Direct Measurement of The Spatial Correlation Function of Ultracold Atoms

We demonstrate a new method to directly measure, from the overlap of two atomic wave packets, the spatial correlation function of metastable helium atoms cooled by velocity selective coherent population trapping. This approach allows us to determine precisely the effective temperature of the atoms and to make quantitative comparison with theory. Temperatures as low as $1/800$ of the recoil temperature are found. Moreover, we extend this method to realize a temporal interferometer with de Broglie matter waves in the subrecoil regime.