Superfluid Density of a Spin-orbit Coupled Bose Gas

TL;DR

This paper investigates the superfluid properties of a spin-orbit coupled Bose-Einstein condensate, revealing a finite normal fluid density at zero temperature and analyzing the effects of excitations and phase transitions.

Contribution

It demonstrates the existence of a finite normal fluid density at zero temperature in spin-orbit coupled Bose gases and explores its dependence on Raman coupling and phase transitions.

Findings

Normal fluid density is finite at zero temperature.

Superfluid density equals total density away from phase transition.

Normal fluid density becomes equal to total density at the phase transition.

Abstract

We discuss the superfluid properties of a Bose-Einstein condensed gas with spin-orbit coupling, recently realized in experiments. We find a finite normal fluid density $\rho_n$ at zero temperature which turns out to be a function of the Raman coupling. In particular, the entire fluid becomes normal at the transition point from the zero momentum to the plane wave phase, even though the condensate fraction remains finite. We emphasize the crucial role played by the gapped branch of the elementary excitations and discuss its contributions to various sum rules. Finally, we prove that an independent definition of superfluid density $\rho_s$, using the phase twist method, satisfies the equality $\rho_n+\rho_s=\rho$, the total density, despite the breaking of Galilean invariance.