Three-level rate equations in cold, disordered Rydberg gases

We have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these rate equations and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these rate equations in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general agreement.