Quantum and Classical Chaos in Kicked Coupled Jaynes-Cummings Cavities

We consider two Jaynes-Cummings cavities coupled periodically with a photon hopping term. The semi-classical phase space is chaotic, with regions of stability over some ranges of the parameters. The quantum case exhibits dynamic localization and dynamic tunneling between classically forbidden regions. We explore the correspondence between the classical and quantum phase space and propose a scheme for implementing the system experimentally.