistent with the effective energy minima of Bloch-Floquet bandstructure? 2. How realistic is it to experimentally enter the Harper-Hofstadter regime which involves extreme parameter values (such as for hopping and shaking frequency)? 3. An important attribute of applying these Bloch-Floquet recipes to cold atoms is that there are easily tunable many-body interactions present, which are necessary for equilibration. One can
then be concerned that they undermine the single-particle Floquet bandstructure. In this talk we address these issues, and in the process
provide advice for experimentalists in implementing these shaking recipes for arriving at a Hofstader BEC. Additionally, in our simulations we investigate what underlies ”heating” and how it is affected by the strength of the interactions g.
  

Inhomogeneous mean-field approach for collective modes at the superfluid-Mott glass transition

We employ an inhomogeneous mean-field approach plus Gaussian fluctuations to investigate disordered Bose-Hubbard models with particle-hole symmetry in two and three dimensions. Within this framework, the collective excitations, i.e., Goldstone mode and the Higgs (amplitude) mode, are described by two effective, decoupled, disordered single-particle Hamiltonians whose properties are determined by the underlying mean-field solution. Based on multifractal analysis, we investigate the localization properties of each mode separately as a function of energy and the distance from the superfluid-Mott glass transition. Furthermore, we calculate susceptibility functions and compare the results with Monte Carlo simulations and experiments.
  

Realizing Z2 phases and Majorana Spectroscopy in extended Bose-Hubbard systems

The connection between transverse XY spin chains and the fermionic Kitaev chain with nearest-neighbor hopping and pairing has been well known for decades, and has lately drawn attention for its rich phase diagram and relevance to realizations of Majorana fermions. Here, we study the novel system comprised of a Bose-Hubbard chain connected to a reservoir that can generate analogous pairing terms for bosons. We describe a cold-atom realization of such a system in a biased zig-zag optical lattice. We show that in certain limits, the Bosonic Kitaev chain maps on to the XY spin chain, resulting in an unsual Z₂ phase that has number fluctuation but no off-diagonal long range order associated with boson condensation. Noteworthy features include the possibility of a strongly correlated many-body qubit ground state and the potential for cold-atom measurements of the Kitaev chain energy spectrum, including zero-energy Majorana bound states.   

Dark states of multilevel fermionic atoms in doubly-filled optical lattices

We propose to use fermionic atoms with degenerate ground and excited internal levels (F_g→F_e), loaded into the motional ground state of an optical lattice with two atoms per lattice site, to realize dark states with no radiative decay. The physical mechanism behind the dark states is an interplay of Pauli blocking and multilevel dipolar interactions. The dark states are independent of lattice geometry, can support an extensive number of excitations and can be coherently prepared using a Raman scheme taking advantage of the quantum Zeno effect. These attributes make them appealing for atomic clocks, quantum memories, and quantum information on decoherence free subspaces.   

Numerical study of antiferromagnetic nearest-neighbor spin correlations of an SU(6) Fermi gas in an optical lattice

Experimental progress with ultracold alkaline-earth-like atoms allows quantum simulation of novel phenomena and phases of matter. Many interesting SU($N$) phases are characterized by their magnetic correlations. Recently, the experiment at Kyoto has detected nearest-neighbor antiferromagnetic (AFM) spin-correlations in an SU(6) $^{173}$Yb Fermi gas loaded in 1D, 2D and 3D optical lattices. Such systems are effectively described by the SU($N$) Fermi Hubbard Model. We have developed and applied the Exact Diagonalization and Determinant Quantum Monte Carlo methods to solve such model in all of the relevant geometries. With these tools we calculate the density, double occupancy, entropy and magnetic correlations in a trapped gas under the local density approximation. We compare the calculated and measured nearest-neighbor AFM correlations, and we find they agree quantitatively. In 2D and 3D the experiments reach lower temperatures than is possible to accurately compute with theory, but in 1D, the temperature estimated from theory comparison is $k_BT/t = 0.08(2)$, being the lowest temperature ever reported for a Fermi gas in an optical lattice.   

Dynamics of an almost lattice gauge theory realized by an ultracold atom system

Recently carried out experiments with ultracold atoms have realized the first building blocks to simulate lattice gauge theories quantum. Despite the great progress, the influence of experimental imperfections on the phase structure or the non-equilibrium dynamics is unclear. In this thesis we study the effect of terms violating the local gauge invariance as they occur in a typical experimental setup. In particular, we focus on ultracold atom setups which exploit angular momentum conservation in order to realize local gauge invariance. We also study the influence of dissipation in these systems and compare the dynamics of a theory with exact and almost lattice gauge theory. Especially we determine the time scales and observables when the difference between the two theories becomes significant.   

Z2 Lattice Gauge System and Dynamical Localization

Gauge theory has been playing a fundamental role in our understanding of the deepest mysteries of physics. And recent advances in cold atom physics have also made the study of dynamical gauge systems a new frontier. Using Floquet approach, we propose to realize a one-dimensional Z₂ lattice gauge model, featuring extensive local constants of motions, using two specifies of Rb atoms. The resulting Floquet Hamiltonian turns out to be quite simple. Within a given symmetry sector of good quantum numbers, the system can be viewed as a 1D transverse quantum Ising model with a binary random longitudinal field. Therefore, the dynamics of the system is essentially controlled by disordered Hamiltonians, implying that the system can feature many body localization (MBL) as a result of dynamical localization. Numerical studies of energy level statistics and quench dynamics clearly demonstrate the existence of MBL phase in this system.   

Unusual superfluid behavior of population imbalanced atomic Fermi gases in a two-dimensional optical lattice

We study the superfluid behavior of population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a two-dimensional optical lattice (2DOL), using a pairing fluctuation theory, within the context of BCS-BEC crossover. We find that population imbalance now has highly unusual effects on the behavior of pairing and superfluidity, caused by the continuum-lattice mixing in 2DOL. We find that, in the presence of a finite population imbalance (p>0), the pair density at Tc unexpectedly approaches zero towards to deep BEC regime and thus the transition Tc is dramatically enhanced in the BEC regime and becomes proportional to the interaction strength $U$ in the BEC limit. This should be contrasted to the balanced case, for which Tc decreases as $1/U$. And the system is an intermediate-temperature polarized superfluid state at unitarity and in the BCS regime. We perform stability analysis, and present complete phase diagrams along with the behavior of superfuild density. We show that a stable polarized superfluid emerges at relatively high temperature.