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Dynamics and equilibration of Rydberg excitations in dissipative atomic ensembles

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.