Control of multiatom entanglement in a cavity

We propose a general formalism for analytical description of multiatomic ensembles interacting with a single-mode quantized cavity field under the assumption that most atoms remain unexcited on average. By combining the obtained formalism with the nilpotent technique for the description of multipartite entanglement we are able to overview in a unified fashion different probabilistic control scenarios of entanglement among atoms or examine atomic ensembles. We then apply the proposed control schemes to the creation of multiatom states useful for quantum information.