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 ...

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We discuss techniques for probing the effects of a constant force acting on cold atoms using two configurations of a grating echo-type atom interferometer. Laser-cooled samples of 85 Rb with temperatures as low as 2.4 µK have been achieved in a new experimental apparatus with a wellcontrolled magnetic environment. We demonstrate interferometer signal lifetimes approaching the transit time limit in this system (∼ 270 ms), which is comparable to the timescale achieved by Raman interferometers. Using these long timescales, we experimentally investigate the influence of a homogeneous magnetic field gradient using two-and three-pulse interferometers, which enable us to sense changes in externally applied magnetic field gradients as small as ∼ 4 × 10 −5 G/cm. We also provide an improved theoretical description of signals generated by both interferometer configurations that accurately models experimental results. With this theory, absolute measurements of B-gradients at the level of 3 × 10 −4 G/cm are achieved. Finally, we contrast the suitability of the two-and three-pulse interferometers for precision measurements of the gravitational acceleration, g.

We have developed two configurations of an echo interferometer that rely on standing wave excitation of a laser-cooled sample of rubidium atoms. Both configurations can be used to measure acceleration a along the axis of excitation. For a two-pulse configuration, the signal from the interferometer is modulated at the recoil frequency and exhibits a sinusoidal frequency chirp as a function of pulse spacing. In comparison, for a three-pulse stimulated echo configuration, the signal is observed without recoil modulation and exhibits a modulation at a single frequency as a function of pulse spacing. The three-pulse configuration is less sensitive to effects of vibrations and magnetic field curvature leading to a longer experimental timescale. For both configurations of the atom interferometer (AI), we show that a measurement of acceleration with a statistical precision of 0.5% can be realized by analyzing the shape of the echo envelope that has a temporal duration of a few microseconds. Using the two-pulse AI, we obtain measurements of acceleration that are statistically precise to 6 parts per million (ppm) on a 25 ms timescale. In comparison, using the three-pulse AI, we obtain measurements of acceleration that are statistically precise to 0.4 ppm on a timescale of 50 ms. A further statistical enhancement is achieved by analyzing the data across the echo envelope so that the statistical error is reduced to 75 parts per billion (ppb). The inhomogeneous field of a magnetized vacuum chamber limited the experimental timescale and resulted in prominent systematic effects. Extended timescales and improved signal-to-noise ratio observed in recent echo experiments using a non-magnetic vacuum chamber suggest that echo techniques are suitable for a high precision measurement of gravitational acceleration g. We discuss methods for reducing systematic effects and improving the signal-to-noise ratio. Simulations of both AI configurations with a timescale of 300 ms suggest that an optimized experiment with improved vibration isolation and atoms selected in the mF = 0 state can result in measurements of g statistically precise to 0.3 pbb for the two-pulse AI and 0.6 ppb for the three-pulse AI.

We have demonstrated a method of generation and real-time detection of nanostructures in a cold Rb cloud. These structures, which are periodic gratings of atomic density, appear as a result of interference of atoms diffracted by pulses of an optical standing wave of wavelength . We have detected structures of period /2 and /4. Calculations indicate that these density gratings have period /2N for integer N. While the structures with the period /2 are easily detected by Bragg scattering of an optical probe beam, the shorter-period structures are not. For their detection we have developed a three-pulse echo method, in which the shorterperiod gratings get converted into the structures with period /2, readily detected in real time. Applications related to lithography are discussed.