Full spectrum of nonlinear Jaynes–Cummings and anti-Jaynes–Cummings models

The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Speci ̄cally, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.