Time-evolution of the population of a four-level atom in a two-mode cavity

The time-evolution of the state of the system consisting of the cavity modes with an injected four-level atom ()~(40)Ca in a two-mode cavity is solved by means of the perturbation method in the interaction picture. The reduced atomic density operator and the time-evolution of the atomic population are derived on the basis of the above solving, which is useful for further research on the atomic dynamic behavior in the cavity field.