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By utilizing the property of the supersymmetric structure in the two-levelmultiphoton Jaynes-Cummings model, an invariant is constructed in terms of thesupersymmetric generators by working in the sub-Hilbert-space corresponding toa particular eigenvalue of the conserved supersymmetric generators. We obtainthe exact solutions of the time-dependent Schr\"{o}dinger equation whichdescribes the time-dependent supersymmetric two-level three-photonJaynes-Cummings model (TLTJCM) by using the invariant-related unitarytransformation formulation. The case under the adiabatic approximation is alsodiscussed.  Keywords: Supersymmetric Jaynes-Cummings model; exact solutions; invarianttheory; geometric phase factor; adiabatic approximationComment: 7 pages, Late

An Approach to Exact Solutions of the Time-dependent Supersymmetric Two-Level Three-Photon Jaynes–Cummings Model