  We comprehensively investigate two distinct mechanisms leading to memory loss
of non-Gaussian correlations after switching off the interactions in an
isolated quantum system undergoing out-of-equilibrium dynamics. The first
mechanism is based on spatial scrambling and results in the emergence of
locally Gaussian steady states in large systems evolving over long times. The
second mechanism, characterized as `canonical transmutation', is based on the
mixing of a pair of canonically conjugate fields, one of which initially
exhibits non-Gaussian fluctuations while the other is Gaussian and dominates
the dynamics, resulting in the emergence of relative Gaussianity even at finite
system sizes and times. We evaluate signatures of the occurrence of the two
candidate mechanisms in a recent experiment that has observed Gaussification in
an atom-chip controlled ultracold gas and elucidate evidence that it is
canonical transmutation rather than spatial scrambling that is responsible for
Gaussification in the experiment. Both mechanisms are shown to share the common
feature that the Gaussian correlations revealed dynamically by the quench are
already present though practically inaccessible at the initial time. On the
way, we present novel observations based on the experimental data,
demonstrating clustering of equilibrium correlations, analyzing the dynamics of
full counting statistics, and utilizing tomographic reconstructions of quantum
field states. Our work aims at providing an accessible presentation of the
potential of atom-chip experiments to explore fundamental aspects of quantum
field theories in quantum simulations.
