Quantum depletion and superfluid density of a supersolid in Raman spin-orbit coupled Bose gases

TL;DR

This paper theoretically studies a 3D Bose gas with Raman spin-orbit coupling, revealing phase transition shifts, quantum depletion behavior, and superfluid density characteristics across phases, aiding understanding of supersolid properties.

Contribution

It introduces an improved ansatz for the stripe phase, accurately predicts phase transition points, and analyzes quantum depletion and superfluid density in different phases of the system.

Findings

Phase transition from stripe to plane-wave is shifted to higher Rabi frequency.

Quantum depletion shows a discontinuous jump at the phase transition.

Superfluid density is suppressed along the spin-orbit direction and vanishes at the transition.

Abstract

We theoretically investigate a three-dimensional weakly interacting Bose gas with one-dimensional Raman-type spin-orbit coupling at zero temperature. By employing an improved ansatz, including high-order harmonics in the stripe phase, we show that the critical transition from the stripe to the plane-wave phases is shifted to a relatively larger Rabi frequency compared to the prediction by previous work [Li $\textit{et al.}$, Phys. Rev. Lett. $\textbf{108}$, 225301 (2012)] using a first-order stripe ansatz. We also determine the quantum depletion and superfluid density over a large range of Rabi frequency in different phases. The depletion exhibits an intriguing behavior with a discontinuous jump at the transition between the stripe and plane-wave phases, and a maximum at the transition between the plane-wave and zero-momentum phases. The superfluid density is derived through a phase-twist method. In the plane-wave and zero-momentum phases, it is significantly suppressed along the spin-orbit-coupling direction and vanishes at the transition, consistent with a recent work [Zhang $\textit{et al.}$, Phys. Rev. A $\textbf{94}$, 033635 (2016)], while in the stripe phase, it smoothly decreases with increasing Rabi frequency. Our predictions would be useful for further theoretical and experimental studies of the exotic supersolid stripe phase.