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We observe the build-up of a matter wave interference pattern from singleatom detection events in a double-slit experiment. The interference arises fromtwo overlapping atom laser beams extracted from a Rubidium Bose-Einsteincondensate. Our detector is a high-finesse optical cavity which realizes thequantum measurement of the presence of an atom and thereby projects delocalizedatoms into a state with zero or one atom in the resonator. The experimentreveals simultaneously the granular and the wave nature of matter.Comment: 4 pages, 4 figure

Cavity QED detection of interfering matter waves