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

Dynamics and equilibration of Rydberg excitations in dissipative atomic ensembles