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Optics Express

Dependence of the ellipse fitting noise on the differential phase between interferometers in atom gravity gradiometers

Xiaowei Zhang, Jiaqi Zhong, Wei Lyu, Weihao Xu, Lei Zhu, Muyan Wang, Xi Chen, Biao Tang, Jin Wang, Mingsheng Zhan

Published Dec 1, 2023• 4 citations
Publisher

Abstract

Ellipse fitting is widely used in the extraction of the differential phase between atom interferometers amid substantial common phase noise. This study meticulously examines the dependency of extraction noise on the differential phase between atom interferometers during ellipse fitting. It reveals that the minimum extraction noise can manifest at distinct differential phases, contingent upon the dominance of different noise types. Moreover, the outcomes are influenced by whether the interferometers undergo simultaneous detection or not. Our theoretical simulations find empirical validation in a compact horizontal atom gravity gradiometer. The adjustment of the differential phase significantly enhances measurement sensitivity, culminating in a differential gravity resolution of 1.6 × 10−10 g @ 4800 s.

DOI
10.1364/oe.507695

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Ellipse fitting is widely used in the extraction of the differential phase between atom interferometers amid substantial common phase noise. This study meticulously examines the dependency of extraction noise on the differential phase between atom interferometers during ellipse fitting. It reveals that the minimum extraction noise can manifest at distinct differential phases, contingent upon the dominance of different noise types. Moreover, the outcomes are influenced by whether the interferometers undergo simultaneous detection or not. Our theoretical simulations find empirical validation in a compact horizontal atom gravity gradiometer. The adjustment of the differential phase significantly enhances measurement sensitivity, culminating in a differential gravity resolution of 1.6 × 10−10 g @ 4800 s.
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Atom interferometry-based sensors have demonstrated remarkable precision, making them attractive for diverse applications compared to traditional sensors. However, practical experiments inevitably encounter noise, which limits precision. We investigate the performance of two commonly used methods, ellipse fitting (EF) and fringe fitting (FF), for differential phase estimation in a dual atom interferometer under various noise conditions. We comprehensively analyze the efficacy of these methods for each type of Gaussian noise, including phase noise, amplitude noise, and offset noise. Using a colored noise model, we investigate the Allan deviation results. Our investigations will offer valuable insights for future quantum sensing based on dual interferometers.
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Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states, accounting for common-mode phase noise spanning the full 2π2π2π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit. Specifically, we identify optimal squeezed states that minimize the differential phase variance, scaling as N−2/3N^{-2/3}N−2/3, while eliminating bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér-Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
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We present here a method for the extraction of the differential phase of an atom gradiometer that exploits the correlation of the vibration signal measured by an auxiliary classical sensor, such as a seismometer or an accelerometer. We show that sensitivities close to the quantum projection noise limit can be reached, even when the vibration noise induces phase fluctuations larger than $2\ensuremath{\pi}$. This method does not require the correlation between the atomic and classical signals to be perfect and allows for an exact determination of the differential phase, with no bias. It can also be applied to other configurations of differential interferometers, such as gyrometers, conjugate interferometers for the measurement of the fine-structure constant, or differential accelerometers for tests of the equivalence principle or detection of gravitational waves.