Turbulent Relaxation to Equilibrium in a Two-Dimensional Quantum Vortex Gas

We experimentally study the emergence of microcanonical equilibrium states in the turbulent relaxation dynamics of a two-dimensional chiral vortex gas. Same-sign vortices are injected into a quasi-two-dimensional disk-shaped atomic Bose-Einstein condensate using a range of mechanical stirring protocols. The resulting long-time vortex distributions are found to be in excellent agreement with the mean-field Poisson Boltzmann equation for the system describing the microcanonical ensemble at fixed energyHand angular momentumM. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperatureβ^and rotation frequencyω^. We are able to realize equilibria spanning the full phase diagram of the vortex gas, including on-axis states near zero temperature, infinite temperature, and negative absolute temperatures. At sufficiently high energies, the system exhibits a symmetry-breaking transition, resulting in an off-axis equilibrium phase at negative absolute temperature that no longer shares the symmetry of the container. We introduce a point-vortex model with phenomenological damping and noise that is able to quantitatively reproduce the equilibration dynamics.