Abstract

We study the relaxation of a two-dimensional (2D) ultracold Bose gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann equation. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square trap reveal that a large-scale flow field with net angular momentum emerges that is consistent with predictions of the Poisson-Boltzmann equation. The theory presented is subsequently verified in recent experimental work focusing on the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Using carefully designed experimental forcing protocols to inject vortices into the system, we are able torealize equilibria spanning the full phase diagram of the vortex gas, including vortex states near zero temperature, infinite temperature, and negative absolute temperatures. The resulting experimentally measured long-time vortex distributions are found to be in excellent agreement with the mean-field predictions of the Poisson Boltzmann equation. This allows us to verify that, during the relaxation dynamics, the vortex excitations evolve to a state that maximises the entropy of the vortex gas.