Thermal amplification and melting of phases in spin-orbit-coupled spin-1 Bose-Einstein condensates

TL;DR

This study uses Hartree-Fock-Bogoliubov theory to analyze how finite temperature affects phase transitions and melting in spin-orbit-coupled spin-1 Bose-Einstein condensates, revealing thermal effects on supersolid phases.

Contribution

It provides the first finite-temperature phase diagrams for spin-orbit-coupled spin-1 BECs using a self-consistent theoretical approach.

Findings

Supersolid stripe phase melts at finite temperature.

Critical points depend on Raman coupling and Zeeman field.

Quantum and thermal fluctuations differently influence phase boundaries.

Abstract

We implement Hartree-Fock-Bogoliubov theory with Popov approximation for a homogeneous Raman-induced spin-orbit-coupled spin-1 Bose-Einstein condensate and investigate the effects of finite temperature ($T$) on the ground-state phase diagram. We calculate the roton gap as a function of Raman coupling ($\Omega$) or quadratic Zeeman field strength ($\epsilon$) to extract the critical points separating the supersolid stripe phase from the plane wave or zero-momentum phase at finite temperatures. We present a few representative finite-temperature phase diagrams for the system in the $T-\Omega$ and $T-\epsilon$ planes. Our observations indicate that the supersolid stripe phase melts at finite temperatures. We also discuss the contrasting roles of quantum and thermal fluctuations in shifting the phase boundary separating the supersolid stripe from the plane-wave phase.