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arXiv:2510.22350 · Physical Review A

Tensor gravity gradiometry with a single-axis atom gradiometer

Ryan Thomas, Samuel Legge, J. D. Close

Published Nov 12, 2025• 0 citations
arXivHTMLPDF

Abstract

We propose a method for using a single-axis atom interferometric gravity gradiometer to measure off-diagonal elements of the gravity gradient tensor. By tilting the gradiometer, the measured gradient becomes a linear combination of different components of the gravity gradient tensor, and through multiple measurements at different tilts the separate tensor components can be inferred. We present a theoretical and numerical investigation of this technique, both for terrestrial surveys where the tilt is statically set by the user and for surveys where a strapdown sensor is dynamically tilted by the motion of the platform. We show that the gradiometer's sensitivity to the vertical gravity gradient is only slightly reduced by this method while allowing for more gradiometer information to be obtained. Major sources of error and loss of sensitivity on dynamic platforms are shown to be mitigated using an optical-gimbal technique employing commercially-available fibre-optic gyroscopes and tip-tilt mirrors.

DOI
10.1103/vqjd-8qwh

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We propose a method for using a single-axis atom interferometric gravity gradiometer to measure off-diagonal elements of the gravity gradient tensor. By tilting the gradiometer, the measured gradient becomes a linear combination of different components of the gravity gradient tensor, and through multiple measurements at different tilts the separate tensor components can be inferred. We present a theoretical and numerical investigation of this technique, both for terrestrial surveys where the tilt is statically set by the user and for surveys where a strapdown sensor is dynamically tilted by the motion of the platform. We show that the gradiometer's sensitivity to the vertical gravity gradient is only slightly reduced by this method while allowing for more gradiometer information to be obtained. Major sources of error and loss of sensitivity on dynamic platforms are shown to be mitigated using an optical-gimbal technique employing commercially-available fibre-optic gyroscopes and tip-tilt mirrors.
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.
Quantum interferometer gravity gradiometer for 3D mapping is a project for developing the technology of atom interferometer-based gravity sensor in space. The atom interferometer utilizes atomic particles as free fall test masses to measure inertial forces with unprecedented sensitivity and precision. It also allows measurements of the gravity gradient tensor components for 3D mapping of subsurface mass distribution. The overall approach is based on recent advances of laser cooling and manipulation of atoms in atomic and optical physics. Atom interferometers have been demonstrated in research laboratories for gravity and gravity gradient measurements. In this approach, atoms are first laser cooled to micro-kelvin temperatures. Then they are allowed to freefall in vacuum as true drag-free test masses. During the free fall, a sequence of laser pulses is used to split and recombine the atom waves to realize the interferometric measurements. We have demonstrated atom interferometer operation in the Phase I period, and we are implementing the second generation for a complete gradiometer demonstration unit in the laboratory. Along with this development, we are developing technologies at component levels that will be more suited for realization of a space instrument. We will present an update of these developments and discuss the future directions of the quantum gravity gradiometer project.
We demonstrate a proof-of-principle of direct Earth gravity-gradient measurement with an atom interferometer-based gravity gradiometer using a single proof mass of cold 87Rb^{87}\mathrm{Rb}87Rb atoms. The atomic gradiometer is implemented in the so-called double-loop configuration, hence providing a direct gravity-gradient dependent phase shift insensitive to dc acceleration and constant rotation rate. The atom interferometer (AI) can be either operated as a gravimeter or a gradiometer by simply adding an extra Raman $\ensuremath{\pi}$ pulse. We demonstrate gravity-gradient measurements first using a vibration isolation platform and second without seismic isolation using the correlation between the AI signal and the vibration signal measured by an auxilliary classical accelerometer allowing one to bypass the absence of common-mode vibration noise rejection in a double-loop geometry. The simplicity of the experimental setup (a single atomic source and unique detection) and the immunity of the AI to rotation-induced contrast loss make it a possible candidate for onboard gravity-gradient measurements.
We report the demonstration of a sensitive absolute-gravity gradiometer based on light-pulse atom-interference techniques. The gradiometer consists of two absolute accelerometers operated in a differential mode. We report a differential acceleration sensitivity of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}g/{\mathrm{Hz}}^{1/2}$ and an inferred differential acceleration accuracy of less than ${10}^{\ensuremath{-}9}g.$ This corresponds to a gravity-gradient sensitivity of 4E/Hz1/24E/{\mathrm{Hz}}^{1/2}4E/Hz1/2 ${(1E=10}^{\ensuremath{-}9}{\mathrm{s}}^{\mathrm{\ensuremath{-}}2})$ and an accuracy of better than 1E1E1E for a 10-m separation between accelerometers. We demonstrate that the instrument can be used to detect nearby masses in a vibrationally noisy environment and characterize instrument sensitivity to spurious acceleration and rotation noise.
The sensitive axis of an atom gravimeter is defined by the direction of the Raman lasers. Any tilt of the Raman lasers with respect to the vertical direction introduces systematic errors in gravity measurements. In this work, we report a determination of the tilt of Raman lasers, where the fringe of the atom interferometer is scanned by varying the tilt, rather than the phase, of the Raman lasers. Unlike the periodic cosine fringes typically used in atom interferometers, the fringe obtained by changing the tilt, referred to as the tilt-scanned fringe, is aperiodic in tilt and exhibits a shift due to the presence of a nonzero tilt. The tilt-scanned fringe is highly sensitive to the tilt-caused shift, enabling convenient and precise determination of the Raman laser tilt in atom gravimeters. We demonstrate that one tilt-scanned fringe, corresponding to a tilt measurement sampling time of 13 s, can determine the tilt with a typical precision of about $30\phantom{\rule{0.28em}{0ex}}\textmu{}\mathrm{rad}$ in our developed atom gravimeter. The short-term sensitivity and measurement accuracy of the tilt-scanned fringe method were evaluated, demonstrating performance comparable to conventional tilt determination techniques. We expect this method to offer a convenient solution for Raman laser alignment in atom gravimeters and enhance the efficiency of absolute gravity surveys.