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arXiv:quant-ph/0312187 · Physical Review Letters

Sagnac Interferometry Based on Ultraslow Polaritons in Cold Atomic Vapors

Frank Zimmer, Michael Fleischhauer

Published Jun 21, 2004• 52 citations
arXivHTMLPDF

Abstract

The advantages of light and matter-wave Sagnac interferometers--large area on one hand and high rotational sensitivity per unit area on the other--can be combined utilizing ultraslow light in cold atomic gases. While a group-velocity reduction alone does not affect the Sagnac phase shift, the associated momentum transfer from light to atoms generates a coherent matter-wave component which gives rise to a substantially enhanced rotational signal. It is shown that matter-wave sensitivity in a large-area interferometer can be achieved if an optically dense vapor at subrecoil temperatures is used. Already a noticeable enhancement of the Sagnac phase shift is possible, however, with far fewer cooling requirements.

DOI
10.1103/physrevlett.92.253201

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The advantages of light and matter-wave Sagnac interferometers--large area on one hand and high rotational sensitivity per unit area on the other--can be combined utilizing ultraslow light in cold atomic gases. While a group-velocity reduction alone does not affect the Sagnac phase shift, the associated momentum transfer from light to atoms generates a coherent matter-wave component which gives rise to a substantially enhanced rotational signal. It is shown that matter-wave sensitivity in a large-area interferometer can be achieved if an optically dense vapor at subrecoil temperatures is used. Already a noticeable enhancement of the Sagnac phase shift is possible, however, with far fewer cooling requirements.
The light-matter-wave Sagnac interferometer based on ultraslow light proposed recently in Zimmer and Fleischhauer, Phys. Rev. Lett. 92, 253201 (2004), is analyzed in detail. In particular the effect of confining potentials is examined and it is shown that the ultraslow light attains a rotational phase shift equivalent to that of a matter wave, if and only if the coherence transfer from light to atoms associated with slow light is associated with a momentum transfer and if an ultracold gas in a ring trap is used. The quantum sensitivity limit of the Sagnac interferometer is determined and the minimum detectable rotation rate calculated. It is shown that the slow-light interferometer allows for a significantly higher signal-to-noise ratio as possible in current matter-wave gyroscopes.
Since the first atom interferometry experiments in 1991, measurements of rotation through the Sagnac effect in open-area atom interferometers have been investigated. These studies have demonstrated very high sensitivity that can compete with state-of-the-art optical Sagnac interferometers. Since the early 2000s, these developments have been motivated by possible applications in inertial guidance and geophysics. Most matter-wave interferometers that have been investigated since then are based on two-photon Raman transitions for the manipulation of atomic wave packets. Results from the two most studied configurations, a space-domain interferometer with atomic beams and a time-domain interferometer with cold atoms, are presented and compared. Finally, the latest generation of cold atom interferometers and their preliminary results are presented.
The Sagnac effect, manifest in the phase shift of a rotating interferometer proportional to its physical area and to the rotation rate of the frame, plays a crucial role in modern physics being generalized to any kind of interferometer. However, as compared to light, the accurate experimental validation of the Sagnac effect for matter-waves remains challenging. We report the accurate measurement of the Sagnac phase shift, induced by the Earth’s rotation, using a large-area cold atom interferometer. We probe the atomic Sagnac phase shift along the two orthogonal horizontal axes in various orientation of the sensor with respect to geographic north and obtain an agreement with the theoretical prediction at the 20 ppm level, improving by twenty five-fold over the previous achievements for matter waves. Our results underline the universality of the Sagnac effect and open new horizons for testing other fundamental theories, as well as for a number of technological applications in seismology, geodesy and inertial navigation systems.
A gyroscope based on Sagnac interferometer measures the rotation rate relative to an inertial frame of reference. Sagnac effect originally has been derived and experimentally demonstrated with optical waves. Later, matter wave based Sagnac interferometers were developed due to inherent sensitivity over a photon based system. However in any interferometer whether it is photon or matter wave based the resultant phase shift due to counter-rotating waves is independent of the wave velocity. Here we show that one can have a larger phase shift with slower matter waves using Aharonov-Bohm effect: the phase difference of the counter propagating waves is proportional to the inverse square of the particle velocity.
We report on the realization of a compact atomic Mach–Zehnder-type Sagnac interferometer of 13.7 cm length, which covers an area of 19 mm 2 previously reported only for large thermal beam interferometers. According to Sagnac's formula, which holds for both light and atoms, the sensitivity for rotation rates increases linearly with the area enclosed by the interferometer. The use of cold atoms instead of thermal atoms enables miniaturization of Sagnac interferometers without sacrificing large areas. In comparison with thermal beams, slow atoms offer better matching of the initial beam velocity and the velocity with which the matter waves separate. In our case, the area is spanned by a cold atomic beam of 2.79 m s −1 , which is split, deflected and combined by driving a Raman transition between the two hyperfine ground states of 87 Rb in three spatially separated light zones. The use of cold atoms requires a precise angular alignment and high wave front quality of the three independent light zones over the cloud envelope. We present a procedure for mutually aligning the beam splitters at the microradian level by making use of the atom interferometer itself in different configurations. With this method, we currently achieve a sensitivity of .
We realize beam splitters and mirrors for atom waves by employing a sequence of light pulses rather than individual ones. In this way we can tailor atom interferometers with improved sensitivity and accuracy. We demonstrate our method of composite pulses by creating a symmetric matter-wave interferometer which combines the advantages of conventional Bragg- and Raman-type concepts. This feature leads to an interferometer with a high immunity to technical noise allowing us to devise a large-area Sagnac gyroscope yielding a phase shift of 6.5 rad due to the Earth's rotation. With this device we achieve a rotation rate precision of 120 nrad s(-1) Hz(-1/2) and determine the Earth's rotation rate with a relative uncertainty of 1.2%.