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Physical Review A

Rotating matter-wave beam splitters and consequences for atom gyrometers

Charles Antoine

Published Sep 18, 2007• 19 citations
Publisher

Abstract

The effect of a rotation on a matter-wave-laser beam splitter is studied and modeled. This modeling is shown to give important nontrivial corrections to the Sagnac phase shift of matter-wave gyrometers when the duration of the laser action cannot be neglected with respect to the propagation time between beam splitters. This result is illustrated on a Mach-Zehnder atom gyrometer (rate gyroscope) with running laser beam splitters. A quasiclassical description of the interferometer arms inside the beam splitters is proposed to interpret the corrected Sagnac phase shift in terms of an effective interferometer area.

DOI
10.1103/physreva.76.033609

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The effect of a rotation on a matter-wave-laser beam splitter is studied and modeled. This modeling is shown to give important nontrivial corrections to the Sagnac phase shift of matter-wave gyrometers when the duration of the laser action cannot be neglected with respect to the propagation time between beam splitters. This result is illustrated on a Mach-Zehnder atom gyrometer (rate gyroscope) with running laser beam splitters. A quasiclassical description of the interferometer arms inside the beam splitters is proposed to interpret the corrected Sagnac phase shift in terms of an effective interferometer area.
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 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.
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%.
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.
In the framework of the ABCD ξ formulation of atom optics and with an adequate modelization of the beam splitters, we establish an exact analytical phase shift expression for atom interferometers. This result is valid for a time-dependent external Hamiltonian at most quadratic in position and momentum operators and is expressed in terms of coordinates and momenta of the wave packet centres at the interaction vertices only. As a specific application, the case of atom gyrometers and accelerometers is presented in detail.