Nonlinear dynamics of the two-photon Dicke model

We derive an effective two-photon Hamiltonian for a collection of two-level atoms interacting with a quantized field in the regime of two-photon reson ance. This Hamiltonian naturally includes the dynamical Stark shift terms. Considering, in detail, the case of an initially strong quantum field, we s how that the effective Hamiltonian acquires nonlinear terms in the su(2) al gebra generators. For this case we find the evolution operator and prove th e wavefunction factorization for special initial states. We show that colle ctive effects modify the dynamics of the atomic inversion leading to a modu lation of the collapse-revival structure.