  We establish a new theoretical framework, based on a time-dependent mean
field approach, to address the dynamics of the driven Dicke model. The joint
evolution of both mean fields and quantum fluctuations gives rise to a rich and
generally non-linear dynamics, featuring a normal (stable) regime and an
unstable, super-radiant one. Various dynamical phenomena emerge, such as the
spontaneous amplification of vacuum fluctuations, or the appearance of special
points around which the mean-field amplitudes rotate during driven time
evolution, signalling a dynamical symmetry breaking. We also provide a
characterization of the driving-induced photon production in terms of the work
done by the driving agent, of the non-adiabaticity of the process and of the
entanglement generated between the atomic system and the cavity mode.
