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Physical Review Letters

Rotation Sensing with an Atom Interferometer

Alan Lenef, Troy D. Hammond, Edward T. Smith, Michael Chapman, Richard A. Rubenstein, David E. Pritchard

Published Feb 3, 1997• 198 citations
Publisher

Abstract

We have measured the phase shift induced by rotation of an atom interferometer at rates of $\ensuremath{-}2$ to $+2$ earth rates and obtained $1%$ agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was $42$ milliearth rates for $1$ sec of integration time, within $9%$ of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.

DOI
10.1103/physrevlett.78.760

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Feb 8, 2007•0 citations
We have measured the phase shift induced by rotation of an atom interferometer at rates of \ensuremath−2\ensuremath{-}2\ensuremath−2 to +2+2+2 earth rates and obtained 11%1 agreement with the predicted Sagnac phase shift for atomic matter waves. The rotational rms noise of our interferometer was 424242 milliearth rates for 111 sec of integration time, within 99%9 of shot noise. The high sensitivity and agreement of predicted and measured behavior suggest useful future scientific applications of atom interferometers as inertial sensors.
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 rotation-rate sensor was developed using atom interferometry and the Sagnac effect for matter waves. This device has a short-term sensitivity of 6× 10−10 rad/sec for a 1 second integration time, which is the best publicly reported value to date. It has high intrinsic accuracy because it relies on interactions between atoms and laser light that is stabilized to an atomic transition. Long-term stability is promising and characterization is currently underway. Potential applications include inertial navigation, geophysical studies, and general relativity tests such as verification of the Lense-Thirring and geodetic effects. The principle of operation is as follows: A thermal cesium atomic beam crosses three laser interaction regions where two-photon stimulated Raman transitions between cesium ground states transfer momentum to atoms and divide, deflect, and recombine the atomic wavepackets. Rotation induces a phase shift between the two possible trajectories and causes a change in the detected number of atoms with a particular internal state. Counterpropagating atomic beams form two interferometers using shared lasers for common-mode rejection, and the rotation phase shifts have opposite sign since the phase shift is proportional to the vector velocity of the atoms. Therefore, subtracting or adding the interferometer signals discriminates between rotation and transverse acceleration summed with laser arbitrary phase. Furthermore, in the inertial reference frame of the atoms, rotations Doppler-shift the Raman lasers. Adding Raman frequency shifts to cancel these Doppler-shifts allows operation at an effective zero rotation rate, improving sensitivity and bandwidth. Modulating these frequency shifts facilitates sensitive lock-in detection readout techniques.
The exquisite precision of atom interferometers has sparked the interest of a large community for uses ranging from fundamental physics to geodesy and inertial navigation. However, their implementation for onboard applications is still limited, not least because rotation and acceleration are intertwined in a single phase shift, which makes the extraction of a useful signal more challenging. Moreover, the spatial separation of the wave packets due to rotations leads to a loss of signal. We present an atom interferometer operating over a large range of random angles, rotation rates and accelerations. A model of the expected phase shift allows us to untangle the rotation and acceleration signals. We also implement a real-time compensation system using fiber-optic gyroscopes and a rotating reference mirror to maintain the full contrast of the interferometer. We demonstrate a single-shot sensitivity to acceleration of 24 μg for rotation rates reaching 14° s−1. Cold atoms inertial sensors offer great precision and sensitivity, yet their use in mobile applications has been hindered by the effects of rotations on their measurements. Here, authors demonstrate an atom interferometer operating over a wide range of orientations and rotation rates, thanks to hybridisation with accelerometers and gyroscopes.
We reports improvements to our Sagnac effect matter-wave interferometer gyroscope. This device now has a short-term rotation-rate sensitivity of 6 × 10 -10 rad s -1 over 1 s of integration, which is the best publicly reported value to date. Stimulated Raman transitions are used to coherently manipulate atoms from counterpropagating thermal beams, forming two interferometers with opposite rotation phase shifts, allowing rotation to be distinguished from acceleration and laser arbitrary phase. Furthermore, electronically compensating the rotation-induced Doppler shifts of the Raman lasers allows operation at an effective zero rotation rate, improving sensitivity and facilitating sensitive lock-in detection readout techniques. Long-term stability is promising but not yet fully characterized. Potential applications include inertial navigation, geophysical studies and tests of general relativity.
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.
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.