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arXiv:0809.0243 · Physical Review A

Dispersion compensation in atom interferometry by a Sagnac phase

Marion Jacquey, Alain Miffre, G. Trénec, M Büchner, J. Vigué, Alexander D. Cronin

Published Jul 31, 2008• 12 citations
arXivHTMLPDF

Abstract

We reanalyzed our atom interferometer measurement of the electric polarizability of lithium, now accounting for the Sagnac effect due to the Earth's rotation. The resulting correction to the polarizability is very small, but the visibility as a function of the applied phase shift is now better explained. The fact that the Sagnac and polarizability phase shifts are both proportional to ${v}^{\ensuremath{-}1}$, where $v$ is the atom velocity, suggests that a phase shift of the Sagnac type could be used as a counterphase to compensate for the electric polarizability phase shift. This exact compensation opens the way to higher-accuracy measurements of atomic polarizabilities, and we discuss how this can be done in practice and the final limitations of the proposed technique.

DOI
10.1103/physreva.78.013638

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We reanalyzed our atom interferometer measurement of the electric polarizability of lithium, now accounting for the Sagnac effect due to the Earth's rotation. The resulting correction to the polarizability is very small, but the visibility as a function of the applied phase shift is now better explained. The fact that the Sagnac and polarizability phase shifts are both proportional to v\ensuremath−1{v}^{\ensuremath{-}1}v\ensuremath−1, where vvv is the atom velocity, suggests that a phase shift of the Sagnac type could be used as a counterphase to compensate for the electric polarizability phase shift. This exact compensation opens the way to higher-accuracy measurements of atomic polarizabilities, and we discuss how this can be done in practice and the final limitations of the proposed technique.
A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms' velocity is compensated by applying an engineered counterphase. The counterphase is equivalent to a rotation, is precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 rad (5 times larger than previously possible) have now been measured in an atom beam interferometer, and we suggest that this technique can enable comparisons of atomic polarizability with precision of one part in 10,000.
We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium $\ensuremath{\alpha}=(24.33\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{3}$ with a 0.66% uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and the interference signals have a large intensity and a high visibility, resulting in accurate phase measurements. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for our largest field, is measured with a ${10}^{\ensuremath{-}3}$ accuracy.
A rotating interferometer with paths that enclose a physical area exhibits a phase shift proportional to this area and to the rotation rate of the frame. Understanding the origin of this so-called Sagnac effect has played a key role in the establishment of the theory of relativity and has pushed for the development of precision optical interferometers. The fundamental importance of the Sagnac effect motivated the realization of experiments to test its validity for waves beyond optical, but precision measurements remained a challenge. Here, we report the accurate test of the Sagnac effect for matter waves, by using a Cesium atom interferometer featuring a geometrical area of 11 cm 2 and two sensitive axes of measurements. We measure the phase shift induced by Earth’s rotation and find agreement with the theoretical prediction at an accuracy level of 25 parts per million. Beyond the importance for fundamental physics, our work opens practical applications in seismology and geodesy.
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.
Atom-interferometer-based gyroscopes are expected to have a wide range of applications due to their high sensitivity; however, their dynamic range is limited by dephasing from the velocity-dependent Sagnac phase shift and the longitudinal velocity distribution of the atoms, restricting measurements of large angular velocities. In this study, we present a method for restoring the contrast deterioration in angular velocity measurements with interferometer gyroscopes using atomic beams. We show that by introducing a pseudorotation effect with appropriate two-photon detunings for Raman light in the interferometer, it is possible to effectively cancel the Sagnac phase shift for all atoms in the velocity distribution of the beam. Consequently, the contrast is unaffected by the rotation. Furthermore, we apply this method to an interferometer gyroscope with counterpropagating atomic beams sharing the same Raman light. It is found that the angular velocity of the system can be estimated through the detuning point where the phase difference between the two interferometers is zero. This approach ensures that the scale factor of the atom interferometer gyroscope is independent of the change in the longitudinal velocity distribution of the atomic beam. We demonstrate our technique using an interferometer gyroscope with thermal atomic beams of rubidium-87, achieving a measurement of angular velocity of $1.0{\phantom{\rule{0.2em}{0ex}}}^{\ensuremath{\circ}}/\mathrm{s}$ even with an acceleration of 0.68m/s20.68\phantom{\rule{0.2em}{0ex}}\mathrm{m}/{\mathrm{s}}^{2}0.68m/s2 on a three-axis rotation table. This simple and robust dispersion-compensation method with Raman-light detuning will benefit dynamic angular velocity measurements in field applications such as the inertial navigation of vehicles.