  The ability to modify light-matter coupling in time (e.g. using external
pulses) opens up the exciting possibility of generating and probing new aspects
of quantum correlations in many-body light-matter systems. Here we study the
impact of such a pulsed coupling on the light-matter entanglement in the Dicke
model as well as the respective subsystem quantum dynamics. Our dynamical
many-body analysis exploits the natural partition between the radiation and
matter degrees of freedom, allowing us to explore time-dependent
intra-subsystem quantum correlations by means of squeezing parameters, and the
inter-subsystem Schmidt gap for different pulse duration (i.e. ramping
velocity) regimes -- from the near adiabatic to the sudden quench limits. Our
results reveal that both types of quantities indicate the emergence of the
superradiant phase when crossing the quantum critical point. In addition, at
the end of the pulse light and matter remain entangled even though they become
uncoupled, which could be exploited to generate entangled states in
non-interacting systems.
