Solving a generalized Jaynes-Cummings model by supersymmetric unitary transformation

For the generalized Jaynes-Cummings model Hamiltonian which can describe tw o collectively radiation atoms, we find Its supersymmetric structure. Based on supersymmetric quantum mechanics theory, we introduce a supersymmetric unitary transformation, in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie a lgebra, to diagonalize the Hamiltonian. On doing so, its eigenvalue and eig enstates are obtained.