Finite-size effects in strongly interacting Rydberg gases

The dependence of the number of Rydberg excitations in a laser-driven cloud of atoms on the interaction strength is found to be affected by the finite size of the system. A theoretical model predicting a simple power-law dependence is compared with results extracted from a numerical many-body simulation. We find that for finite-size systems the numerical results do not agree with the analytical prediction. By individually testing the assumptions leading to the theoretical prediction using the results from the numerical analysis, we identify the origin of the deviations, and explain it as arising from the finite size of the system. Furthermore, finite-size effects in the pair correlation function g((2)) are predicted. Finally, in larger ensembles, we find that the theoretical predictions and the numerical results agree, provided that the system is sufficiently homogeneous.