  The collapses and revivals of a coherent matter wave field of interacting
particles can serve as a sensitive interferometric probe of the interactions
and the number statistics of the underlying quantum field. Here we show how the
ability to observe long time traces of collapse and revival dynamics of a
Bose-Einstein condensate loaded into a three-dimensional (3D) optical lattice
allowed us to directly reveal the atom number statistics and the presence of
effective coherent multi-particle interactions in a lattice. The multi-particle
interactions are generated via virtual transitions to higher lattice orbitals
and can find use for simulations of effective field theories with ultracold
atoms in optical lattices. We measured their absolute strengths up to the case
of six-particle interactions and compare our findings with theory.
