We study the Bardeen–Cooper–Shrieffer (BCS) pairing state of a two-component Bose gas with a symmetric spin–orbit coupling (SOC). In the dilute limit at low temperature, this system is essentially a dilute gas of diatomic molecules. We compute the effective mass of the molecule and find that it is anisotropic in momentum space. The critical temperature of the pairing state is about eight times smaller than the Bose–Einstein condensation (BEC) transition temperature of an ideal Bose gas with the same density.
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 Bose gas with attractive intra-species and repulsive inter-species interactions. The critical temperature of Rashbon condensation is about six times smaller than the Bose–Einstein condensation transition temperature of an ideal Bose gas. Due to the Rashba SOC, excitations in the Rashbon condensation phase are anisotropic in momentum space.
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 semiclassical 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 a small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to finite spin-orbit coupling. For a large coupling strength and a finite number of particles
N, the critical temperature scales as
N2/5 and
N2/3 in three and two dimensions, respectively, contrasted to the predictions of
N1/3 and
N1/2 in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.