## Dynamics and equilibration of Rydberg excitations in dissipative atomic ensembles - Figure 3.

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**Figure 3.** Steady-state values of the mean number of Rydberg excitations 〈*n*_{R}〉 and the corresponding *Q* parameter versus the number *N* ≤ 45 of atoms in the volume of size d = (1,\sqrt{2},2)d_{\mathrm{b}}, (a), (b), (c), respectively, for Γ_{r} = 0.075Ω, Γ_{z} = 0 (blue lines, open diamonds) and Γ_{z} = 0.3Ω (black lines, open circles). The graphs on the right show the probability distributions *p*_{R}(*n*) for *N* = 45 atoms in the corresponding volume: Γ_{z} = 0 (blue open bars) and Γ_{z} = 0.3Ω (black filled bars). The dashed lines show the Poisson distribution for the corresponding 〈*n*_{R}〉.

**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.