Critical temperature of a Rashba spin-orbit-coupled Bose gas in a harmonic trap

Abstract

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 ${N}^{2/5}$ and ${N}^{2/3}$ in three and two dimensions, respectively, contrasted to the predictions of ${N}^{1/3}$ and ${N}^{1/2}$ in the absence of spin-orbit coupling. Finite-size corrections in three dimensions are also discussed.