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arXiv:1812.09199 · Physical Review A

Simultaneous accurate determination of both gravity and its vertical gradient

Romain Caldani, Kanxing Weng, Sébastien Merlet, Franck Pereira dos Santos

Published Mar 1, 2019• 43 citations
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Abstract

We present a method for accurate measurements of both the gravity acceleration and its vertical gradient using a dual-atom interferometer, in principle, free from any uncertainty related to the absolute or relative positions of the two atomic samples. The method relies on the use of a dual-lock technique, which simultaneously stirs the chirp rate applied to the frequency difference between the interferometer lasers to compensate the gravity acceleration and the frequency jump applied to the lasers at the mid pulse of the interferometer to compensate for the gravity gradient. This allows one, in the end, to determine the two inertial quantities of interest in terms of frequencies.

DOI
10.1103/physreva.99.033601

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Gravity gradients represent a major obstacle in high-precision measurements by atom interferometry. Controlling their effects to the required stability and accuracy imposes very stringent requirements on the relative positioning of freely falling atomic clouds, as in the case of precise tests of Einstein's equivalence principle. We demonstrate a new method to exactly compensate the effects introduced by gravity gradients in a Raman-pulse atom interferometer. By shifting the frequency of the Raman lasers during the central π pulse, it is possible to cancel the initial position- and velocity-dependent phase shift produced by gravity gradients. We apply this technique to simultaneous interferometers positioned along the vertical direction and demonstrate a new method for measuring local gravity gradients that does not require precise knowledge of the relative position between the atomic clouds. Based on this method, we also propose an improved scheme to determine the Newtonian gravitational constant G towards the 10 ppm relative uncertainty.
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.
As the existence of the gravity gradient, the output of gravimeters is actually the gravitational acceleration at the reference instrumental height. Precise knowledge of the reference height is indispensable in the utilization of gravity measurements, especially for absolute gravimeters. Here, we present an interferometric method to measure the distance between the atomic cloud and a reflecting mirror directly, which consequently determines the reference height of our atom gravimeter. This interferometric method is based on a frequency jump of Raman lasers applied at the π pulse of the atom interferometer, which induces an additional phase shift proportional to the interested distance. An uncertainty of 2 mm is achieved here for the distance measurement, and the effect of the gravity gradient on absolute gravity measurements can thus be constrained within 1 μGal. This work provides a concrete-object-based measurement of the reference height for atom gravimeters.
This paper derives the phase difference produced by an atom interferometer, building from the phase of a matter wave and the momentum and phase that each laser pulse transfers to an atom in a sequence. It derives this phase difference first for a constant acceleration, where it takes the form k_eff·a·τ². It then uses this form to derive the phase difference from rotation and a gravity gradient. It also derives the proportion of atoms in one output state, the quantity the atom interferometer measures, and its relation to the phase difference.
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. Here we demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. Using this method, we suppress the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by 2 orders of magnitude and precisely measure these differences. We realize a relative precision of Δg/g≈6×10^{-11} per shot, which improves on the best previous result for a dual-species atom interferometer by more than 3 orders of magnitude. By reducing gravity gradient systematic errors to one part in 10^{13}, these results pave the way for an atomic test of the equivalence principle at an accuracy comparable with state-of-the-art classical tests.