A rigorous investigation on the interaction between two three-level ?-type atoms and a single-mode cavity field

In this paper, we study quantum entanglement and non-classical statistical aspects for a model describing two three-level A atoms interacting with a single-mode cavity field. The Hamiltonian describes multi-photon processes and includes the Kerr-like medium in the resonance case. The constants of motion are obtained from the Hamiltonian operators under the rotating wave approximation. The exact solution of the wave function for the whole system is obtained under the special initial conditions when the atom is in the ground state and the field in the coherent states. The results are used to perform some studies on the temporal evolution of collapse revival, normal squeezing function, photon antibunching and Q-function to measure the degree of entanglement between subsystems. Entanglement dynamics using von Neumann entropy and Shannon information is used to quantify the entanglement in the quantum subsystems. The numerical results show that the presence of these parameters plays an essential role in developing these aspects. The above optical schemes have many advantages and can be used in various experiments in quantum optics and information, such as trapped ions and quantum electrodynamics resonators.