The weakly coupled infinite Dicke model

For the Dicke model including all modes in 3, the infinite atom limit within a weak coupling to the photon field is performed. Hereby, the infinite atomic system is treated as a mean field quantum lattice system. The global limiting dynamics is given by cocycle equations depending on the classical part of the atomic part and the one-photon structure. It is shown how the collective atomic behaviour influences the emitted quantized radiation in different photonic subsectors. The growth of expectation values, especially of the photon mean number, and the spatial distribution of the emitted photons in the time asymptotic photon states are calculated. In the photonic Fock sector the (un)necessity of the rotating-wave-approximation of the Dicke model and the quantum optical coherence of the time asymptotic photon states are discussed.