Emergence of order from turbulence in an isolated planar superfluid

We study the relaxation dynamics of an isolated zero temperature quasi-two-dimensional superfluid Bose-Einstein condensate (BEC) that is imprinted with a spatially random distribution of quantum vortices. Following a period of vortex annihilation, we find that the remaining vortices self-organise into two macroscopic coherent `Onsager vortex' clusters that are stable indefinitely. We demonstrate that this occurs due to a novel physical mechanism --- the evaporative heating of the vortices --- that results in a negative temperature phase transition in the vortex degrees of freedom. At the end of our simulations the system is trapped in a non-thermal state. Our computational results provide a pathway to observing Onsager vortex states in a superfluid Bose gas.