Pseudo invariant eigenoperator and energy gap for nonlinear Jaynes-Cummings model

Using the pseudo invariant eigenoperator (PIEO) method, we theoretically study a nonlinear multiphoton Jaynes-Cummings (J C) model, which includes any forms of the nonlinearities of both the field and the atom-field coupling. Our main task is to search for the so called pseudo invariant eigenoperator in terms of the supersymmetric generators and derive the energy-level gap of the above system. This approach seems concise and revealing.