Entanglement Dynamics of a Three-level Atom in a Momentum Eigenstate Interacting with Non-linear Effect

We consider a general Hamiltonian for a system which consists of a three level lambda configuration atom interacting with a one-mode cavity field. Besides the intensity-dependent coupling the model includes multi-photon process as well as a non-linear Kerr-Like medium effect. Furthermore, the atom and the field are assumed to be coupled with modulated coupling parameter which depends explicitly on time. The atom is initially prepared in a superposition state and field in a coherent state. Under a rotating wave approximation where fast oscillations are ignored, an exact solution for the wave function in Schrödinger equation is obtained. The momentum increment, the momentum diffusion and the field entropy are calculated. The results shown that in existence of the time dependent coupling parameter leads to a time delaying in the interaction which is twice the delay time for the independent case. The general conclusions reached are illustrated by numerical results.