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.
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