Spontaneous Generation and Evolution of Defects in a Quenched Bose Gas*

We provide a detailed numerical analysis of the Trento experiments with quenched Bose-Einstein condensates in an elongated harmonic trap (Donadello et al., PRA 94, 023628 (2016)) where defects in the order parameter are spontaneously generated by the Kibble-Zurek mechanism. Using the stochastic projected Gross-Pitaevskii equation, and by quenching both temperature and chemical potential, we are able to capture both the early-time phase transition dynamics and the observed long-term coarse-graining evolution, reproducing the experimentally-observed condensate growth dynamics, and long-term defect evolution. The emerging picture sheds light into how the initial thermal state passes through a transient “turbulent” state of many highly-excited vortical structures, before settling into a few interacting long-lived solitonic vortices. By numerically tracking the number of spontaneously-formed defects during and after the quench, we quantify the dependence of vortex number, vortex linelength and coherence length on quench rate, also demonstrating the observed breakdown of Kibble-Zurek scaling for fast quenches, arising as a result of coarse-graining dynamics prior to experimental measurements.