  We study resonant optical excitations of strongly-interacting Rydberg states
of atoms in the presence of relaxations. We employ the quantum stochastic
(Monte Carlo) wavefunctions to simulate the dissipative dynamics of tens of
atoms in two-dimensional lattices. We show that under typical experimental
conditions involving slow Rydberg state decay and sizable relaxation of atomic
coherences, on the time scale of several microseconds the atomic ensemble
approaches a stationary state in which much of the quantum correlations between
the atoms have decayed away. The steady state, however, exhibits strong
classical correlations of Rydberg excitation probabilities.
