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

TL;DR

This paper provides a theoretical analysis of how Rashba spin-orbit coupling affects the critical temperature and condensate fraction of an ideal Bose gas in harmonic traps, revealing significant decreases and new scaling behaviors.

Contribution

It derives analytic expressions for the critical temperature and condensate fraction considering spin-orbit coupling, and compares semi-classical approximations with exact discrete level calculations.

Findings

Critical temperature decreases with spin-orbit coupling.

Scaling of critical temperature with particle number changes due to spin-orbit coupling.

Finite size effects are analyzed in three dimensions.

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 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 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.