Evolution of the N-ion Jaynes–Cummings model beyond the standard rotating wave approximation

A unitary transformation of the N-ion Jaynes–Cummings Hamiltonian is proposed. It is shown that any approximate expression of the evolution operator associated with the transformed Hamiltonian retains its validity independent of the intensity of the external driving field. In particular, using the rotating wave approximation, one obtains a solution for the N-ion Jaynes–Cummings model which improves the standard rotating wave approximation solution.