We experimentally study the emergence of high-energy equilibrium states in a
chiral vortex gas of like-circulation vortices realized within a disk-shaped
atomic Bose-Einstein condensate. In contrast to the familiar triangular
Abrikosov lattice, the lowest-energy state of the superfluid in a rotating
frame, we observe the formation of rotating vortex equilibria that are highly
disordered and have significant energy per vortex. Experimental stirring
protocols realize equilibrium states at both positive and negative absolute
temperatures of the vortex gas. At sufficiently high energies the system
exhibits a symmetry breaking transition, resulting in an off-axis equilibrium
phase that no longer shares the symmetry of the container. By initializing
vortices in a non-equilibrium distribution with sufficient energy, relaxation
to equilibrium is observed within experimental timescales and an off-axis
equilibrium state emerges at negative absolute temperature. The observed
equilibria are in close agreement with mean field theory of the microcanonical
ensemble of the vortex gas.Comment: V1: 13 pages, 6 figures, 5 in main tex