Abstract
The recent development of single-atom-resolved probes has made full counting statistics measurements accessible in quantum gas experiments. This capability provides access to high-order moments of physical observables, from which cumulants, or equivalently connected correlations, can be precisely determined. Through a selection of recent cold atom experiments, this article illustrates the significance of connected correlations in characterizing ensembles of interacting quantum particles. First, non-zero connected correlations of order n > 2 unambiguously identify non-Gaussian quantum states. Second, connected correlations of order n identify clusters made of n elements whose statistical properties are irreducible to combinations of smaller clusters. The ability to identify such multi-particle clusters offers a an interesting perspective on strongly correlated quantum states of matter at the microscopic scale.