Dissipative dynamics of the Jaynes-Cummings model in the dispersive approximation: Analytical results

Abstract

We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems $(\mathrm{atom}+\mathrm{field}).$ Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.