Turbulent relaxation to equilibrium in a two-dimensional quantum vortex gas

TL;DR

This study experimentally investigates how a two-dimensional quantum vortex gas relaxes to equilibrium, confirming theoretical predictions and revealing phase transitions, including negative temperature states, through vortex distribution measurements in a Bose-Einstein condensate.

Contribution

The paper demonstrates experimental realization of microcanonical equilibrium states in a 2D vortex gas, validating mean-field theory and exploring phase transitions including negative temperature states.

Findings

Vortex distributions match Poisson-Boltzmann predictions

Equilibria cover the full phase diagram, including negative temperatures

Observation of symmetry-breaking transition at high energies

Abstract

We experimentally study 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 meanfield Poisson-Boltzmann equation for the system describing the microcanonical ensemble at fixed energy $\cal{H}$ and angular momentum $\cal{M}$. The equilibrium states are characterized by the corresponding thermodynamic variables of inverse temperature $\hat{\beta}$ and rotation frequency $\hat{\omega}$. 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.