Overcoming the sign problem in rotating Bose Einstein Condensates

We numerically investigate the structure and thermodynamic properties of quantized vortices in samples of rotating Bose-Einstein condensates of interacting particles at finite temperature in three dimensions. Thus far, numerical study of such systems has been largely limited to mean field and zero-temperature analysis. Exact particle-based simulations at finite temperature, such as path integral Monte Carlo, are limited in this regime due to the complex nature of the action. To circumvent this problem, we employ coherent states field theoretic methods rather than particle coordinate methods, and Complex Langevin sampling rather than Monte Carlo sampling. We visualize quantized vortices in fully fluctuating simulations at finite temperature, and calculate the free energy of a select number of energetically competitive arrangements of vortices as a function of rotation speed and temperature to create a vortex phase diagram.