By utilizing the property of the supersymmetric structure in the two-level
multiphoton Jaynes-Cummings model, 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. We obtain
the exact solutions of the time-dependent Schr\"{o}dinger equation which
describes the time-dependent supersymmetric two-level three-photon
Jaynes-Cummings model (TLTJCM) by using the invariant-related unitary
transformation formulation. The case under the adiabatic approximation is also
discussed.
Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invariant
theory; geometric phase factor; adiabatic approximation