Direct measurement of the spatial correlation function of ultracold atoms

hk of the photon momentum (subrecoil cooling). The implementation of methods to measure such a small momentum width or the associated large coherence length of the atomic wave packets is therefore a main issue. Two methods have been used to measure dp in subrecoil cooling experiments: time-of-flight techniques (TOF) [4] for VSCPT and velocity selective Raman transitions [5] for Raman cooling. We present, in this Letter, a new approach which is based on a direct measurement of the atomic spatial correlation function and fits in the current effort to investigate first and higher order correlation functions in ultracold atomic samples [6]. We apply our method to metastable helium atoms cooled by onedimensional VSCPT. We deduce from our measurements effective temperatures as low as TRy800, where TR is the recoil limit [7]. This is well below the lowest temperatures we can measure by TOF. The high resolution of this method allows quantitative tests to be made of theoretical predictions based on Levy statistics. In addition, we can recombine the atomic wave packets after they have flown apart, achieving in this way a Mach-Zender type interferometer with subrecoil cooled atoms (for a review on atomic interferometry see [8,9]; see also [10]). The idea followed here is that the dispersion of a variable, which is too narrow to be precisely measured, can be inferred from the correlation function of the conjugate variable. In classical optics, for example, the width dv of a very narrow spectral line can be more easily obtained from the time correlation function Gstd › R