Coupling n-level Atoms with l-modes of Quantised Light in a Resonator

We study the quantum phase transitions associated to the Hamiltonian of a system of n-level atoms interacting with l modes of electromagnetic radiation in a resonator. The quantum phase diagrams are determined in analytic form by means of a variational procedure where the test function is constructed in terms of a tensorial product of coherent states describing the matter and the radiation field. We demonstrate that the system can be reduced to a set of Dicke models. (paper)