We show that in a two-component Bose gas with Rashba spin-orbit coupling (SOC) two atoms can form bound states (Rashbons) with any intra-species scattering length. At zero center-of-mass momentum there are two degenerate Rashbons due to time-reversal symmetry, but the degeneracy is lifted at finite in-plane momentum with two different effective masses. A stable Rashbon condensation can be created in a dilute system with weakly attractive intra-species and repulsive inter-species interactions. The critical temperature of Rashbon condensation is about six times smaller than the BEC transition temperature of an ideal Bose gas. Due Rashba SOC, excitations in the Rashbon condensation phase are anisotropic in momentum space.
Synthetic non-Abelian gauge fields in cold atom systems produce a Rashba spin-orbit interaction described by a vector $\blam = (λ_x, λ_y, λ_z)$. It was recently shown [Phys. Rev. B 84, 014512 (2011)] that on increasing $λ= |\blam|$, fermions at a finite density $ρ\approx\kf^3$ evolve to a BEC like state even in the presence of a weak attractive interaction (described by a scattering length $\as$). The BEC obtained at large spin-orbit coupling ($λ\gg k_F$) is a condensate of rashbons -- novel bosonic bound pairs of fermions whose properties are determined solely by the gauge field. Here we stud…
Motivated by the prospect of realizing a Fermi gas of $^{40}$K atoms with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We show that this anisotropic superfluidity can be probed via measuring the momentum distribution and single-particle spectral function in a trapped atomic $^{40}$K cloud near a Feshbac…
Fermi gases with generalized Rashba spin orbit coupling inducedby a synthetic gauge field have the potential of realizing many interesting states such as rashbon condensates and topological phases. Here we develop a fluctuation theory of such systems and demonstrate that beyond-Gaussian effects are essential to capture the physics of such systems. We obtain their phase diagram by constructing an approximate non-Gaussian theory. We conclusively establish that spin-orbit coupling can enhance the exponentially small transition temperature ($T_c$) of a weakly attracting superfluid to the order of …
We present a theoretical study of the superfluidity and the corresponding collective modes in two-component atomic Fermi gases with s-wave attraction and synthetic Rashba spin-orbit coupling. The general effective action for the collective modes is derived from the functional path integral formalism. By tuning the spin-orbit coupling from weak to strong, the system undergoes a crossover from an ordinary BCS/BEC superfluid to a Bose-Einstein condensate of rashbons. We show that the properties of the superfluid density and the Anderson-Bogoliubov mode manifest this crossover. At large spin-orbit…
We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean-field, particularly in the strong-coupling unitary limit. We also investiga…
We investigate the pair condensation of a two-spin-component Fermi gas in the presence of both Rashba and Dresselhaus spin-orbit couplings. We calculate the condensate fraction in the BCS-BEC crossover both in two and in three dimensions by taking into account singlet and triplet pairings. These quantities are studied by varying the spin-orbit interaction from the case with the only Rashba to the equal-Rashba-Dresselhaus one. We find that, by mixing the two couplings, the singlet pairing decreases while the triplet pairing is suppressed in the BCS regime and increased in the BEC regime, both i…
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 …
By adopting a $T$-matrix-based method within the $G_0G$ approximation for the pair susceptibility, we study the effects of the pairing fluctuation on the three-dimensional spin-orbit coupled Fermi gases at finite temperature. The critical temperatures of the superfluid/normal phase transition are determined for three different types of spin-orbit coupling (SOC): (1) the extreme oblate (EO) or Rashba SOC, (2) the extreme prolate (EP) or equal Rashba-Dresselhaus SOC, and (3) the spherical (S) SOC. For EO- and S-type SOC, the SOC dependence of the critical temperature signals a crossover from BCS…
A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a dispersion minimum on a circle in momentum space; we show that kinematic constraints due to this dispersion cause interactions to renormalize to universal, angle-dependent values that govern the phase structure in the dilute-gas limit. We find that, regardless of microscopic interactions, (a) the ground state involves condensation at two opposite momenta, and is, in finite systems, a fragmented condensate; and (b) there is a nonzero-temperature instability toward the condensation of pairs of bosons. We discuss how our…
Ground-state phase diagram of two-component Bose gases with Rashba spin-orbit coupling is determined via a variational approach. A phase in which the fully polarized condensate occupies zero momentum is identified. This zero-momentum phase competes with the spin density wave phase when interspecies interaction is stronger than intraspecies interaction, and the former one is always the ground state for weak spin-orbit coupling. When the energies of these two phases are close, there is a phase separation between them. At finite temperature, such a zero-momentum condensation can be induced by a f…
Bose-Einstein condensation in the presence of a synthetic spin-momentum interaction is considered, focusing on the case where a Dirac or Rashba potential is generated via a tripod scheme. We found that the ground states can be either plane wave states or superpositions of them, each characterized by their unique density distributions.
We investigate theoretically BEC-BCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance between the two components. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We study the properties of Rashba pairs using a standard pair fluctuation theory. At zero temperature, the Rashba pairs condense into a macroscopic mixed spin state. We discuss in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various…
We study the Feshbach resonance of spin-1/2 particles in the presence of a uniform synthetic non-Abelian gauge field that produces spin orbit coupling along with constant spin potentials. We develop a renormalizable quantum field theory that includes the closed channel boson which engenders the Feshbach resonance, in the presence of the gauge field. By a study of the scattering of two particles in the presence of the gauge field, we show that the Feshbach magnetic field, where the apparent low energy scattering length diverges, depends on the conserved centre of mass momentum of the two partic…
We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the $G_0G$ pair fluctuation theory. These fluctuations generate a pseudogap even persistent above $T_c$. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting $T_c$ curves show that the enhancement of pairing due to the SOC roughly cancels out the…
We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy $E_{\text B}$ and effective mass $m_{\text B}$ of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable…
We investigated effects of a Rashba-type spin-orbit coupling (SOC) on the condensed density and superfluid density tensor of a two-component Fermi gas in the BCS-BEC crossover at zero temperature. In anisotropic three dimensions (3D), we found that SOC has an opposite effect on condensation (enhanced) and superfluidity (suppressed in the SOC direction) and this effect becomes most pronounced for very weak interactions and the SOC strength being larger than a characteristic value. Furthermore, as functions of SOC strength, the condensed density changes monotonously for all interaction parameter…
We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived, based on a semi-classical approximation to the single-particle energy spectrum and density of states, and are compared with exact results obtained by explicitly summing discrete energy levels for small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to a finite spin-orbit coupling. For large coupling strength and fi…
The recent realization of synthetic spin-orbit coupling represents an outstanding achievement in the physics of ultracold quantum gases. In this review we explore the properties of a spin-orbit-coupled Bose-Einstein condensate with equal Rashba and Dresselhaus strengths. This system presents a rich phase diagram, which exhibits a tricritical point separating a zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In the stripe phase translational invariance is spontaneously broken, in analogy with supersolids. Spin-orbit coupling also strongly affects the dynamics of the …
We theoretically predict an exotic topological superfluid state with spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. This inhomogeneous topological superfluidity is induced by applying simultaneously a perpendicular Zeeman magnetic field and an equally weighted Rashba and Dresselhaus spin-orbit coupling in one-dimensional optical lattices. Based on the self-consistent Bogoliubov--de Gennes theory, we confirm that this novel topological phase is a unique condensation of Cooper pairs, which manifests the interplay between the inhomogeneity of superfluid and its…
A weakly interacting, spin-orbit coupled, two-component, ultracold Bose gas bound to a Bravais lattice is studied. Motivated by recent experimental advances in the field of synthetically spin-orbit coupled, ultracold, neutral atomic gases showing Bose-Einstein condensation, an analytic framework with which to describe such systems in the superfluid regime is presented. This is applied to a Rashba spin-orbit-coupled Bose gas in a two-dimensional optical lattice. The exotic nature of Bose-Einstein condensation in the presence of spin-orbit coupling is an interesting study by itself. Additionally…
Using Bogoliubov theory we calculate the excitation spectrum of a spinor Bose-Einstein condensed gas with 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 th…
We investigate the superfluid phases of a Rashba spin-orbit coupled Bose-Einstein condensate residing on a two dimensional square optical lattice in the presence of an effective Zeeman field $Ω$. At a critical value $Ω=Ω_c$, the single-particle spectrum $ E_k $ changes from having a set of four degenerate minima to a single minimum at $k=0$, corresponding to condensation at finite or zero momentum, respectively. We describe this quantum phase transition and the symmetry breaking of the condensate phases. We use the Bogoliubov theory to treat the superfluid phases and determine the phase diagra…
We consider Bose-Einstein condensation of an ideal bose gas with an equal mixture of `Rashba' and `Dresselhaus' spin-orbit interactions and study its effect on the critical temperature. In uniform bose gas a `cusp' and a sharp drop in the critical temperature occurs due to the change in the density of states at a critical Raman coupling where the degeneracy of the ground states is lifted. Relative drop in the critical temperature depends on the diluteness of the gas as well as on the spin-orbit coupling strength. In the presence of a harmonic trap, the cusp in the critical temperature smoothen…
Spin-orbit coupling with bosons gives rise to novel properties that are absent in usual bosonic systems. Under very general conditions, the conventional ground state wavefunctions of bosons are constrained by the "no-node" theorem to be positive-definite. In contrast, the linear-dependence of spin-orbit coupling leads to complex-valued condensate wavefunctions beyond this theorem. In this article, we review the study of this class of unconventional Bose-Einstein condensations focusing on their topological properties. Both the 2D Rashba and 3D $\vecσ \cdot \vec{p}$-type Weyl spin-orbit coupling…
We compute the finite-temperature phase diagram of a pseudospin-$1/2$ Bose gas with contact interactions, using two complementary methods: the random phase approximation (RPA) and self-consistent Hartree-Fock theory. We show that the inter-spin interactions, which break the (pseudo) spin-rotational symmetry of the Hamiltonian, generally lead to the appearance of a magnetically ordered phase at temperatures above the superfluid transition. In three dimensions, we predict a normal easy-axis/easy-plane ferromagnet for sufficiently strong repulsive/attractive inter-species interactions respectivel…
