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Quantum Science and Technology

Optimized squeezing for accurate differential sensing under large phase noise

Robin Corgier, Marco Malitesta, Leonid A. Sidorenkov, Franck Pereira dos Santos, G. Rosi, Guglielmo Maria Tino, Augusto Smerzi, Leonardo Salvi, Luca Pezzè

Published Jul 22, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.1088/2058-9565/adf2d8

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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.
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.
Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here we show that differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Our protocol uses a single spin-squeezed state that is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.
Thanks to common-mode noise rejection, differential configurations are crucial for realistic applications of phase and frequency estimation with atom interferometers. Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here we show that differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Our protocol uses a single spin-squeezed state that is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.
Spin-squeezed states constitute a valuable entanglement resource capable of surpassing the standard quantum limit (SQL). However, spin-squeezed states only enable sub-SQL uncertainty within a narrow parametric window near some specific points. Identifying optimal measurement protocols for spin-squeezed states remains an outstanding challenge. Here we present an adaptive Bayesian quantum estimation protocol that achieves optimal measurement precision with spin-squeezed states under noises. Our protocol operates by maintaining measurements near the optimal point and employing Bayesian inference to sequentially perform phase estimation, enabling robust high-precision measurement. To account for realistic experimental conditions, we explicitly incorporate phase noises into the Bayesian likelihood function for more accurate estimation. Our protocol can be applied to various scenarios, such as quantum gravimeters and atomic clocks, achieving precision enhancement over conventional fitting methods under noises. Our approach offers superior precision and enhanced robustness against noises, making it highly promising for squeezing-enhanced quantum sensing.
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.
Field sensing with state-of-the-art atom interferometers is restricted to the use of uncorrelated devices op- erating in parallel. We can overcome this limitation by using distributed sensing protocols where quantum correlations among spatially-separated devices are engineered in the spatial mode carrying the signal. We show that a tweezer array in a cavity offers an ideal testbed to engineer quantum states for distributed sensing, with the possibility to generate entanglement both within and between the clouds. The competition between local and intercloud cavity-mediated exchange allows the sign and spatial pattern of the intercloud couplings to select the squeezed mode. For two ensembles, positive coupling produces uniform collective squeezing, whereas negative coupling generates strong staggered, nonlocal squeezing. A semiclassical analysis reveals a counter-twisting- like phase-space flow, qualitatively distinct from standard one-axis twisting. The analysis and results can be further generalized to a larger number of ensembles. We apply the scheme to differential Ramsey interferometry with common phase noise spanning the full 2 πrange, the resulting staggered states reduce the phase uncertainty below the standard quantum limit, with an ellipse estimator approaching the Cramèr-Rao bound. These results establish programmable cavity interactions as a scalable route to entanglement tailored to distributed signals.