Long-range ordering of topological excitations in a two-dimensional superfluid far from equilibrium

Abstract

We study the relaxation of a two-dimensional (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 nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann 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 Poisson-Boltzmann equation. The results allow us to characterize the spectral energy condensate in a 2D quantum fluid that bears striking similarity to 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.By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

“…Our results indicate that, during the coarsening process, the scaling exponent β switches from the anomalous to the Gaussian value, when the clustering of like-sign defects disappears, see figures 7 and 9. Hence, it is imaginable that in a driven situation, with a vortex ensemble containing a constant number of defects on average and representing a state close to the clustering transition of [88,89], the respective critical dynamics is related to the anomalous fixed point we report here.…”

“…For charge-neutral atoms in a closed trap without external fields, a potentially related clustering transition has been reported [88,89]. Onsager's point-vortex model [79] implies a maximum entropy state in which an equal number of elementary vortices and anti-vortices are randomly distributed in the system.…”

Einstein–Bose condensation of Onsager vortices

“…The successes of the recent experimental developments have also spawned novel theoretical investigations [13,[34][35][36][37][38][39][40][41][42][43][44][45]. In addition to visual inspection, the presence of Onsager vortices has been associated with indicators such as the vortex dipole moment [13,34], vortex clustering measures [7,8,36,37,40], or a peak in the power spectral density of incompressible kinetic energy [8,13,38,46].…”

Vortex Thermometry for Turbulent Two-Dimensional Fluids

“…Despite this, many recent theoretical works involving superfluid Bose-Einstein condensates (BECs) have suggested that largescale, same-sign Onsager vortex clusters play an important role in 2D quantum turbulence [8][9][10][11][12][13][14][15][16][17]. In superfluids, much of the focus to date has been on decaying-rather than driventurbulence [9,[11][12][13][14][17][18][19][20][21][22][23][24], since this scenario removes the complications of stirring. A variety of concepts have been applied to the problem, including holographic duality [25,26] and nonthermal fixed points [27][28][29].Experimentally, BECs provide unprecedented opportunities to investigate 2D superfluid turbulence due to the high degree of controllability available in these systems.…”