Two-photon Jaynes-Cummings model without rotatingwave approximation

The three-level atomic system interacting with one mode of the electromagnetic field in a Ξ-configuration is investigated. Effective Hamiltonians for two-photon processes without the rotating wave approximation are obtained by application of the perturbation method of multiple time scales. Some inaccuracies in the form of Hamiltonians of this type recently presented are pointed out and corrected.