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We study the vortex nucleation dynamics in inhomogeneous atomic Bose gasesquenched into a superfluid phase and investigate the dependence of theKibble-Zurek (KZ) scaling exponent on the underlying trap configuration. Forsamples in a number of different inhomogeneous traps, we observe thecharacteristic power-law scaling of the vortex number with the thermal quenchrate, as well as an enhanced vortex suppression in the outer regions with lowerparticle density, in agreement with the causality effect as encapsulated in theinhomogeneous Kibble-Zurek mechanism (IKZM). However, the measured KZ scalingexponents show significant differences from the theoretical estimates, andfurthermore their trends as a function of the underlying trap configurationdeviate from the IKZM prediction. We also investigate the early-time coarseningeffect using a two-step quench protocol as proposed in a recent study and showthat the interpretation of the measurement results without including thecausality effect might be misleading. This paper provides a comprehensive studyof vortex formation dynamics in quenched Bose gases confined in inhomogeneoustrapping potentials and calls for a refined theoretical framework forquantitative understanding of the phase transition and defect formationprocesses in such inhomogeneous systems.

Variations of the Kibble-Zurek scaling exponents of trapped Bose gases