  A significant problem facing next-generation quantum technologies is how to
generate and manipulate macroscopic entanglement in light and matter systems.
Here we report a new regime of dynamical light-matter behavior in which a
giant, system-wide entanglement is generated by varying the light-matter
coupling at \emph{intermediate} velocities. This enhancement is far larger and
broader-ranged than that occurring near the quantum phase transition of the
same model under adiabatic conditions. By appropriate choices of the coupling
within this intermediate regime, the enhanced entanglement can be made to
spread system-wide or to reside in each subsystem separately.
