Vortex pairing in two-dimensional Bose gases

TL;DR

This study investigates vortex pairing and phase transitions in two-dimensional Bose gases at finite temperature using classical field simulations, revealing vortex unbinding and phase boundaries consistent with experimental observations.

Contribution

The paper introduces a method to incorporate higher momentum states into classical field simulations and analyzes vortex pairing and phase boundaries in finite-sized 2D Bose gases.

Findings

Vortex unbinding occurs above the BKT transition.

Condensate and superfluid fractions decrease with temperature.

Experimental correlation inference methods are validated against direct calculations.

Abstract

Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. While this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.