Hidden long-range order in a spin-orbit coupled two-dimensional Bose gas

TL;DR

This paper reveals that a 2D spin-orbit coupled Bose gas exhibits both quasi-long-range order in total phase and true long-range order in relative phase, with phase transitions driven by temperature and anisotropic spin-orbit coupling.

Contribution

It demonstrates the coexistence of different types of long-range order in a 2D Bose gas due to spin-orbit coupling, combining analytical and numerical methods.

Findings

Total phase shows BKT transition with quasi long-range order.

Relative phase exhibits an Ising-type transition with true long-range order.

Analytical predictions agree well with numerical simulations.

Abstract

A spin-orbit coupled two-dimensional (2D) Bose gas is shown to simultaneously possess quasi and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii- Kosterlitz-Thouless transition to a low temperature phase with quasi long-range order, as expected for a two- dimensional quantum gas. Additionally, the relative phase undergoes an Ising-type transition building up true long-range order, which is induced by the anisotropic spin-orbit coupling. Based on the Bogoliubov approach, expressions for the total- and relative-phase fluctuations are derived analytically for the low temperature regime. Numerical simulations of the stochastic projected Gross-Pitaevskii equation (SPGPE) give a good agreement with the analytical predictions.