Kibble-Zurek dynamics in a trapped ultracold Bose gas

The study of driven phase transitions is a central question of non-equilibrium physics.  Central to this is the Kibble-Zurek (KZ) scaling law, describing how fundamental observables behave close to criticality and their scaling with quench duration. Significant experimental work on this has been done in recent years, including in controlled experiments in elongated 3D harmonic traps [1], which we have previously shown to reproduce by means of stochastic numerical simulations [2]. A related question concerns whether, and under what conditions, the inhomogeneous nature of the trapping potential is consistent with predictions of the standard (homogeneous) KZ law as the system is driven across the Bose-Einstein condensation phase transition. To address this question, we analyze our simulated dynamics for the experimental conditions in the context of the linearized stochastic Gross-Pitaevskii model in the homogeneous limit. We find an exponential scaling behaviour of the momentum occupation after the transition sets in and the corresponding determined phase domain and defect number match the KZ prediction [3]. Specifically, considering the sonic horizon condition [4], we demonstrate that Ref. [1,2] fall deeply within the "homogeneous" KZ regime, with the role of inhomogeneity requiring much slower quench speeds. Our findings serve as a guide for choosing appropriate observables and parameter regimes for further experiments aimed at probing inhomogeneous effects during a driven phase transition.