Session W41: Bose Gauge Fields

3D quaternionic condensation and spin textures with Hopf invariants from synthetic spin-orbit coupling

We study unconventional condensations of two-component bosons in a harmonic trap subject to the 3D $\vec{\sigma}\cdot \vec{p}$-type spin-orbit (SO) coupling. The topology of condensate wavefunctions manifests in the quaternionic representation. The spatial distributions of the $S^3$ quaternionic phase exhibit 3D skyrmion configurations, while those of the $S^2$ spin orientation possess non-zero Hopf invariants. As increasing SO coupling strength, spin textures evolve from concentric distributions to lattice structures at weak interactions. Strong interactions change condensates into spin-polarized plane-wave states, or, superpositions of two plane-waves exhibiting helical spin spirals.   

Rashba Spin-Orbit Coupled Bose-Einstein Condensates with Magnetic Dipole-Dipole Interactions

In this talk we consider the effect of Rashba spin-orbit coupling on a quasi-two dimensional Bose-Einstein Condensate with dipolar interactions. The interplay of the spin-orbit coupling, which favors textured and vortex-antivortex lattice ground states, and the dipole-dipole interaction, which introduces non-local spin-exchange processes and a strongly geometry-dependent interaction character, leads to a variety of novel ground states including combinations of spin and purely motional vortices. With the assistance of a numerical Bogoliubov-de Gennes analysis, we map the relevant phase boundaries, thereby characterizing the rich ground-state phase diagram of this system.   

Exotic Quantum States of Rashba Bosons

The recently discovered spin-orbit coupled boson systems are remarkable for their capacity to explore physics that may not be revealed in any other way. The spin-orbit couplings, which can be artificially engineered in cold-atom experiments, in many instances lead to single-particle dispersion relations exhibiting multiple minima or even degenerate manifold of minimal energy states. It is entirely the effect of collisions (i.e. boson-boson interactions) which lifts this degeneracy and leads to an amazing variety of completely new quantum many-body states. This talk describes a theoretical discovery of a novel phase of matter that realizes for Rashba spin-orbit coupled bosons, where, at low densities, bosons essentially redress themselves and behave as fermions. This state is a composite fermion state with a Chern-Simons gauge field and filling factor one.   

Exotic Quantum Spin Models in Spin-Orbit-Coupled Mott Insulators

We study cold atoms in an optical lattice with synthetic spin-orbit coupling in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model using Peierls substitution and ``localized Wannier states method'' and derive the low-energy spin Hamiltonian for bosons and fermions. The spin Hamiltonian is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interactions and it has a rich classical phase diagram with collinear, spiral and vortex phases. We discuss the state of the art of experiments to realize and detect magnetic orderings in strongly correlated optical lattices.   

The Fate of Bose-Einstein Condensate in the Presence of Spin-orbit Coupling

We show that spin-orbit coupling can destroy a Bose-Einstein condensate. For non-interacting bosons, some types of spin-orbit coupling destroy a condensate at any finite temperature or even at the ground state, due to the drastic change of single-particle Density of States at low energies. Whereas interaction stabilizes the condensate at zero temperature, condensate depletion is significantly enhanced by spin-orbit coupling. Particularly, thermal depletion becomes divergent when both interaction and spin-orbit coupling become isotropic, leading to the disappearance of a three-dimensional condensate at any finite temperature.   

Emergence of Topological and Strongly Correlated Ground States in Rashba Spin-Orbit Coupled Bose Gases

We theoretically study an interacting few-body system of two-component Bose gases with isotropic Rashba spin-orbit coupling in a 2D isotropic harmonic trap. We show that the Hamiltonian is gauge-equivalent to particles subject to a pure non-abelian vector potential preserving time-reversal symmetry. We use Exact Diagonalization scheme to obtain the low-energy states of the system with large Rashba spin-orbit coupling strength for a range of interatomic interaction strengths. At small particle numbers, we observe that the bosons condense to an array of topological ground states that have $n+1/2$ -quantum angular momentum vortex configuration, with $n = 0, 1, 2, 3$. At relatively large particle numbers, we observe two distinct regimes: (a) at weak interaction strengths (mean-field regime), we observe ground states with topological and symmetry properties that are also obtained via mean-field theory computations. (b) at intermediate to strong interaction strengths (beyond mean-field regime), we report the emergence of strongly correlated ground states. We analyze ground state properties using various techniques: energy spectrum, density distribution, pair-correlation function, conditional wavefunction, entanglement spectrum, and entanglement entropy.   

Many-body ground states for bosons with Rashba spin-orbit coupling

The ground state of $N$ non-interacting bosons with a Rashba dispersion is macroscopically degenerate. It is of fundamental interest---and also relevant to current experiments in cold atomic gases with synthetic spin-orbit coupling---to determine whether a unique ground state is stabilized by interactions and what the properties of such a state might be. Motivated by exact solutions for the two-body problem, we construct many-body bosonic wave functions that saturate the kinetic energy and minimize the interaction energy, and compare with other recently proposed trial ground states.   

Flat-band engineering of interactions in spin-orbit coupled optical lattices

The recent experimental realization of spin-orbit coupled ultra cold atomic gases established a new platform to investigate many-body states of matter. In this talk we show that for such a system in optical lattices we can tune the spin-orbit coupling to achieve a flat energy band. We then model this system with a tight-binding Hamiltonian and further project the Hamiltonian to the Hilbert subspace of the lowest flat band. We will also discuss the important effect of interactions in such a projected flat-band system.   

Bosons on the Kagome lattice with artificial gauge fields

We investigate bosons on the Kagome lattice subject to artificial gauge fields such that no net flux is applied on a unit cell [1]. This allows for example the existence of quantized and non-quantized anomalous Hall effects on the Kagome lattice [2]. If two layers or two-component bosons are introduced, the topological phase is robust to inter-species interactions of moderate strength. We study the conditions under which the total density degree of freedom undergoes a Mott transition, while the pseudo-spin, or charge difference between layers, is in a superfluid phase with topological properties. Similar results can be obtained for two-component bosons on the honeycomb lattice. Such systems could work as a template for the realization of interacting topological phases in cold atom or cavity QED systems. \\[4pt] [1] Jens Koch, Andrew A. Houck, Karyn Le Hur, and S. M. Girvin, Phys. Rev. A 82, 043811 (2010).\\[0pt] [2] Alexandru Petrescu, Andrew A. Houck and Karyn Le Hur, Phys. Rev. A 86, 053804 (2012).   

A spin Hall effect in a quantum gas

The spin Hall effect is a phenomenom that couples spin current to particle current via spin-orbit coupling. The effect may be used to develop useful devices for spintronics, which may have advantages over corresponding conventional electronic devices. In addition, the spin-Hall effect is intimately related to certain types of topological insulators. Spin-orbit coupling in an ultracold bosonic sample of $^{87}$Rb has been demonstrated. We now use this spin-orbit coupling to produce a spin Hall effect in a bosonic sample, the first demonstration of the effect in an ultracold atom system.   

Experiments on BECs with Synthetic Gauge Fields and Spin Orbit Coupling

We report experiments on $^{87}$Rb BECs subject to synthetic gauge fields and spin orbit interactions created by optical Raman fields that couple different hyperfine spin and momentum states. We have reproduced several recently shown results of the effects of such synthetic gauge potentials by characterizing the quasimomentum of the dressed states. We have also observed a spin Hall-like effect on our BECs in a spatially inhomogeneous synthetic spin orbit coupling. We create BECs with equal populations of $|F=1,m_F=-1>$ and $|F=1,m_F=0>$, representing a pseudo spin 1/2 system, and launch them into a common mode oscillation within an optical dipole trap. When an inhomogeneous spin orbit coupling Raman field is applied, they exhibit an anticorrelated transverse oscillation, manifesting in cyclotron motions of opposite chirality. Measurements of such a spin dependent transport versus the intensity and detuning of the Raman coupling and versus the position of the BEC are also presented with discussions of possible interpretations.   

Measuring the Berry Curvature of Optical Lattices

New schemes propose how artificial gauge fields may be imprinted on ultracold atomic gases in optical lattices, allowing experiments to access strongly correlated phenomena. In particular, fractional quantum Hall physics may be explored in systems where the lowest energy band resembles a Landau level, as in the proposed ``optical flux lattices". These energy bands have a nonzero Chern number and are topologically nontrivial. The physical properties of such a band are encoded not only in its energy spectrum over the Brillouin zone (the ``bandstructure" in the usual sense) but also importantly, in its Berry curvature. When the Berry curvature is nonzero, it can have many important physical consequences; for example it can modify the semiclassical dynamics of a wave packet undergoing Bloch oscillations. We will explain how experimentalists may turn such physical consequences into new tools to determine the topological properties of a band. We will discuss how Berry curvature effects may be observed in ultracold gases and give examples in systems relevant to future experiments. [H. M. Price and N. R. Cooper, Phys. Rev. A 85, 033620 (2012) ]   

Controllable Transport of Ultra-Cold Atoms in 1D Optical Lattices with Uniform Peierls Substitution

We show that the recently developed optical lattices with Peierls substitution (PRL 108, 225303 and 225304 (2012)) -- which can be modeled as a lattice with a complex tunneling coefficient -- may be used to induce quantum transport of ultra-cold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi steady-state current (QSSC) ensues from the exact dynamics of non-interacting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed non-interacting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and temperature are present, which suggests that our findings should be observable with available experimental capabilities. Our study could be useful in developing novel devices in the thriving field of atomtronics.   

Phase Transitions and Collective Modes in Spin-Orbit Coupled Bose-Einstein Condensates

Recent experiments on trapped bosonic atomic gases interacting with Raman lasers have realized an artificial spin-orbit coupling (SOC) among two dressed spin states of bosons. The phase diagram of this system, as a function of the interaction parameters, strength of SOC, and the densities of the two species of bosons, possesses regimes of mixed superfluid (featuring two interpenetrating dressed-state condensates), and phase separation (between regions of single dressed-state condensate). We present our results on the Bogoliubov sound velocity in the mixed phase, and propose that it can be used as a probe of the spatially-varying density (i.e. stripe order) of the mixed phase as well as of the phase transition to the phase separation regime. The effects of the trapping potential are also discussed.   

Phase-modulated superfluids of bosons in spin-orbit coupled optical lattice

We study the phase diagram of spin-orbit coupled ultra-cold bosons in a square lattice using the Gutzwiller method. In the superfluid regime, we show that the interplay between spin independent and spin-dependent tunnelings may give rise to a few different types of phase-modulated superfluids. The transitions between different superfluids are found to be the first-order. We investigate the rich~periodic structure of the phases of the superfluids, which may be directly probed using the spin structure factor. Different types of superfluids may also possess different excitation spectra.