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

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.