A nonlinear interaction between SU(1,1) quantum system and a three-level atom in different configurations with damping term

The effect of nonlinear medium and phase damping is investigated on an atom of three levels in different forms interacting with the SU(1,1) Lie algebra. The SU(1,1)system starts the interaction from the Perelomov coherent state, while the atom starts the interaction from excited-most state. The time dependent wave function is calculated by using the Schredinger equation. The density matrix is obtained. The influences of damping, nonlinearity (Kerr-like medium), Perelomov coherent parameter and the Bargmann index on some non-classical properties, such as: Revivals-collapses phenomenon, entanglement and atomic variables squeezing, are investigated.