We report the development of an atom interferometer that uses optical standing waves as phase gratings and operates in the time domain. The observed signal is entirely caused by the wave nature of the atomic center-of-mass motion. The opportunities to measure recoil frequency and gravity acceleration are demonstrated. [S0031-9007(97) PACS numbers: 03.75. Dg, 06.20.Jr, 32.80.Pj, 42.50.Md Atom optics and interferometry is a field that has undergone considerable development in recent years [1]. Atom interferometric techniques have been used to make a number of new and high precision measurements. Examples are measurements of the atomic index of refraction of a gas [2], the loss of atomic coherence in spontaneous emission [3], the Earth's gravitational acceleration g [4],h͞m [5], and precise values of atomic level spacings [6,7]. Atom interferometers (AI) fall into two classes, "microfabricated structure AI" [8-10], which use microfabricated structures as beam splitters, and "optical field AI" [4][5][6][7][11][12][13][14], which use optical fields as beam splitters. The atoms in different arms of microfabricated structure AI are in the same internal state, while in optical field AI they can be in different [4][5][6][7]11], or the same [12 -14] internal states.In this paper we report the development of an optical field atom interferometer in which pulsed standing wave optical fields act as phase gratings on an "uncollimated" cloud of cold atoms. As in Refs. [8-10,12 -14] this interferometer is a "de Broglie wave" interferometer in that the beam splitters do not alter the atomic internal state; the interference occurs between different paths of the atomic center-of-mass. In contrast to optical field AI using atomic beams [12,13], all the atoms in our interferometer interact with the light fields for the same amount of time, eliminating broadening effects due to velocity dispersion, and the time delay between the standing wave fields can easily be varied. The operation of the interferometer depends critically on a mechanism similar to that occurring in photon echo formation. As in other echolike interferometers [6,7,10,11], collimation of the transverse atomic velocity distribution to better than a photon recoil momentum is not necessary. As is discussed below, a time-domain atom interferometer of this type offers a unique combination of features that are well suited to high precision measurements and complement those of other atom interferometers. We have used this interferometer to measure the recoil frequency of a 85 Rb atom and the acceleration due to gravity ("little g").In our experiments two off-resonant standing wave pulses separated by a time T are applied to a sample of cold (150 mK) 85 Rb atoms [15]. The first laser pulse imposes a spatial phase modulation on the initial atomic state, which, due to the dispersion of de Broglie waves in free space, evolves into an amplitude modulation (representing an atomic population grating). For short times this population grating can be explained as the focusing of ...

We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the Fϭ3 ground state in a cloud of laser-cooled 85 Rb atoms. The rephasing results in a magnetic grating echo ͑MGE͒. We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.

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We have used two sets of opposite circularly polarized traveling wave pulses separated in time to establish, and subsequently rephase, a spatially modulated coherence between the magnetic sublevels of the Fϭ3 ground state in Doppler broadened 85 Rb vapor. The rephasing results in a magnetic grating echo whose duration is an accurate measure of the velocity distribution. We demonstrate that the time scale of the experiment is determined solely by the transit time of atoms across the laser beam. The shortening of the lifetime due to a perturber ͑Ar͒ allows us to infer the Rb-Ar velocity changing collision cross section.

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