Abstract
The competition between resonant optical excitation of Rydberg states of atoms and their strong, long-range van der Waals interaction results in spatial ordering of Rydberg excitations in a two-dimensional lattice gas, as observed in a recent experiment of Schauß et al. [Nature 491, 87 (2012)]. Here we use semiclassical Monte Carlo simulations to obtain stationary states for hundreds of atoms in finite-size lattices. We show the formation of regular spatial structures of Rydberg excitations in a system of increasing size, and find highly sub-Poissonian distribution of the number of Rydberg excitations characterized by a large negative value of the Mandel Q parameter which is nearly independent of the system size.
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