Matter-field entanglement within the Dicke model

Abstract

We use the Dicke model to describe a system of NA two level atoms interacting with a one mode electromagnetic field. Symmetry Adapted Coherent States are used to obtain the ground and first-excited wave-functions of the model. These are constructed from linear combinations of the standard coherent states, thus resembling much better the behavior of the exact quantum states obtained through the diagonalization of the Hamiltonian. By means of the linear and von Neumann entropies we determine the entanglement properties between the matter and field degrees of freedom as a function of the coupling strength of the model. We find that their maximum value determines the position of the quantum phase transition of the normal to the superradiant regime for a finite number of atoms.