Exact Solution for a Multiphoton Generalized Jaynes-Cummings Model with Inverse Operators

A new exactly solvable multiphoton generalized Jaynes-Cummings model is presented, whose Hamiltonian is related to the inverse of field mode creation and annihilation operators. Then we use supersymmetric unitary operators to diagonalize the Hamiltonian above and obtain their energy spectra and eigenstates. In addition, its pseudo-invariant eigen-operator is found as well, directly leading to the corresponding energy-level gap.