Multiple-path interferometer with a single quantum obstacle

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We consider the scattering of particles by an obstacle which tunnels coherently between two positions. We show that the obstacle mimics two classical scatterers at fixed positions when the kinetic energy epsilon of the incident particles is smaller than the tunnel splitting Delta: If the obstacles are arranged in parallel, one observes an interference pattern as in the conventional double-slit experiment. If they are arranged in series, the observations conform with a Fabry-Perot interferometer. At larger epsilon inelastic processes result in more complex interference phenomena. Interference disappears when epsilon >> Delta, but can be recovered if only the elastic scattering channel is detected. We discuss the realization of a quantum obstacle in mesoscopic systems.