Evolution of the quantum fidelity in a system of multimode light field interacting resonantly with a two-level atom through degenerate multi-photon process

The time evolution properties of the quantum fidelity in a system of multi-mode coherent light field resonantly interacting with a two-level atom via any Nj-degenerate N∑-photon transition process are studied by the fully quantum theory and numerical calculations. The analytical expressions of the quantum fidelity of field and atom, and the numerical calculation results for three-mode field interacting with the atom are obtained. Our attention focuses on the discussion of the influences of the initial average photon number, the atomic distribution angle, the phase angle of the atom dipole, the field excitation angle, and the atomic degeneracy on the evolution of the quantum fidelity. The results obtained from the numerical calculation indicate that the above factors lead to the quantum fidelity changing with oscillation behavior. The quantum fidelity of field and atom will drastically decrease as the initial light increases, which is correlated sensitively with the fidelity. The speed change of quantum fidelity is strongly dependent on the atomic degeneracy and the intensity coupling between atoms and fields. The value and frequency of the quantum fidelity change lightly with the atomic distribution angle and the angle of light field excitation as well. The phase angles of the atom dipole almost have no influences on the quantum fidelity of field and atom. According to these properties of the quantum fidelity, we can control the speed and value of quantum fidelity in the system by these constraint conditions.