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 a 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. We present a setup which is suited for applications in atom interferometry and cavity QED.