Quantum-geometric perspective on spin-orbit-coupled Bose superfluids

TL;DR

This paper investigates how quantum geometry influences superfluid properties in spin-orbit-coupled Bose gases, revealing geometric effects on sound velocity, phase transitions, and superfluid density using the Bogoliubov approximation.

Contribution

It provides a detailed analysis of the geometric contributions to superfluid characteristics in spin-orbit-coupled Bose gases, including derivations of the Bogoliubov spectrum and superfluid density tensor.

Findings

Geometric contributions to sound velocity depend linearly on interaction strength.

Identified the phase boundary for the transition from plane-wave to stripe phase.

Quantified the role of interband processes in superfluid density related to quantum geometry.

Abstract

We employ the Bogoliubov approximation to study how the quantum geometry of the helicity states affects the superfluid properties of a spin-orbit-coupled Bose gas in continuum. In particular we derive the low-energy Bogoliubov spectrum for a plane-wave condensate in the lower helicity band and show that the geometric contributions to the sound velocity are distinguished by their linear dependences on the interaction strength, i.e., they are in sharp contrast to the conventional contribution which has a square-root dependence. We also discuss the roton instability of the plane-wave condensate against the stripe phase and determine their phase transition boundary. In addition we derive the superfluid density tensor by imposing a phase-twist on the condensate order parameter and study the relative importance of its contribution from the interband processes that is related to the quantum geometry.