Phase Transitions in Ultra-Cold Two-Dimensional Bose Gases

TL;DR

This paper reviews the theory of phase transitions in two-dimensional Bose gases, identifying three phases and analyzing vortex pair formation using classical field simulations.

Contribution

It provides a phase diagram for trapped 2D Bose gases and links vortex dynamics to phase transitions, extending understanding of BKT physics.

Findings

Identifies three distinct phases in 2D Bose gases

Determines a critical temperature for vortex pair formation

Confirms vortex-antivortex pair activation via simulations

Abstract

We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.