  We study effects of direct interatomic interaction on cooperative processes
in atom-photon dynamics. Using a model of two-level atoms with Ising-type
interaction as an example, it is demonstrated that interparticle interaction
combined with atom-field coupling can introduce additional interatomic
correlations acting as a phase synchronizing factor. For the case of weakly
interacting atoms with $J<\hbar\omega_0$, where $J$ is the interparticle
coupling constant and $\omega_0$ is the atomic frequency, dynamical regimes of
cooperative relaxation of atoms are analyzed in Born-Markov approximation both
numerically and using the mean field approximation. We show that interparticle
correlations induced by the direct interaction result in inhibition of
incoherent spontaneous decay leading to the regime of collective pulse
relaxation which differs from superradiance in nature. For superradiant
transition, the synchronizing effect of interatomic interaction is found to
manifest itself in enhancement of superradiance. When the interaction is strong
and $J>\hbar\omega_0$, one-partice one-photon transitions are excluded and
transition to the regime of multiphoton relaxation occurs. Using a simple model
of two atoms in a high-Q single mode cavity we show that such transition is
accompanied by Rabi oscillations involving many-atom multiphoton states.
Dephasing effect of dipole-dipole interaction and solitonic mechanism of
relaxation are discussed.
