Tensor gravity gradiometry with a single-axis atom gradiometer

TL;DR

This work demonstrates that a single-axis atom interferometric gravity gradiometer, when tilted, can recover off-diagonal elements of the gravity-gradient tensor by forming linear combinations of tensor components across multiple tilt angles. The authors analyze fixed-tilt and dynamic-platform implementations, deriving 2D and 3D measurement schemes and quantifying sensitivities, while introducing an optical-gimbal approach to mitigate rotation-induced losses on moving platforms. Key results show that, for representative parameters, the vertical gradient sensitivity $G_{zz}$ can approach that of commercial full-tensor gradiometers, while off-diagonal components remain more challenging but accessible with modest averaging; large-momentum-transfer techniques and advanced pulse optimization offer pathways to significant sensitivity improvements. Overall, the tilted-axis tensor gradiometry method enables compact, adaptable measurements of full gravity gradient tensors, broadening the applicability of atom-interferometric gravimetry to geophysical surveys and inertial navigation, including dynamic platforms.

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.

Figures (4)

• Figure 1: Simplified schematic of an AIGG, comprising two atomic samples, $a$ and $b$, that are separated by vector $\boldsymbol{\ell}$. Both samples participate in simultaneous Mach-Zehnder interferometers with pulse separation time $T$ and effective wavevector $\mathbf{k}_{\rm eff}$. The samples are launched upward to a height $h = \frac{1}{2}gT^2$ with the constraint $\ell + h = L$. The AIGG can also be rotated about the $y$ axis by an angle $\theta$ with respect to the vertical (right).
• Figure 2: 2D AIGG sensitivities when alternating the tilt of the gradiometer between $\pm\theta_{\rm max}$ for different total device lengths $L$ using a numerical model with temperature $\mathcal{T} = 3µK$ and $w = 25mm$. (a) Sensitivities $\delta\mathrm{G}_{zz}$ (solid lines) and $\delta\mathrm{G}_{xz}$ (dashed lines) for $\boldsymbol{\ell}\parallel\mathbf{k}_{\rm eff}$. (b) Sensitivities $\delta\mathrm{G}_{zz}$ (solid lines) and $\delta\mathrm{G}_{xz}$ (dashed lines) for $\boldsymbol{\ell}\perp\mathbf{k}_{\rm eff}$. (c) Sensitivities $\delta\mathrm{G}_{zz}$ and $\delta\mathrm{G}_{xz}$ for the parallel and perpendicular cases when $\theta_{\rm max}$ is chosen to optimize sensitivity to either $\mathrm{G}_{xz}$ (parallel) or $\mathrm{G}_{zz}$ (perpendicular).
• Figure 3: (a) Contours of the mirror's angular velocity and acceleration error which lead to a reduction in fringe contrast by a factor of $2$ (solid lines) and an error in the differential phase of 1 (dashed lines). (b) Contours of the platform's angular velocity and acceleration which lead to a total mirror angle adjustment of 10mrad and/or a required frequency shift of 10GHz for a laser frequency of 384.230THz corresponding to the $^{87}$Rb D2 transition.
• Figure 4: Performance of an AIGG on a dynamic platform with $L = 1m$, $\ell = 0.5m$, $\epsilon_m = 10^{-3}$, $\delta\epsilon^2 = 2\epsilon_m^2$, $w = 25mm$, $\theta_{\textrm{tt,max}} = 10mrad$, and $\delta\Phi = 2mrad$. (a) Optimal interferometer time as a function of angle for $\theta_{\rm max} = 3^\circ$ and $2\pi/\omega = 10s$ when measurements with $\delta\mathrm{G}_{\rm RCA} > \delta\mathrm{G}_{\rm RCA,max}$ are included (solid blue line) and when they are discarded (red dashed line). (b-c) Uncertainties $\delta\mathrm{G}_{zz}$ and $\delta\mathrm{G}_{xz}$ after 10min of measurements for different maximum tilt angles $\theta_{\rm max}$ and angular periods $2\pi/\omega$ with $T_{\rm rep} = 1s$. Solid lines are when measurements with $\delta\mathrm{G}_{\rm RCA} > \delta\mathrm{G}_{\rm RCA,max}$ are included, and dashed lines are when they are discarded.