Abstract

Here we propose an analytical solution for semiclassical dynamical equations through a renormalized perturbation theory, applicable to many-body systems. The many-atom emission of a dilute cloud of two-level atoms is addressed as a nontrivial example. We show that, as a result of secular terms elimination, an effective many-body spectrum emerges in the temporal solutions, which depends on initial conditions. It allows us to detect a cooperativity reduction in the semiclassical total power radiated that cannot be described by a classical model from linear optics. The second-order cooperative emission remains accurate over several single-atom lifetimes and for interacting regimes stronger than those permitted in conventional perturbation theory. We can compute the semiclassical dynamics of a few hundred thousand interacting atoms with ordinary computational resources, which makes our formalism particularly promising to probe the nonlinear dynamics of quantum many-body systems that result from cumulant expansions.