**Figure 1.** Dynamics and the steady state of a resonantly driven ensemble of *N* atoms in a 2D lattice of diameter *d* = 0.7*d*_{b}. (a) Time dependence of the number of Rydberg excitations 〈*n*_{R}〉 for *N* = 9, 16, 25 and different Γ_{r, z}. Thin dotted lines in the top graph correspond to a single atom, *N* = 1. Time is in units of Ω^{−1} 1.87 μs. (b) Steady-state values of 〈*n*_{R}〉 and *Q* versus *N* ≤ 45 for Γ_{z} = 0 (blue, open diamonds) and Γ_{z} = 0.3Ω (black, open circles).

**Abstract**

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 the slow Rydberg state decay and sizable relaxation of atomic coherences, on the timescale of several μs 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.