Exact Solution for Jaynes-Cummings Model with Bosonic Field Nonlinearity and Strong Boson-Fermion Coupling

We use Lewis-Riesenfeld invariant approach to treatthe modified Jaynes-Cummings models involving any forms of nonlinearty ofthe bosonic field when strong boson-fermion couplings are nilpotentGrassmann valued. The general state functions, time evolution operator andthe time-evolution expressions for both the bosonic number and the fermionicnumber are presented.