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Abstract

In this thesis models for clouds of Rydberg atoms with strong interaction effects are investigated. Since the capabilities of straightforward calculations in many-body systems are limited in general, we discuss simplified models, which approximate correlations between the atoms. In addition, we present an enhanced version of the rate equation model which takes into account higher order, namely exact two-body correlations. Different methods to improve the runtime of the models are suggested. We exploit the facts that some correlations can be neglected for large atomic seperations and that different Monte Carlo algorithms can be used to propagate into the steady state. The models are analysed and compared from a technical and a physical point of view with the aim to decide which model is most appropriate for a given setup. We identify fundamental limitations and estimate the range of validity in the field of parameters. The models are used to calculate different observables which gives an understanding of their capabilities. In particular, we find resonance conditions in the pair correlation function and explain the super- and sub-Poissonian characters of excitation counts.