  We study the emergence of many-body correlations in the stationary state of
continuously-driven, strongly-interacting dissipative system. Specifically, we
examine resonant optical excitations of Rydberg states of atoms interacting via
long-range dipole-dipole and van der Waals potentials employing exact numerical
solutions of the density matrix equations and Monte-Carlo simulations.
Collection of atoms within a blockade distance form a "superatom" that can
accommodate at most one Rydberg excitation. The superatom excitation
probability saturates to 1/2 for coherently driven atoms, but is significantly
higher for incoherent driving, approaching unity as the number of atoms
increases. In the steady state of uniformly-driven, extended one-dimensional
system, the saturation of superatoms leads to quasi-crystallization of Rydberg
excitations whose correlations exhibit damped spatial oscillations. The
behavior of the system under the van der Waals interaction potential can be
approximated by an analytically soluble model based on a "hard-rod" interatomic
potential.
