  The dynamics of non-equilibrium closed quantum systems and their route to
thermalization are of fundamental interest to several fields, from cosmology to
particle physics. However, a comprehensive description of non-equilibrium
phenomena still presents a significant challenge. In this work, we report the
observation of distinct stages during the relaxation of the decaying turbulence
in trapped Bose-Einstein condensates. Our findings show a direct particle
cascade from low to high momenta, a consequence of the energy injection in the
system, exhibiting a characteristic universal scaling. This stage is followed
by an inverse particle cascade responsible for repopulating the previously
depleted condensate. Both cascades can be explained through self-similar
solutions provided by wave turbulence theory. These findings provide important
insights into the relaxation stages of out-of-equilibrium quantum many-body
systems.
