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arXiv:1504.05530 · Physical Review Letters

Sagnac Interferometry with a Single Atomic Clock

R. Stevenson, Michael Hush, T. Bishop, Igor Lesanovsky, T. Fernholz

Published Oct 13, 2015• 58 citations
arXivHTMLPDF

Abstract

The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology.

DOI
10.1103/physrevlett.115.163001

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The Sagnac effect enables interferometric measurements of rotation with high precision. Using matter waves instead of light promises resolution enhancement by orders of magnitude that scales with particle mass. So far, the paradigm for matter wave Sagnac interferometry relies on de Broglie waves and thus on free propagation of atoms either in free fall or within waveguides. However, the Sagnac effect can be expressed as a proper time difference experienced by two observers moving in opposite directions along closed paths and has indeed been measured with atomic clocks flown around Earth. Inspired by this, we investigate an interferometer comprised of a single atomic clock. The Sagnac effect manifests as a phase shift between trapped atoms in different internal states after transportation along closed paths in opposite directions, without any free propagation. With analytic models, we quantify limitations of the scheme arising from atomic dynamics and finite temperature. Furthermore, we suggest an implementation with previously demonstrated technology.
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.
We describe our progress in the development of an atom based rotation sensor, which employs state-dependent trapping potentials to transport ultracold atoms along a closed path and perform Sagnac interferometry. Whilst guided atom interferometers are sought after to build miniaturized devices that overcome size restrictions from free-falling atoms, fully trapped interferometers also remove free-propagation along an atomic waveguide. This provides additional control of motion, e.g. removing wave-packet dispersion and enabling operation that remains independent of external acceleration. Our experimental scheme relies on radio-frequency and microwave-fields, which are partly generated via atom-chip technology, providing a step towards implementing a small, robust, and eventually portable atomic-gyroscope.
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.
Matter-wave interferometry with atoms propagating in a guiding potential is expected to provide compact, scalable and precise inertial sensing. However, a rotation sensing device based on the Sagnac effect with atoms guided in a ring has not yet been implemented despite continuous efforts during the last two decades. Here we discuss some intrinsic effects that limit the coherence in such a device and propose a scheme that overcomes these limitations and enables a multi-pass guiding Sagnac interferometer with a Bose-Einstein condensate (BEC) on a chip in a ring potential. We analyze crucial dephasing effects: potential roughness, phase diffusion due to atom-atom interactions and number uncertainty, and phase fluctuations. Owing to the recent progress in achieving high momentum beam splitting, creating smooth guides, and manipulating the matter-wavepacket propagation, guided interferometry can be implemented within the coherence time allowed by phase diffusion. Despite the lower particle flux in a guided Sagnac ring and the miniaturization of the interferometer, the estimated sensitivity, for reasonable and practical realizations of an atom chip-based gyroscope, is comparable to that of free-space interferometers, reaching 45 nrads^{-1}Hz^{-1/2}. A significant improvement over state-of-the-art free-space gyrocope sensitivities can be envisioned by using thermal atoms instead of a BEC, whereby the interferometer can be operated in a continuous fashion with the coherence limited by the scattering rate of the atoms with the background gas. Taking into account the sensitivity times length of the interferometer as the figure of merit which takes into account compactness, our configuration is expected to deliver a potential improvement of 2-4 orders of magnitude over state-of-the-art free-space gyroscopes for a BEC, and 4-6 orders of magnitude for thermal atoms.
We discuss a scheme to implement a gyroscopic atom sensor with magnetically trapped ultra-cold atoms. Unlike standard light or matter wave Sagnac interferometers no free wave propagation is used. Interferometer operation is controlled only with static, radio-frequency and microwave magnetic fields, which removes the need for interferometric stability of optical laser beams. Due to the confinement of atoms, the scheme may allow the construction of small scale portable sensors. We discuss the main elements of the scheme and report on recent results and efforts towards its experimental realization.
We simulate ultracold Sagnac atom interferometers using quantum-mechanical matter wavepackets, e.g. Bose-Einstein condensates, that counter-propagate within a rotating ring-trap. We find that the accumulation of the relative phase difference between wavepackets, i.e. the matter wave Sagnac effect, is manifested as discrete phase jumps. These plateaus result from three effects; that the atoms should be initially trapped at rest with respect to the rotating frame, that they counter-propagate with the same group velocities in the rotating frame, and that the imaging is performed in the rotating frame. We show that the plateaus persist in the presence of nonlinear atom-atom interactions, and in atoms undergoing various rotations, and thus will occur during matter wavepacket experiments. We also introduce the simplest possible Sagnac atom interferometry scheme which relies on wavepacket dispersion around a ring-trap.