Quantum coherence and correlations of optical radiation by atomic ensembles interacting with a two-level atom in a microwave cavity

We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second-order coherence degree, von Neumann entropy, spin squeezing for multiparticle entanglement, as well as genuine two- and three-mode entanglement parameters for steady-state and nonequilibrium situations. Coherent transfer of population between the radiation modes and quantum-state mapping between the two-level atom and the optical modes are discussed. A potential experimental realization of the theoretical results in a superconducting coplanar waveguide resonator containing diamond crystals with nitrogen-vacancy color centers and a superconducting artificial two-level atom is discussed.