Finite temperature spin dynamics of a two-dimensional Bose-Bose atomic mixture

TL;DR

This paper investigates how thermal fluctuations influence the phase behavior and spin dynamics of two-dimensional binary Bose mixtures, revealing limitations of mean-field theory near phase transitions.

Contribution

It demonstrates that mean-field predictions of phase stability can be invalidated by thermal fluctuations, and compares analytical and numerical approaches to understand these effects.

Findings

Mean-field theory predicts instability of the fully miscible phase at finite temperature.

Numerical simulations show thermal fluctuations smooth phase transition features.

Mean-field approximation fails near the miscible-immiscible transition due to thermal effects.

Abstract

We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at $T=0$ may become unstable at $T\neq0$, as a consequence of a divergent behaviour in the spin susceptibility. We test this prediction by performing numerical simulations with the Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity.