  We study the quench of a degenerate ultracold Bose gas to the unitary regime,
where interactions are as strong as allowed by quantum mechanics. We lay the
foundations of a cumulant theory able to capture simultaneously the three-body
Efimov effect and ergodic evolution. After an initial period of rapid quantum
depletion, a universal prethermal stage is established characterized by a
kinetic temperature and an emergent Bogoliubov dispersion law while the
microscopic degrees of freedom remain far-from-equilibrium. Integrability is
then broken by higher-order interaction terms in the many-body Hamiltonian,
leading to a momentum-dependent departure from power law to decaying
exponential behavior of the occupation numbers at large momentum. We find also
signatures of the Efimov effect in the many-body dynamics and make a precise
identification between the observed beating phenomenon and the binding energy
of an Efimov trimer. Throughout the work, our predictions for a uniform gas are
quantitatively compared with experimental results for quenched unitary Bose
gases in uniform potentials.
