Entanglement of a three-level atom interacting with two-modes field in a cavity

The dynamics of an atom of three levels in Lambda configuration interacting with a quantized field of two modes in a cavity is studied within the rotating wave approximation by considering experimental values of accessible hyperfine levels of alkali atoms. The Hamiltonian model is constructed on the basis of the direct product of the atomic states with Fock states of light. This simplified basis allows us to generalize the state of light to any quantum field. The interaction term of the Hamiltonian restricts the system to a 3D Hilbert space. The system's time evolution results show some similarities with the effective two-level system, such as the presence of collapses and revivals and the atom-field entanglement. By an analysis of the statistics of the photons, we show that when the three-level atom is interacting with a coherent field of two modes, it is possible to control experimentally the statistics of the field to be super-Poissonian or sub-Poissonian by the choice of the initial atomic state.