  We investigate the non-equilibrium quantum dynamics of a canonical
light-matter system, namely the Dicke model, when the light-matter interaction
is ramped up and down through a cycle across the quantum phase transition. Our
calculations reveal a rich set of dynamical behaviors determined by the cycle
times, ranging from the slow, near adiabatic regime through to the fast, sudden
quench regime. As the cycle time decreases, we uncover a crossover from an
oscillatory exchange of quantum information between light and matter that
approaches a reversible adiabatic process, to a dispersive regime that
generates large values of light-matter entanglement. The phenomena uncovered in
this work have implications in quantum control, quantum interferometry, as well
as in quantum information theory.
