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Physical Review A

Operating an atom-interferometry-based gravity gradiometer by the dual-fringe-locking method

Xiao‐Chun Duan, Min-Kang Zhou, Dekai Mao, Hui-Bing Yao, Xiao-Bing Deng, Jun Luo, Zhong-Kun Hu

Published Aug 11, 2014• 81 citations
Publisher

Abstract

We report a gravity gradiometer composed of two atom interferometers which are simultaneously locked to the respective fringe center by feedback control of the Raman laser phase and magnetic field gradient. Compared with the conventional full-fringe recording method, this dual-fringe-locking strategy is capable of increasing the sampling rate and improving the sensitivity for gravity gradient measurements. Meanwhile, it retains the intrinsic advantage of rejecting common mode noises for gravity gradiometers. A short-term sensitivity of $670 \mathrm{E}/{Hz}^{1/2}$ with a 0.25 Hz sampling rate is achieved in our gravity gradiometer. This approach may also find possible applications in other atom-interferometry-based experiments utilizing dual atomic clouds.

DOI
10.1103/physreva.90.023617

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We report a gravity gradiometer composed of two atom interferometers which are simultaneously locked to the respective fringe center by feedback control of the Raman laser phase and magnetic field gradient. Compared with the conventional full-fringe recording method, this dual-fringe-locking strategy is capable of increasing the sampling rate and improving the sensitivity for gravity gradient measurements. Meanwhile, it retains the intrinsic advantage of rejecting common mode noises for gravity gradiometers. A short-term sensitivity of 670E/Hz1/2670 \mathrm{E}/{Hz}^{1/2}670E/Hz1/2 with a 0.25 Hz sampling rate is achieved in our gravity gradiometer. This approach may also find possible applications in other atom-interferometry-based experiments utilizing dual atomic clouds.
Abstract Dual atom interferometer configurations have been extensively applied in gyroscopes and gradiometers to suppress common mode noise and extract inertial signals with high precision. However, the intrinsic phase coupling between the two interferometers poses a significant challenge for simultaneous fringe locking. Here, we demonstrate a dual atom interferometric gyroscope-accelerometer, where the simultaneous fringe locking is realized by employing independent direct digital synthesizer (DDSs) signals to control the laser phase shifts of each interferometer. This dual-fringe-locking approach enables both interferometer fringes in independent phase control and simultaneous feedback stabilization while preserving the common mode noise rejection inherent to the dual configuration. It facilitates the rotation and acceleration accurately and simultaneously measured; besides, compared with the traditional full-fringe recording, the data acquisition rate and the sensitivity of rotation and acceleration are enhanced. Thus, this solution is promising for high precision quantum inertial sensing applications.
We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short-term sensitivity of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ g/Hz\sqrt{\text{Hz}}Hz​ to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows us to reach a resolution of $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ g after 8000 s on the measurement of differential gravity acceleration. The long-term stability is compatible with a measurement of the gravitational constant GGG at the level of ${10}^{\ensuremath{-}4}$ after an integration time of about 100 h.
We investigated the Raman-pulse-duration effect in a gravity gradiometer with two atom interferometers. Since the two atom clouds in the gradiometer experience different gravitational fields, it is hard to compensate for the Doppler shifts of the two clouds simultaneously by chirping the frequency of a common Raman laser. This leads to an appreciable phase shift. The magnitude of the phase shift relative to the differential phase shift of the two interferometers is in an order of $\ensuremath{\tau}/T$, and cannot be neglected in the precision measurements such as measuring the gravity gradient and the Newtonian gravitational constant.
We here present a high sensitivity gravity-gradiometer based on atom interferometry. In our apparatus, two clouds of laser-cooled rubidium atoms are launched in fountain configuration and interrogated by a Raman interferometry sequence to probe the gradient of gravity field. We recently implemented a high-flux atomic source and a newly designed Raman lasers system in the instrument set-up. We discuss the applications towards a precise determination of the Newtonian gravitational constant G. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement precision below the 100 ppm level.
A transportable atom interferometer-based gravity gradiometer has been developed at JPL to carry out measurements of Earth's gravity field at ever finer spatial resolutions, and to facilitate high-resolution monitoring of temporal variations in the gravity field from ground- and flight-based platforms. Existing satellite-based gravity missions such as CHAMP and GRACE measure the gravity field via precise monitoring of the motion of the satellites; i.e. the satellites themselves function as test masses. JPL's quantum gravity gradiometer employs a quantum phase measurement technique, similar to that employed in atomic clocks, made possible by recent advances in laser cooling and manipulation of atoms. This measurement technique is based on atomwave interferometry, and individual laser-cooled atoms are used as drag-free test masses. The quantum gravity gradiometer employs two identical atom interferometers as precision accelerometers to measure the difference in gravitational acceleration between two points (Figure 1). By using the same lasers for the manipulation of atoms in both interferometers, the accelerometers have a common reference frame and non-inertial accelerations are effectively rejected as common mode noise in the differential measurement of the gravity gradient. As a result, the dual atom interferometer-based gravity gradiometer allows gravity measurements on a moving platform, while achieving the same long-term stability of the best atomic clocks. In the laboratory-based prototype (Figure 2), the cesium atoms used in each atom interferometer are initially collected and cooled in two separate magneto-optic traps (MOTs). Each MOT, consisting of three orthogonal pairs of counter-propagating laser beams centered on a quadrupole magnetic field, collects up to 10(exp 9) atoms. These atoms are then launched vertically as in an atom fountain by switching off the magnetic field and introducing a slight frequency shift between pairs of lasers to create a moving rest frame for the trapped atoms. While still in this moving-frame molasses, the laser frequencies are further detuned from the atomic resonance (while maintaining this relative frequency shift) to cool the atom cloud's temperature to 2 K or below, corresponding to an rms velocity of less than 2 cm/s. After launch, the cold atoms undergo further state and velocity selection to prepare for atom interferometry. The atom interferometers are then realized using laser-induced stimulated Raman transitions to perform the necessary manipulations of each atom, and the resulting interferometer phase is measured using laser-induced fluorescence for state-normalized detection. More than 20 laser beams with independent controls of frequency, phase, and intensity are required for this measurement sequence. This instrument can facilitate the study of Earth's gravitational field from surface and air vehicles, as well as from space by allowing gravity mapping from a low-cost, single spacecraft mission. In addition, the operation of atom interferometer-based instruments in space offers greater sensitivity than is possible in terrestrial instruments due to the much longer interrogation times available in the microgravity environment. A space-based quantum gravity gradiometer has the potential to achieve sensitivities similar to the GRACE mission at long spatial wavelengths, and will also have resolution similar to GOCE for measurement at shorter length scales.
As part of a program to determine the gravitational constant G using multiple independent methods in the same laboratory, an atom gravity gradiometer is being developed. The gradiometer is designed with two magneto-optical traps to ensure both the fast simultaneous launch of two atomic clouds and an optimized configuration of source masses. Here, the design of the G measurement by atom interferometry is detailed, and the experimental setup of the atom gravity gradiometer is reported. A preliminary sensitivity of 3 × 10−9 g/Hz to differential gravity acceleration is obtained, which corresponds to 99 E/Hz (1 E = 10−9 s−2) for the gradiometer with a baseline of 0.3 m. This provides access to measuring G at the level of less than 200 parts per million in the first experimental stage.