Winding up superfluid in a torus via Bose Einstein condensation

Abstract

Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point ("critical slowing downg"). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains ĝ€" fragments of broken symmetry ĝ€" and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth ĝ€" both experimentally measurable ĝ€" follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition.