  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 un-excited 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.
