Cavity QED Detection of Interfering Matter Waves

We observe the build-up of a matter wave interference pattern from single atom detection events in a double-slit experiment. The interference arises from two overlapping atom laser beams extracted from a Rubidium Bose-Einstein condensate. Our detector is a high-finesse optical cavity which realizes the quantum measurement of the presence of an atom and thereby projects delocalized atoms into a state with zero or one atom in the resonator. The experiment reveals simultaneously the granular and the wave nature of matter.