Cluster-expansion representation in quantum optics
M. Kira, S. W. Koch · Physical Review A · 2008
A theoretical framework is developed that combines the systematic many-body cluster-expansion approach with the standard quantum-optical representations. A cluster-expansion transformation is derived to obtain a flexible one-to-one mapping between correlated clusters and the usual phase-space and marginal distributions discussed in quantum optics. The convergence and correlation properties of this transformation are explored through several quantum-field examples including coherent, thermal, squeezed, Fock, and Schr\"odinger cat states. The resulting correlation properties can be used as a basis to characterize and control many-body correlations when quantum light interacts with matter. As an application, a cluster-expansion-restoration scheme is developed that allows for the retrieval of the true quantum statistics of light from realistic measurements that are deteriorated by the reduced quantum efficiency of the detectors.