Finite temperature ferromagnetic transition in coherently coupled Bose gases

TL;DR

This study investigates how the zero-temperature paramagnetic-ferromagnetic quantum phase transition in coherently coupled Bose gases evolves at finite temperatures using numerical simulations, revealing a line of critical points with temperature-dependent scaling behaviors.

Contribution

It provides the first detailed analysis of the finite temperature phase transition in coherently coupled Bose gases, including the critical line and scaling laws using stochastic Gross-Pitaevskii simulations.

Findings

Critical point shifts linearly with temperature.

Magnetization and fluctuations follow power-law scaling.

Critical slowing down correlates with the spin excitation gap.

Abstract

A paramagnetic-ferromagnetic quantum phase transition is known to occur at zero temperature in a two-dimensional coherently-coupled Bose mixture of dilute ultracold atomic gases provided the interspecies interaction strength is large enough. Here we study the fate of such a transition at finite temperature by performing numerical simulations with the stochastic (projected) Gross-Pitaevskii formalism, which includes both thermal and beyond mean-field effects. By extracting the average magnetization, the magnetic fluctuations and characteristic relaxation frequency (or, critical slowing down), we identify a finite temperature critical line for the transition. We find that the critical point shifts linearly with temperature and, in addition, the three quantities used to probe the transition exhibit a temperature power-law scaling. The scaling of the critical slowing down is found to be consistent with thermal critical exponents and is very well approximated by the square of the spin excitation gap at the zero-temperature.