Coherent collisional decoherence

We study the decoherence of a system of $N$ non-interacting heavy particles (atoms) due to coherent scattering with a background gas. We introduce a framework for computing the induced phase shift and loss of contrast for arbitrary preparations of $N$-particle quantum states. We find phase shifts that are inherently $(N\geq 2)$-body effects and may be searched for in future experiments. We analyze simple setups, including a two-mode approximation of an interferometer. We study fully entangled $N00N$ states, which resemble the correlated positions in a matter interferometer, as well as totally uncorrelated product states that are representative of a typical state in an atom interferometer. We find that the extent to which coherent enhancements increase the rate of decoherence depends on the observable of interest, state preparation, and details of the experimental design. In the context of future ultralow-recoil (e.g., light dark matter) searches with atom interferometers we conclude that: {\it i}) there exists a coherently enhanced scattering phase which can be searched for using standard (i.e., contrast/visibility and phase) interferometer observables; {\it ii}) although decoherence rates of one-body observables are {\it not} coherently enhanced, a coherently enhanced loss of contrast can still arise from dephasing; and {\it iii}) higher statistical moments (which are immediately accessible in a counting experiment) {\it are} coherently enhanced and may offer a new tool with which to probe the soft scattering of otherwise undetectable particles in the laboratory.