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The interaction between a moving four-level atom and a single-mode cavity field are discussed in the presence of intensity dependent atom field coupling. For this purpose, we first demonstrate the feasibility of the effective Hamiltonian and evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field. Considering the field to be initially in a coherent state, and the atom is initially prepared in the excited state. The wave function is obtained in three different cases: resonance case, off-resonance case, finally we obtained it in the general form. We study the nonclassical features of the system such as Atomic inversion, Filed entropy, purity, Fidelity, Mandel Q-parameter, Mean photon number and normal squeezing. The results show that, The temporal evolution of field entropy (entanglement), Mandel parameter, mean photon number and normal squeezing are sensitive to intensity-dependent coupling, which changes the quantum statistical behaviour of the atom-field state to a full sub-Poissonian statistics. Finally, conclusions and some features and comments are given.

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