Dynamical Algebraic Approach to the Modified Jaynes-CummingsModel

The modified Jaynes-Cummings model of a single two-level atom placed in the common domain of two cavities or interacting with two quantized modes is studied by a dynamical algebraic method. With the help of an SU(2) algebraic structure, we then obtain the eigenvalues, eigenstates, time evolution operator and atomic inversion operator for the system. We proceed to investigate the modified Jaynes-Cummings model governed by the Milburn equation and present the exact solution of the Milburn equation.