Thermodynamically activated vortex-dipole formation in a two-dimensional Bose-Einstein condensate

TL;DR

This paper investigates the formation of vortex-antivortex pairs in a two-dimensional Bose-Einstein condensate and estimates the temperature at which the system transitions from a coherent BEC to a BKT-like phase, aligning with recent simulations.

Contribution

It provides a simple free energy estimate for vortex dipole formation in a 2D Bose gas, predicting the BEC to BKT transition temperature based on particle number and temperature.

Findings

Vortex dipoles lower free energy in the BKT phase

Estimated transition temperature aligns with numerical simulations

Vortex proliferation signals the BEC to BKT phase crossover

Abstract

Three distinct types of behaviour have recently been identified in the two-dimensional trapped bosonic gas, namely; a phase coherent Bose-Einstein condensate (BEC), a Berezinskii-Kosterlitz-Thouless-type (BKT) superfluid and normal gas phases in order of increasing temperature. In the BKT phase the system favours the formation of vortex-antivortex pairs, since the free energy is lowered by this topological defect. We provide a simple estimate of the free energy of a dilute Bose gas with and without such vortex dipole excitations and show how this varies with particle number and temperature. In this way we can estimate the temperature for cross-over from the coherent BEC to the (only) locally ordered BKT-like phase by identifying when vortex dipole excitations proliferate. Our results are in qualitative agreement with recent, numerically intensive, classical field simulations.