Spin-orbit coupled spinor Bose-Einstein condensates

Mobile magnetic impurities in a Fermi superfluid: a route to designer molecules

A magnetic impurity in a fermionic superfluid hosts bound quasiparticle states known as Yu-Shiba-Rusinov states. We argue here that, if the impurity is mobile (i.e., has a finite mass), the impurity and its bound Yu-Shiba-Rusinov quasiparticle move together as a midgap molecule, which has an unusual "Mexican-hat" dispersion that is tunable via the fermion density. We map out the impurity dispersion, which consists of an "atomic" branch (in which the impurity is dressed by quasiparticle pairs) and a "molecular" branch (in which the impurity binds a quasiparticle). We discuss the experimental realization and detection of midgap Shiba molecules, focusing on Li-Cs mixtures, and comment on the prospects they offer for realizing exotic many-body states.

Spin and field squeezing in a spin-orbit coupled Bose-Einstein condensate

Recently, strong spin-orbit coupling with equal Rashba and Dresselhaus strength has been realized in neutral atomic Bose-Einstein condensates via a pair of Raman lasers. In this report, we investigate spin and field squeezing of the ground state in spin-orbit coupled Bose-Einstein condensate. By mapping the spin-orbit coupled BEC to the well-known quantum Dicke model, the Dicke type quantum phase transition is presented with the order parameters quantified by the spin polarization and occupation number of harmonic trap mode. This Dicke type quantum phase transition may be captured by the spin and field squeezing arising from the spin-orbit coupling. We further consider the effect of a finite detuning on the ground state and show the spin polarization and the quasi-momentum exhibit a step jump at zero detuning. Meanwhile, we also find that the presence of the detuning enhances the occupation number of harmonic trap mode, while it suppresses the spin and the field squeezing.

Thermal phase transitions of strongly correlated bosons with spin-orbit coupling

Experiments on ultracold atoms have started to explore lattice effects and thermal fluctuations for two-component bosons with spin-orbit coupling (SOC). Motivated by this, we derive and study a tJ model for lattice bosons with equal Rashba-Dresselhaus SOC and strong Hubbard repulsion in a uniform Zeeman magnetic field. Using the Gutzwiller ansatz, we find strongly correlated ground states with stripe superfluid (SF) order. We formulate a finite temperature generalization of the Gutzwiller method, and show that thermal fluctuations in the doped Mott insulator drive a two-step melting of the stripe SF, revealing a wide regime of a stripe normal fluid.

Discrete and continuum composite solitons in Bose-Einstein condensates with the Rashba spin-orbit coupling in one and two dimensions

We introduce one- and two-dimensional (1D and 2D) continuum and discrete models for the two-component BEC, with the spin-orbit (SO) coupling of the Rashba type between the components, and attractive cubic interactions, assuming that the condensate is fragmented into a quasidiscrete state by a deep optical-lattice potential. In 1D, it is demonstrated, in analytical and numerical forms, that the ground states of both the discrete system and its continuum counterpart switch from striped bright solitons, featuring deep short-wave modulations of its profile, to smooth solitons, as the strength ratio of the inter- and intracomponent attraction, γ, changes from γ<1 to γ>1. At the borderline, γ=1, there is a continuous branch of stable solitons, which share a common value of the energy and interpolate between the striped and smooth ones. Unlike the 2D system, the 1D solitons, which do not represent the ground state at given γ, are nevertheless stable against small perturbations, and they remain stable too in collisions with other solitons. In 2D, a transition between two different types of discrete solitons, which represent the ground state, viz., semivortices and mixed modes, also takes place at γ=1. A specific property of 2D discrete solitons of both types is their discontinuous transition into a delocalized state at a critical value of the SO-coupling strength. We also address the continuum 2D model in the borderline case of γ=1, which was not studied previously, and demonstrate the existence of an energy-degenerate branch of dynamically stable solitons connecting the semivortex and the mixed mode. Last, it is demonstrated that 1D and 2D discrete solitons are mobile, in a limited interval of velocities.

Light-induced gauge fields for ultracold atoms

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle-the graviton-that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms 'feeling' laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials-both Abelian and non-Abelian-in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

Strong interaction effects and criticality of bosons in shaken optical lattices

We study the quantum phase transitions and identify a tricritical point between a normal Bose superfluid, a superfluid that breaks additional Z(2) Ising symmetry, and a Mott insulator in a recent shaken optical lattice experiment. We show that near the transition between normal and Z(2) symmetry breaking superfluids, bosons can condense into a momentum state with high or even locally maximum kinetic energies due to the interaction effect. We present a general low-energy effective field theory that treats both the superfluid transition and the Ising transition in a uniform framework. Using the perturbative renormalization group method, we find that the critical behavior of the quantum phase transition belongs to a universality class different from that of a dilute Bose gas.

Tunable spin-orbit coupling and quantum phase transition in a trapped Bose-Einstein condensate

Spin-orbit coupling (SOC), the intrinsic interaction between a particle spin and its motion, is responsible for various important phenomena, ranging from atomic fine structure to topological condensed matter physics. The recent experimental breakthrough on the realization of SOC for ultra-cold atoms provides a completely new platform for exploring spin-orbit coupled superfluid physics. However, the SOC strength in the experiment is not tunable. In this report, we propose a scheme for tuning the SOC strength through a fast and coherent modulation of the laser intensities. We show that the many-body interaction between atoms, together with the tunable SOC, can drive a quantum phase transition (QPT) from spin-balanced to spin-polarized ground states in a harmonic trapped Bose-Einstein condensate (BEC), which resembles the long-sought Dicke QPT. We characterize the QPT using the periods of collective oscillations of the BEC, which show pronounced peaks and damping around the quantum critical point.

The confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling

The confinement induced resonance provides an indispensable tool for the realization of the low-dimensional strongly interacting quantum system. Here, we investigate the confinement induced resonance in spin-orbit coupled cold atoms with Raman coupling. We find that the quasi-bound levels induced by the spin-orbit coupling and Raman coupling result in the Feshbach-type resonances. For sufficiently large Raman coupling, the bound states in one dimension exist only for sufficiently strong attractive interaction. Furthermore, the bound states in quasi-one dimension exist only for sufficient large ratio of the length scale of confinement to three dimensional s-wave scattering length. The Raman coupling substantially changes the confinement-induced resonance position. We give a proposal to realize confinement induced resonance through increasing Raman coupling strength in experiments.

Fundamental, multipole, and half-vortex gap solitons in spin-orbit coupled Bose-Einstein condensates

Using the parity and time reversal symmetries of a two-dimensional spin-orbit coupled Bose-Einstein condensate in a lattice created by the Zeeman field, we identify and find numerically various families of localized solutions, including multipole and half-vortex solitons. The obtained solutions may exist at any direction of the gauge field with respect to the lattice and can be found either in finite gaps (for repulsive interatomic interactions) or in a semi-infinite gap (for attractive interactions). The existence of half-vortices requires higher symmetry (the reflection with respect to the field direction). Stability of these modes makes them feasible for experimental observation.

Bose-Einstein condensates with cavity-mediated spin-orbit coupling

We propose a novel scheme to generate the spin-orbit coupling for a condensate placed inside an optical cavity by using a standing wave and a traveling wave. It is shown that the interplay of the laser lights and the cavity gives rise to rich quantum phases. Our scheme also generates a large synthetic magnetic field for the dressed spin state, which may facilitate the study of the quantum Hall effect in ultracold atomic gases.

Interaction-tuned dynamical transitions in a Rashba spin-orbit-coupled Fermi gas

We consider the time evolution of the magnetization in a Rashba spin-orbit coupled Fermi gas, starting from a fully polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting nonlinear system of equations gives rise to three distinct dynamical regimes with qualitatively different asymptotic behaviors of the magnetization at long times. The distinct regimes and the transitions between them are controlled by the ratio of interaction and spin-orbit coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero, and for large λ, a partially magnetized state is dynamically stabilized. The dynamics we find is a spin analog of interaction induced self-trapping in double-well Bose Einstein condensates. The predicted phenomena can be realized in trapped Fermi gases with synthetic spin-orbit interactions.

Creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space

It is commonly known that two-dimensional mean-field models of optical and matter waves with cubic self-attraction cannot produce stable solitons in free space because of the occurrence of collapse in the same setting. By means of numerical analysis and variational approximation, we demonstrate that the two-component model of the Bose-Einstein condensate with the spin-orbit Rashba coupling and cubic attractive interactions gives rise to solitary-vortex complexes of two types: semivortices (SVs, with a vortex in one component and a fundamental soliton in the other), and mixed modes (MMs, with topological charges 0 and ±1 mixed in both components). These two-dimensional composite modes can be created using the trapping harmonic-oscillator (HO) potential, but remain stable in free space, if the trap is gradually removed. The SVs and MMs realize the ground state of the system, provided that the self-attraction in the two components is, respectively, stronger or weaker than the cross attraction between them. The SVs and MMs which are not the ground states are subject to a drift instability. In free space (in the absence of the HO trap), modes of both types degenerate into unstable Townes solitons when their norms attain the respective critical values, while there is no lower existence threshold for the stable modes. Moving free-space stable solitons are also found in the present non-Galilean-invariant system, up to a critical velocity. Collisions between two moving solitons lead to their merger into a single one.

Non-Abelian gauge fields in photonic cavities and photonic superfluids

We show that the TE-TM modes splitting and the structure anisotropy of a semiconductor microcavity combine into a non-Abelian gauge field for exciton-polaritons or cavity photons. The field texture can be tuned simply by rotating the sample and ranges continuously from a Rashba to a monopolar field. In the noninteracting regime, the latter leads to remarkable focusing and conical diffraction effects. In the interacting regime, the spin-orbit coupling induces a breakdown of superfluidity. The spatially homogeneous flows become unstable and dynamically evolve into spin textured states, such as stripes or domain walls.

Orbit-induced spin squeezing in a spin-orbit coupled Bose-Einstein condensate

In recent pioneer experiment, a strong spin-orbit coupling, with equal Rashba and Dresselhaus strengths, has been created in a trapped Bose-Einstein condensate. Moreover, many exotic superfluid phenomena induced by this strong spin-orbit coupling have been predicted. In this report, we show that this novel spin-orbit coupling has important applications in quantum metrology, such as spin squeezing. We first demonstrate that an effective spin-spin interaction, which is the heart for producing spin squeezing, can be generated by controlling the orbital degree of freedom (i.e., the momentum) of the ultracold atoms. Compared with previous schemes, this realized spin-spin interaction has advantages of no dissipation, high tunability, and strong coupling. More importantly, a giant squeezing factor (lower than −30 dB) can be achieved by tuning a pair of Raman lasers in current experimental setup. Finally, we find numerically that the phase factor of the prepared initial state affects dramatically on spin squeezing.

Quantum quasicrystals of spin-orbit-coupled dipolar bosons

We study quasi-two-dimensional dipolar Bose gases in which the bosons experience a Rashba spin-orbit coupling. We show that the degenerate dispersion minimum due to the spin-orbit coupling, combined with the long-range dipolar interaction, can stabilize a number of quantum crystalline and quasicrystalline ground states. Coupling the bosons to a fermionic species can further stabilize these phases. We estimate that the crystalline and quasicrystalline phases should be detectable in realistic dipolar condensates, e.g., dysprosium, and discuss their symmetries and excitations.

Meron ground state of Rashba spin-orbit-coupled dipolar bosons

We study the effects of dipolar interactions on a Bose-Einstein condensate with synthetically generated Rashba spin-orbit coupling. The dipolar interaction we consider includes terms that couple spin and orbital angular momentum in a way perfectly congruent with the single-particle Rashba coupling. We show that this internal spin-orbit coupling plays a crucial role in the rich ground-state phase diagram of the trapped condensate. In particular, we predict the emergence of a thermodynamically stable ground state with a meron spin configuration.

Disclination classes, fractional excitations, and the melting of quantum liquid crystals

We consider how fractional excitations bound to a dislocation evolve as the dislocation is separated into a pair of disclinations. We show that some dislocation-bound excitations (such as Majorana modes and half-quantum vortices) are possible only if the elementary dislocation consists of two inequivalent disclinations, as is the case for stripes or square lattices but not for triangular lattices. The existence of multiple inequivalent disclination classes governs the two-dimensional melting of quantum liquid crystals (i.e., nematics and hexatics), determining whether superfluidity and orientational order can simultaneously vanish at a continuous transition.

Superstripes and the excitation spectrum of a spin-orbit-coupled Bose-Einstein condensate

Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with an equal Rashba and Dresselhaus spin-orbit coupling in the stripe phase. The emergence of a double gapless band structure is pointed out as a key signature of Bose-Einstein condensation and of the spontaneous breaking of translational invariance symmetry. In the long wavelength limit the lower and upper branches exhibit, respectively, a clear spin and density nature. For wave vectors close to the first Brillouin zone, the lower branch acquires an important density character responsible for the divergent behavior of the structure factor and of the static response function, reflecting the occurrence of crystalline order. The sound velocities are calculated as functions of the Raman coupling for excitations propagating orthogonal and parallel to the stripes. Our predictions provide new perspectives for the identification of supersolid phenomena in ultracold atomic gases.

Fate of a Bose-Einstein condensate in the presence of spin-orbit coupling

Intensive theoretical studies have recently predicted that a Bose-Einstein condensate will exhibit a variety of novel properties if spin-orbit coupling is present. However, an unambiguous fact has also been pointed out: Rashba coupling destroys a condensate of noninteracting bosons even in high dimensions. Therefore, a conceptually important question arises as to whether or not a condensate exists in the presence of interaction and a general type of spin-orbit coupling. Here we show that interaction qualitatively changes the ground state of bosons under Rashba spin-orbit coupling. Any infinitesimal repulsion forces bosons either to condense at one or two momentum states or to form a superfragmented state that is a superposition of infinite numbers of fragmented condensates. The superfragmented state is unstable against the anisotropy of spin-orbit coupling in systems with large numbers of particles, leading to the revival of a condensate in current experiments.

Condensation transition of ultracold Bose gases with Rashba spin-orbit coupling

We study the Bose-Einstein condensate phase transition of three-dimensional ultracold bosons with isotropic Rashba spin-orbit coupling. Investigating the structure of Ginzburg-Landau free energy as a function of the condensate density, we show, within the Bogoliubov approximation, that the condensate phase transition is first order with a jump in the condensate density. We calculate the transition temperature and the jump in the condensate density at the transition for large spin-orbit coupling, where the transition temperature depends linearly on the density of particles. Finally, we discuss the feasibility of producing the phase transition experimentally.

Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect

We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.

Molecule and polaron in a highly polarized two-dimensional fermi gas with spin-orbit coupling

We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.

Collective dipole oscillations of a spin-orbit coupled Bose-Einstein condensate

In this Letter, we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. The dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region as a function of spin-orbit coupling parameters as well as the oscillation amplitude. The anharmonic properties beyond the effective-mass approximation are revealed, such as the amplitude-dependent frequency and finite oscillation frequency at a place with a divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of the spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility--a static physical quantity--can be measured via the dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates the magnetic nonzero-momentum condensate from the nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a benchmark for recently developed theoretical approaches.

Spin-orbit coupled degenerate Fermi gases

In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum distribution and momentum-resolved radio-frequency spectroscopy, we observe the change of fermion population in different helicity branches consistent with a finite temperature calculation, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system.

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.

Bose-Hubbard models with synthetic spin-orbit coupling: Mott insulators, spin textures, and superfluidity

Motivated by the experimental realization of synthetic spin-orbit coupling for ultracold atoms, we investigate the phase diagram of the Bose-Hubbard model in a non-Abelian gauge field in two dimensions. Using a strong coupling expansion in the combined presence of spin-orbit coupling and tunable interactions, we find a variety of interesting magnetic Hamiltonians in the Mott insulator (MI), which support magnetic textures such as spin spirals and vortex and Skyrmion crystals. An inhomogeneous mean-field treatment shows that the superfluid (SF) phases inherit these exotic magnetic orders from the MI and display, in addition, unusual modulated current patterns. We present a slave-boson theory which gives insight into such intertwined spin-charge orders in the SF, and discuss signatures of these orders in Bragg scattering, in situ microscopy, and dynamic quench experiments.

Stability of ultracold atomic Bose condensates with Rashba spin-orbit coupling against quantum and thermal fluctuations

We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit coupling in three dimensions against quantum and thermal fluctuations. The ground state depletion of the plane-wave condensate due to quantum fluctuations is, as we show, finite, and therefore the condensate is stable. We also calculate the corresponding shift of the ground state energy. Although the system cannot condense in the absence of interparticle interactions, by estimating the number of excited particles we show that interactions stabilize the condensate even at nonzero temperature. Unlike in the usual Bose gas, the normal phase is not kinematically forbidden at any temperature; calculating the free energy of the normal phase at finite temperature, and comparing with the free energy of the condensed state, we infer that generally the system is condensed at zero temperature, and undergoes a transition to normal at nonzero temperature.

Stable Skyrmions in SU(2) gauged Bose-Einstein condensates

We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions are physically understandable with the concept of the helical modulation in a unified way. These topological objects might potentially be realizable in two-component Bose-Einstein condensates experimentally.

Synthetic 3D spin-orbit coupling

We describe a method for creating a three-dimensional analogue to Rashba spin-orbit coupling in systems of ultracold atoms. This laser induced coupling uses Raman transitions to link four internal atomic states with a tetrahedral geometry, and gives rise to a Dirac point that is robust against environmental perturbations. We present an exact result showing that such a spin-orbit coupling in a fermionic system always gives rise to a molecular bound state.

Quantum tricriticality and phase transitions in spin-orbit coupled Bose-Einstein condensates

We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.

Emergence of chiral magnetism in spinor Bose-Einstein condensates with Rashba coupling

Hydrodynamic theory of the spinor BEC condensate with Rashba spin-orbit coupling is presented. A close mathematical analogy of the Rashba-Bose-Einstein condensate model to the recently developed theory of chiral magnetism is found. Hydrodynamic equations for mass density, superfluid velocity, and the local magnetization are derived. The mass current is shown to contain an extra term proportional to the magnetization direction, as a result of the Rashba coupling. Elementary excitations around the two known ground states of the Rashba-Bose-Einstein condensate Hamiltonian, the plane-wave, and the stripe states, are worked out in the hydrodynamic framework, highlighting the cross coupling of spin and superflow velocity excitations due to the Rashba term.

Spin-orbit-coupled dipolar Bose-Einstein condensates

We propose an experimental scheme to create spin-orbit coupling in spin-3 Cr atoms using Raman processes. By employing the linear Zeeman effect and optical Stark shift, two spin states within the ground electronic manifold are selected, which results in a pseudospin-1/2 model. We further study the ground state structures of a spin-orbit-coupled Cr condensate. We show that, in addition to the stripe structures induced by the spin-orbit coupling, the magnetic dipole-dipole interaction gives rise to the vortex phase, in which a spontaneous spin vortex is formed.

Mean-field dynamics of spin-orbit coupled Bose-Einstein condensates

Spin-orbit coupling (SOC), the interaction between the spin and momentum of a quantum particle, is crucial for many important condensed matter phenomena. The recent experimental realization of SOC in neutral bosonic cold atoms provides a new and ideal platform for investigating spin-orbit coupled quantum many-body physics. In this Letter, we derive a generic Gross-Pitaevskii equation as the starting point for the study of many-body dynamics in spin-orbit coupled Bose-Einstein condensates. We show that different laser setups for realizing the same SOC may lead to different mean-field dynamics. Various ground state phases (stripe, phase separation, etc.) of the condensate are found in different parameter regions. A new oscillation period induced by the SOC, similar to the Zitterbewegung oscillation, is found in the center-of-mass motion of the condensate.

Spin-orbit coupled weakly interacting Bose-Einstein condensates in harmonic traps

We investigate theoretically the phase diagram of a spin-orbit coupled Bose gas in two-dimensional harmonic traps. We show that at strong spin-orbit coupling the single-particle spectrum decomposes into different manifolds separated by ℏω{⊥}, where ω{⊥} is the trapping frequency. For a weakly interacting gas, quantum states with Skyrmion lattice patterns emerge spontaneously and preserve either parity symmetry or combined parity-time-reversal symmetry. These phases can be readily observed in a spin-orbit coupled gas of ^{87}Rb atoms in a highly oblate trap.

Trapped two-dimensional condensates with synthetic spin-orbit coupling

We study trapped 2D atomic Bose-Einstein condensates with spin-independent interactions in the presence of an isotropic spin-orbit coupling, showing that a rich physics results from the nontrivial interplay between spin-orbit coupling, confinement and interatomic interactions. For low interactions two types of half-vortex solutions with different winding occur, whereas strong-enough repulsive interactions result in a stripe-phase similar to that predicted for homogeneous condensates. Intermediate interaction regimes are characterized for large enough spin-orbit coupling by an hexagonally-symmetric phase with a triangular lattice of density minima similar to that observed in rapidly rotating condensates.

Spin-orbit coupled Bose-Einstein condensate under rotation

We examine the combined effects of Rashba spin-orbit (SO) coupling and rotation on trapped spinor Bose-Einstein condensates. The nature of single particle states is thoroughly examined in the Landau level basis and is shown to support the formation of a half-quantum vortex. In the presence of weak s-wave interactions, the ground state at strong SO coupling develops ringlike structures with domains whose number shows step behavior with increasing rotation. For the fast rotation case, the vortex pattern favors a triangular lattice, accompanied by density depletion in the central region and a weakened Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is facilitated when SO coupling and rotation are both strong.

Anomalous Hall conductivity from the dipole mode of spin-orbit-coupled cold-atom systems

Motivated by recent experiments by Lin et al., [Nature (London) 471, 83 (2011)] that engineered spin-orbit coupling in ultracold mixtures of bosonic atoms, we study the dipole oscillation of trapped spin-orbit-coupled noncondensed Bose and Fermi gases. We find that different directions of oscillation are coupled by the spin-orbit interactions. The phase difference between oscillatory motion in orthogonal directions and the trapping frequencies of the modes are shown to be related to the anomalous Hall conductivity. Our results can be used to experimentally determine the anomalous Hall conductivity for cold-atom systems.

Spin-orbit coupled Fermi gases across a Feshbach resonance

In this Letter we study both ground state properties and the superfluid transition temperature of a spin-1/2 Fermi gas across a Feshbach resonance with a synthetic spin-orbit coupling, using the mean-field theory and the exact solution of two-body problem. We show that a strong spin-orbit coupling can significantly enhance the pairing gap for negative scattering length a(s), due to increased density of state at Fermi surface. Strong spin-orbit coupling can also significantly enhance the superfluid transition temperature Tc to a sizable fraction of Fermi temperature when a(s) ≤ 0, while it suppresses Tc slightly for positive a(s). The interaction energy and pair size at resonance are also discussed.

Bose-Einstein condensates with spin-orbit interaction

Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.

Condensate fluctuations of interacting Bose gases within a microcanonical ensemble

Based on counting statistics and Bogoliubov theory, we present a recurrence relation for the microcanonical partition function for a weakly interacting Bose gas with a finite number of particles in a cubic box. According to this microcanonical partition function, we calculate numerically the distribution function, condensate fraction, and condensate fluctuations for a finite and isolated Bose-Einstein condensate. For ideal and weakly interacting Bose gases, we compare the condensate fluctuations with those in the canonical ensemble. The present approach yields an accurate account of the condensate fluctuations for temperatures close to the critical region. We emphasize that the interactions between excited atoms turn out to be important for moderate temperatures.