Semiclassical spectra of the single- and two-photon Tavis-Cummings models

We obtain explicit analytical expressions for the energy spectra of the resonant single- and two-photon Tavis-Cummings models in the asymptotic limit of a large number of atoms, A ≫1, and a large number of total excitations, N ≫1. We show that both the spectral singularities in the regime N / A ∼1 and the equidistant spectra in the regime N / A ≫1 can be accurately described in the semiclassical framework.