Out-of-equilibrium phenomena is a subject of considerable interest in many
fields of physics. Ultracold quantum gases, which are extremely clean,
well-isolated and highly controllable systems, offer ideal platforms to
investigate this topic. The recent progress in tailoring trapping potentials
now allows the experimental production of homogeneous samples in custom
geometries, which is a key advance for studies of the emergence of coherence in
interacting quantum systems. Here we review recent experiments in which
temperature quenches have been performed across the Bose-Einstein condensation
(BEC) phase transition in an annular geometry and in homogeneous 3D and
quasi-2D gases. Combined, these experiments give a comprehensive picture of the
Kibble-Zurek (KZ) scenario through complementary measurements of correlation
functions and topological defects density. They also allow the measurement of
KZ scaling laws, the direct confirmation of the "freeze-out" hypothesis that
underlies the KZ theory, and the extraction of critical exponents of the
Bose-Einstein condensation transition.Comment: 11 pages, 6 figures; topical revie