  We study the influence of quantum density fluctuations in ultracold atoms in
an optical lattice on the scattering of matter waves. Such fluctuations are
characteristic of the superfluid phase and vanish due to increased interactions
in the Mott insulating phase. We employ an analytical treatment of the
scattering and demonstrate that the fluctuations lead to incoherent processes,
which we propose to observe via decoherence of the fringes in a Mach-Zender
interferometer. In this way we extract the purely coherent part of the
scattering. Further, we show that the quantum density fluctuations can also be
observed directly in the differential angular scattering cross section for an
atomic beam scattered from the atoms in a lattice. Here we find an explicit
dependence of the scale of the inelastic scattering on the quantum density
fluctuations.
