Semianalytical model for nonlinear absorption in strongly interacting Rydberg gases

Rate equation models are extensively used to describe the many-body states of laser driven atomic gases. We show that the properties of the rate equation model used to describe nonlinear optical effects arising in interacting Rydberg gases can be understood by considering the excitation of individual superatoms. From this we deduce a simple semianalytical model that accurately describes the Rydberg density and optical susceptibility for different dimensionalities. We identify the previously reported universal dependence of the susceptibility on the Rydberg excited fraction as an intrinsic property of the rate equation model that is rooted in one-body properties. Benchmarking against exact master equation calculations, we identify regimes in which the semianalytical model is particularly reliable. The performance of the model improves in the presence of dephasing which destroys higher-order atomic coherences.