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

Three distinct types of behavior 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 favors 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 crossover 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.