  Atomic Bose-Einstein condensates (BECs) can be viewed as macroscopic objects
where atoms form correlated atom clusters to all orders. Therefore, the
presence of a BEC makes the direct use of the cluster-expansion approach ---
lucrative e.g. in semiconductor quantum optics --- inefficient when solving the
many-body kinetics of a strongly interacting Bose. An excitation picture is
introduced with a nonunitary transformation that exclusively describes the
system in terms of atom clusters within the normal component alone. The
nontrivial properties of this transformation are systematically studied, which
yields a cluster-expansion friendly formalism for a strongly interacting Bose
gas. Its connections and corrections to the standard Hartree-Fock Bogoliubov
approach are discussed and the role of the order parameter and the Bogoliubov
excitations are identified. The resulting interaction effects are shown to
visibly modify number fluctuations of the BEC. Even when the BEC has a nearly
perfect second-order coherence, the BEC number fluctuations can still resolve
interaction-generated non-Poissonian fluctuations.
