Abstract
The dynamical evolution of an inhomogeneous ultracold atomic gas quenched at different controllable rates through the Bose-Einstein condensation phase transition is studied numerically in the premise of a recent experiment in an anisotropic harmonic trap. Our findings based on the stochastic (projected) Gross-Pitaevskii equation are shown to be consistent at early times with the predictions of the homogeneous Kibble-Zurek mechanism. This is demonstrated by collapsing the early dynamical evolution of densities, spectral functions and correlation lengths for different quench rates, based on an appropriate characterization of the distance to criticality felt by the quenched system. The subsequent long-time evolution, beyond the identified dynamical critical region, is also investigated by looking at the behaviour of the density wavefront evolution and the corresponding phase ordering dynamics.
Highlights
The Kibble-Zurek (KZ) mechanism originated from the scenario for defect creation in cosmological symmetrybreaking phase transitions [1]
Having demonstrated the relevance of the homogeneous KZ mechanism for the parameter regime considered in this work, we examine the extent to which the linearized stochastic (projected) Gross-Pitaevskii equation (SPGPE)—supplemented with the time shift (t − tc)—can accurately explain the results of the full nonlinear SPGPE numerical simulations
We performed a detailed analysis of the early stage quenched symmetry-breaking dynamics of an elongated harmonically trapped three-dimensional ultracold atomic gas evaporatively cooled from above the Bose-Einstein condensation phase transition temperature at variable rates
Summary
The Kibble-Zurek (KZ) mechanism originated from the scenario for defect creation in cosmological symmetrybreaking phase transitions [1]. The randomly oriented domains result in topologically nontrivial configurations that survive as topological defects This general scenario was substantiated with a dynamical theory [2,3] that predicts the size of the domains, and the initial density of defects, employing critical exponents of the transition and the quench time τQ. Despite the inhomogeneous nature of the harmonically trapped gas, our present work seems to indicate that the temperature quenches probed in the experiments [19,46,47,51] were such that transition effectively occurs within the remit of the “homogeneous” KZ mechanism; the predicted modifications due to the interplay of causality and geometry [11,96,97] seem not to be needed in this case
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