Long-range Ordering of Topological Excitations in a Two-Dimensional Superfluid Far From Equilibrium

TL;DR

This paper investigates how vortex excitations in a 2D superfluid relax from nonequilibrium states, leading to spontaneous large-scale flow patterns that resemble classical turbulence, with implications for understanding quantum fluid dynamics.

Contribution

It demonstrates the emergence of large-scale coherent flows in a 2D quantum superfluid through maximum entropy states, linking vortex dynamics to classical turbulence phenomena.

Findings

Large-scale monopole flow with angular momentum emerges in square traps.

Flow switches to dipolar pattern with zero angular momentum in rectangular traps.

Spectral energy condensation in quantum fluids resembles classical turbulence flows.

Abstract

We study the relaxation of a 2D ultracold Bose-gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a non-zero coarse-grained vorticity field. The streamfunction of this emergent quasi-classical 2D flow is governed by a Boltzmann-Poisson equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Boltzmann-Poisson equation. The results allow us to characterise the spectral energy condensate in a 2D quantum fluid that bears striking similarity with similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.