# Thermal transitions of the modulated superfluid for spin-orbit coupled correlated bosons in an optical lattice

## TL;DR

This paper explores how spin-orbit coupling influences the thermal phase transitions of correlated bosons in an optical lattice, revealing various superfluid phases and their thermal behaviors.

## Contribution

It introduces a comprehensive analysis of thermal transitions in a spin-orbit coupled Bose-Hubbard model, including phase boundaries and experimental implications.

## Key findings

- Spin-orbit coupling promotes finite wavevector condensation.
- Thermal broadening affects momentum distribution and magnetic textures.
- Critical interactions and temperatures decrease with increasing spin-orbit coupling.

## Abstract

We investigate the thermal physics of a Bose-Hubbard model with Rashba spin-orbit coupling starting from a strong coupling mean-field ground state. The essential role of the spin-orbit coupling $\left(\gamma\right)$ is to promote condensation of the bosons at a finite wavevector ${k}_{0}$. We find that the bosons display either homogeneous or phase-twisted or orbital ordered superfluid phases, depending on $\gamma$ and the inter-species interaction strength $\lambda$. We show that an increase of $\gamma$ leads to suppression of the critical interaction $U_c$ for the superfluid to Mott insulator transition in the ground state, and a reduction of the $T_c$ for superfluid to Bose-liquid transition at a fixed interaction. We capture the thermal broadening in the momentum distribution function, and the real space profiles of the thermally disordered magnetic textures, including their homogenization for $T \gtrsim T_{c}$. We provide a Landau theory based description of the ground state phase boundaries and thermal transition scales, and discuss experiments which can test our theory.