We describe progress toward a precise measurement of the recoil energy of an atom measured using a modified grating-echo atom interferometer (AI) that involves three standing-wave (sw) pulses. With this technique, an additional sw pulse is used to shift the phase of excited momentum states, which produces a modulation in the contrast of the interference pattern. The signal exhibits narrow fringes that revive periodically at twice the two-photon recoil frequency, 2ω_q, as a function of the onset time of the pulse. Experiments are performed using samples of laser-cooled rubidium atoms with temperatures 5 μK in a nonmagnetic apparatus. We demonstrate a measurement of ω_q with a statistical uncertainty of 37 parts per 109 (ppb) on a time scale of ～45 ms in 14 h. Further statistical improvements are anticipated by extending this time scale and narrowing the signal fringe width. However, the total systematic uncertainty is estimated to be ～6 parts per 106 (ppm). We describe methods of reducing these systematic errors.
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