The formation of an equilibrium quantum state from an uncorrelated thermal
one through the dynamical crossing of a phase transition is a central question
of non-equilibrium many-body physics. During such crossing, the system breaks
its symmetry by establishing numerous uncorrelated regions separated by
spontaneously-generated defects, whose emergence obeys a universal scaling law
with the quench duration. Much less is known about the ensuing re-equilibrating
or "coarse-graining" stage, which is governed by the evolution and interactions
of such defects under system-specific and external constraints. In this work we
perform a detailed numerical characterization of the entire non-equilibrium
process, addressing subtle issues in condensate growth dynamics and
demonstrating the quench-induced decoupling of number and coherence growth
during the re-equilibration process. Our unique visualizations not only
reproduce experimental measurements in the relevant regimes, but also provide
valuable information in currently experimentally-inaccessible regimes.Comment: Supplementary Movie Previes: SM-Movie-1: https://youtu.be/3q7-CvuBylg
SM-Movie-2: https://youtu.be/-Gymaiv9rC0 SM-Movie-3:
https://youtu.be/w-O2SPiw3nE SM-Movie-4: https://youtu.be/P4xGyr4dwK