Superfluidity of a Raman spin-orbit-coupled Bose gas at finite temperature

TL;DR

This paper studies the superfluid properties of a three-dimensional Bose gas with Raman spin-orbit coupling at various temperatures, deriving analytic expressions for superfluid density and revealing non-monotonic temperature effects near phase transitions.

Contribution

It provides explicit analytic formulas for superfluid density in spin-orbit-coupled Bose gases at finite temperature, extending previous zero-temperature results and exploring temperature-dependent behaviors.

Findings

Superfluid density matches previous phase-twist predictions at zero temperature.

Superfluid density exhibits non-monotonic temperature dependence near phase transition.

Landau critical velocity shows similar temperature dependence, indicating superfluidity loss.

Abstract

We investigate the superfluidity of a three-dimensional weakly interacting Bose gas with a one-dimensional Raman-type spin-orbit coupling at both zero and finite temperatures. Using the imaginary-time Green's function within the Bogoliubov approximation, we explicitly derive analytic expressions of the current-current response functions in the plane-wave and zero-momentum phases, from which we extract the superfluid density in the limits of long wavelength and zero frequency. At zero temperature, we check that the resultant superfluid density agrees exactly with our previous analytic prediction obtained from a phase-twist approach. Both results also satisfy a generalized Josephson relation in the presence of spin-orbit coupling. At finite temperature, we find a significant non-monotonic temperature dependence of superfluid density near the transition from the plane-wave phase to the zero-momentum phase. We show that this non-trivial behavior might be understood from the sound velocity, which has a similar temperature dependence. The non-monotonic temperature dependence is also shared by Landau critical velocity, above which the spin-orbit-coupled Bose gas loses its superfluidity. Our results would be useful for further theoretical and experimental studies of superfluidity in exotic spin-orbit coupled quantum gases.