True Mechanism of Spontaneous Order from Turbulence in Two-Dimensional Superfluid Manifolds

In a 2D turbulent fluid containing pointlike vortices, Lars Onsager predicted that adding energy to the fluid can lead to the formation of persistent clusters of like-signed vortices, i.e., Onsager vortex (OV) clusters. In the evolution of 2D superfluid turbulence in a uniform disk-shaped Bose-Einstein condensate (BEC), it was discovered that a pair of OV clusters with opposite signs can form without any energy input. This striking spontaneous order was explained as being due to a vortex evaporative-heating mechanism, i.e., annihilations of vortex-antivortex pairs which remove the lowest-energy vortices and thereby boost the mean energy per vortex. However, in our search for exotic OV states in a boundaryless 2D spherical BEC, we found that OV clusters never form despite the annihilations of vortex pairs. Our analysis reveals that contrary to the general belief, vortex-pair annihilation emits intense sound waves, which damp the motion of all vortices and hence suppress the formation of OV clusters. We also present unequivocal evidence showing that the true mechanism underlying the observed spontaneous OV state is the vortices exiting the BEC boundaries. Uncovering this mechanism paves the way for a comprehensive understanding of emergent vortex orders in 2D manifolds of superfluids driven far from equilibrium.