  We develop a theoretical approach for the dynamics of Rydberg excitations in
ultracold gases, with a realistically large number of atoms. We rely on the
reduction of the single-atom Bloch equations to rate equations, which is
possible under various experimentally relevant conditions. Here, we explicitly
refer to a two-step excitation-scheme. We discuss the conditions under which
our approach is valid by comparing the results with the solution of the exact
quantum master equation for two interacting atoms. Concerning the emergence of
an excitation blockade in a Rydberg gas, our results are in qualitative
agreement with experiment. Possible sources of quantitative discrepancy are
carefully examined. Based on the two-step excitation scheme, we predict the
occurrence of an antiblockade effect and propose possible ways to detect this
excitation enhancement experimentally in an optical lattice as well as in the
gas phase.
