Superfluid density of a spin-orbit-coupled Bose gas

We discuss the superfluid properties of a uniform, weakly interacting Bose-Einstein condensed gas with spin-orbit coupling, realized recently 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 breaking of Galilean invariance and by the gapped branch of the elementary excitations whose contribution to various sum rules is discussed explicitly. Our predictions for the superfluid density are successfully compared with the available experimental results based on the measurement of the sound velocities.

Figure 1

Dependence of ${\rho }_s/\rho$ on the Raman coupling strength at $T=0$. Full line: Theoretical prediction [Eqs. (9) and (10)] with $G_1=0.12k_0^2$ and $G_2/G_1={10}^{-3}$, appropriate for the experiment [14]. The experimental values (red squares) are based on Eq. (15), with the measured values of the sound velocities taken from [14] and the value of the compressibility calculated in [19]. The figure reveals the strong quenching of the superfluid density near the transition between the plane wave and the zeroth momentum phase.