Extra terms which describe the phonon absorption and emission associated with Brillouin scattering are added to the usual Dicke Hamiltonian. The general effect on the Dicke phase transition is an enhancement of the photon numbers. When an effective phonon coupling constant B exceeds a certain value, the transition is of the first-order type. The condition epsilon / lambda 2 <1 found by Wang and Hioe (1973) to be necessary for a phase transition to occur, is no longer necessary if the constant B is large enough and in such cases the transition is again first order in type.
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 resonance. This Hamiltonian naturally includes the dynamical Stark shift terms. Considering, in detail, the case of an initially strong quantum field, we show that the effective Hamiltonian acquires nonlinear terms in the su (2) algebra generators. For this case we find the evolution operator and prove the wavefunction factorization for special initial states. We show that collective effects modify the dynamics of the atomic inversion leading to a modulation of the collapse-revival structure.