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EPJ Quantum Technology

An investigation of errors in ellipse-fitting for cold-atom interferometers

Kevin D. Ridley, Anthony Rodgers

Published Nov 22, 2024• 3 citations
Publisher

Abstract

Abstract Ellipse fitting is a technique which is used to extract differential phase in cold-atom interferometers, particularly in situations where common-mode noise needs to be suppressed. We use numerical simulation to investigate errors in the ellipse fitting process; specifically, errors due to the presence of additive noise, linear drift in ellipse offset and amplitude, as well as an error that can arise from fringe normalisation. Errors are found to manifest in two ways: bias in the ellipse phase measurement and incomplete suppression of common mode phase noise. We quantify these errors for three different ellipse fitting algorithms and discuss the applicability of these results to future cold atom sensors.

DOI
10.1140/epjqt/s40507-024-00292-4

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Abstract Ellipse fitting is a technique which is used to extract differential phase in cold-atom interferometers, particularly in situations where common-mode noise needs to be suppressed. We use numerical simulation to investigate errors in the ellipse fitting process; specifically, errors due to the presence of additive noise, linear drift in ellipse offset and amplitude, as well as an error that can arise from fringe normalisation. Errors are found to manifest in two ways: bias in the ellipse phase measurement and incomplete suppression of common mode phase noise. We quantify these errors for three different ellipse fitting algorithms and discuss the applicability of these results to future cold atom sensors.
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.
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.
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.
We apply Bayesian logic to optimally estimate the differential phase in a discrete-time, dual-interferometer measurement. This method is particularly relevant to the case of a gravity gradiometer, where the gravity gradient between cold-atom fountain interferometers can be estimated from the differential phase, despite the presence of large common phase (acceleration) fluctuations. Given an accurate model, the bias-free algorithm we present is optimal and leverages experimental knowledge of the system noise, classical or quantum, to outperform other typical estimators, including ellipse-fitting techniques.
One of the main residual limitations of inertial sensors based on atom interferometry stems from laser beam distortions, which cause parasitic phase shifts and non-homogeneous matter-light couplings. Here we present numerical simulations, accompanied by analytical calculations, which quantify the impact of these effects in a cold atom gradiometer. We demonstrate that the propagation of interferometric laser beam aberrations, combined with initial asymmetry and significant time-of-flight expansion of the the two atomic sources, limit the common-mode rejection of phase noise in a differential configuration. The resulting deviations in gravitational acceleration and its gradient are within reach of current experimental devices. Our study allows us to evaluate the surface quality requirements for retroreflective optics in cold-atom gradiometers of various baselines, and can be extended to other sensors based on different interferometer geometries.
Abstract 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 of N atoms, accounting for common-mode phase noise spanning the full 2 π 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 (SQL). Specifically, we identify optimal squeezed states that minimize the differential phase uncertainty, scaling as N − 2 / 3 , thus overcoming the SQL by a factor N 1 / 6 , while eliminating the 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.