Large dynamic light-matter entanglement from driving neither too fast nor too slow

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.