# Magnetic phase transition in a mixture of two interacting Bose gases at finite temperature

## TL;DR

This paper predicts a first-order phase transition to spatial separation in a two-component Bose-Einstein condensate mixture caused by thermal fluctuations, with explicit calculations of transition temperature and response functions.

## Contribution

It demonstrates how thermal fluctuations induce a first-order demixing transition in binary Bose gases, extending beyond mean-field theory with explicit predictions for transition parameters.

## Key findings

- Thermal fluctuations cause a first-order phase transition to demixing.
- Transition temperature $T_M$ is about 0.7 times the BEC critical temperature.
- Explicit predictions for compressibility and spin susceptibility at transition.

## Abstract

The miscibility condition for a binary mixture of two interacting Bose-Einstein condensates is shown to be deeply affected by interaction driven thermal fluctuations. These give rise to a first order phase transition to a demixed phase with full spatial separation of the two condensates, even if the mixture is miscible at zero temperature. Explicit predictions for the isothermal compressibility, the spin susceptibility, and the phase transition temperature $T_M$ are obtained in the framework of Popov theory, which properly includes beyond mean-field quantum and thermal fluctuations in both the spin and density channels. For a mixture of two sodium condensates occupying the hyperfine states $\lvert F=1, m_F=1 \rangle$ and $\lvert F=1, m_F=-1 \rangle$ respectively, $T_M$ is predicted to occur at about $0.7$ times the usual BEC critical temperature.