Hyperbolic Bloch equations: Atom-cluster kinetics of an interacting Bose gas

•Atom clusters applied to efficiently describe an interacting Bose gas.•Implicit-notation formalism delivers quantum kinetics of all atom clusters.•Common cluster-expansion approach is found for BEC and semiconductors.•Hyperbolic Bloch equations introduced to analyze fast-switch experiments.

Experiments with ultracold Bose gases can already produce so strong atom–atom interactions that one can observe intriguing many-body dynamics between the Bose–Einstein condensate (BEC) and the non-condensed atoms. This dynamics is thoroughly analyzed with the cluster-expansion approach to uniquely identify atom-cluster dynamics within the many-body system. These clusters assign those atoms that are genuinely connected with one another. The excitation picture is applied to express the many-body state in terms of correlated atom clusters among the non-condensed atoms alone. Implicit notation formalism is developed to explicitly derive the quantum kinetics of all   atom clusters. The clusters are shown to build up sequentially, from smaller to larger ones, which is utilized to nonperturbatively describe the interacting BEC with as few clusters as possible. This yields the hyperbolic Bloch equations (HBEs) that not only generalize the Hartree–Fock Bogoliubov approach but are also analogous to the semiconductor Bloch equations (SBEs). This connection is utilized to apply sophisticated many-body techniques of semiconductor quantum optics to BEC investigations. Here, the HBEs are implemented to determine how a strongly interacting Bose gas reacts to a fast switching from weak to strong interactions, often referred to as unitarity. The computations for 8585Rb demonstrate that molecular states (dimers) depend on atom density, and that the many-body interactions create coherent transients on a 100 μs time scale converting BEC into non-condensed atoms via quantum depletion.