  In 1963 Glauber introduced the modern theory of quantum coherence, which
extended the concept of first-order (one-body) correlations, describing phase
coherence of classical waves, to include higher-order (n-body) quantum
correlations characterizing the interference of multiple particles. Whereas the
quantum coherence of photons is a mature cornerstone of quantum optics, the
quantum coherence properties of massive particles remain largely unexplored. To
investigate these properties, here we use a uniquely correlated source of atoms
that allows us to observe n-body correlations up to the sixth-order at the
ideal theoretical limit (n!). Our measurements constitute a direct
demonstration of the validity of one of the most widely used theorems in
quantum many-body theory--Wisck's theorem--for a thermal ensemble of massive
particles. Measurements involving n-body correlations may play an important
role in the understanding of thermalization of isolated quantum systems and the
thermodynamics of exotic many-body systems, such as Efimov trimers.
