Equation of state and phase transition in spin-orbit-coupled Bose gases at finite temperature: A perturbation approach

TL;DR

This paper investigates the phase transition and equation of state in spin-orbit-coupled Bose gases at finite temperature using a perturbation approach, revealing temperature-dependent phase boundary shifts and experimental measurement methods.

Contribution

It introduces a perturbation method to analyze phase transitions in spin-orbit-coupled Bose gases at finite temperature, including a way to measure Raman susceptibility experimentally.

Findings

Phase boundary shifts towards the stripe phase with increasing temperature.

Ferromagnetic order is more thermally robust than crystalline order.

Qualitative agreement with recent experimental results in rubidium gases.

Abstract

We study two-component Bose gases with Raman induced spin-orbit coupling via a perturbation approach at finite temperature. For weak coupling, free energy is expanded in terms of Raman coupling strength up to the second order, where the coefficient (referred to as Raman susceptibility) is determined according to linear response theory. The equation of state for the stripe phase and the plane-wave phase are obtained in Popov approximation, and the first order transition between these two phases is investigated. As temperature increases, we find the phase boundary bends toward the stripe phase side in most temperature regions, which implies the ferromagnetic order is more robust than the crystalline order in presence of thermal fluctuations. Our results qualitatively agree with the recent experimental observation in rubidium atomic gases. A method to measure the Raman susceptibility through the two-photon Bragg scattering experiment is also discussed.