A New Technique for Measuring Atomic Recoil Frequency Using Coherence Functions*

We have developed a new technique for measuring the atomic recoil frequency using a single-state echo type atom interferometer that manipulates laser cooled atoms in the ground state. The interferometer relies on momentum state interference due to 2 standing wave pulses that produce density gratings. The interference is modified by applying a 3$^{rd}$ standing wave pulse during the interferometer pulse sequence. As a result, the grating contrast exhibits periodic revivals at the atomic recoil frequency, $\omega _{r}$ as a function of the time at which the 3$^{rd}$ pulse is applied, allowing $\omega _{r}$ to be measured easily and precisely. The contrast is accurately described by a coherence function, which is the Fourier transform of the momentum distribution, produced by the 3$^{rd}$ pulse and by the theory of echo formation. If the 3$^{rd}$ pulse is a traveling wave, loss of grating contrast is observed, an effect also described by a coherence function. The decay of the grating contrast as a function of continuous wave light intensity is used to infer the cross section for photon absorption. Details of this work will be published in PRA Rapid Comm. (2009).