Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.