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Optics Express

Neural network enhanced time-varying parameter estimation via weak measurement

Yue-Gang Li, Qi Song, Tailong Xiao, Hongjing Li, Jianping Fan B, Guihua Zeng

Published Jul 3, 2024• 3 citations
Publisher

Abstract

Weak measurement is employed to measure faint signals due to its capability to amplify detection results above technical noise. However, achieving high amplification effects requires accurate adjustment to the experimental system. Estimating unknown time-varying phases, accurately estimating phases, and sensitively perceiving phase changes pose challenges, demanding the system to continuously remain at the appropriate working range. To address this issue, we propose a neural network-based adaptive weak measurement scheme via single-channel light intensity detection. Through machine learning calibrating the experimental system, the reference phase can be dynamically and accurately adjusted, accommodating time-varying phase changes and ensuring the system operates optimally. Compared with traditional dual-channel weak measurement systems, the scheme reduces experimental complexity. Meanwhile, by accurately adjusting the reference phase, the scheme has higher sensitivity and estimation precision compared to the non-modulated scheme. We validate the effectiveness of the scheme in estimating the period and stochastic time-varying phase. The proposed method highlights the advancement of machine learning in weak measurement systems and can also be applied to other quantum-enhanced measurement schemes.

DOI
10.1364/oe.529480

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Weak measurement is employed to measure faint signals due to its capability to amplify detection results above technical noise. However, achieving high amplification effects requires accurate adjustment to the experimental system. Estimating unknown time-varying phases, accurately estimating phases, and sensitively perceiving phase changes pose challenges, demanding the system to continuously remain at the appropriate working range. To address this issue, we propose a neural network-based adaptive weak measurement scheme via single-channel light intensity detection. Through machine learning calibrating the experimental system, the reference phase can be dynamically and accurately adjusted, accommodating time-varying phase changes and ensuring the system operates optimally. Compared with traditional dual-channel weak measurement systems, the scheme reduces experimental complexity. Meanwhile, by accurately adjusting the reference phase, the scheme has higher sensitivity and estimation precision compared to the non-modulated scheme. We validate the effectiveness of the scheme in estimating the period and stochastic time-varying phase. The proposed method highlights the advancement of machine learning in weak measurement systems and can also be applied to other quantum-enhanced measurement schemes.
Extending quantum sensing to time-varying parameter estimation is a potential and challenging task in practical application. To achieve this goal, we propose an adaptive method to estimate an unknown time-varying parameter through light-intensity split detection and the insertion of reference phases in the weak measurement. Theoretical analysis and numerical simulation are applied to illustrate the feasibility and practical applications of our method. The results demonstrate that the method has adjustable sensitivity and linear dynamic range, and is robust to nonideal measurement conditions. Moreover, we analyze the precision of our method and show that its precision limit can surpass the standard quantum limit and approach the Heisenberg scaling when using a squeezed light of optimal Gaussian state.
The real-time estimation of a time-varying phase is of great importance in several fields. In order to estimate a time-varying phase with high precision and sensitivity, we propose and experimentally demonstrate an adaptive phase estimation method via weak value amplification by splitting the light into sensing path and monitoring path. In the proposed method, the phase shift can be amplified, an adjustable sensitivity and linear dynamic range can be obtained through the insertion of the reference phase, and a full-range phase estimation could be realized via an appropriate adjustment strategy. Furthermore, detectors with a higher resolution could be selected to detect weak signal by the adjustment of attenuation. Potentially, the phase estimation precision of about 10−8 rad could be achieved with the available equipment.
An adaptive correction algorithm is demonstrated based on weak measurement, which introduces a feedback and an additional interaction to the system and can dynamically adjust the operating point in accordance with the condition of the estimated phase change. Two schemes, fast adaptive correction and slow adaptive correction, are proposed for different conditions of the modulation device. Fast adaptive correction scheme can realize a real-time correction and maintain the high sensitivity. Slow adaptive correction scheme, as a supplement, can correct the distortion of the measured parameter by changing the measuring period. These two schemes are useful for high precision phase estimation with time in modern physics and practical applications, including, but not limited to, timing synchronization, accurate distance measurement, and gravity wave detection. Moreover, we discuss the deviation of the adaptive correction for considering system noise in practical measurement.
Abstract Quantum metrology has emerged as a crucial paradigm for enhancing measurement sensitivity beyond classical limits. While standard weak measurement and static biased phase methods can effectively amplify extremely small signals, they fundamentally suffer from a trade-off between postselection probability and linear response range, leaving them vulnerable to parameter drift. Motivated by realistic experimental applications such as measuring optical birefringence or thickness using a polarization-frequency Sagnac interferometer, we propose an adaptive biased weak measurement (ABWM) scheme that combines the sensitivity enhancement of biased weak measurement with a feedback-assisted adjustment of the bias phase. By dynamically updating the bias phase in response to measurement outcomes, the system can track slow parameter variations and maintain nearoptimal estimation precision. Numerical simulations under technical noise demonstrate reliable convergence from multiple random initial bias phases and show that the proposed adaptive- β strategy achieves more accurate dynamic tracking than standard weak measurement and static biased weak measurement. Our results suggest that ABWM provides a flexible and resource-efficient strategy for high-precision quantum metrology in realistic experimental scenarios.
Abstract Weak measurement technique can provide high sensitivity for parameter estimation tasks. However in practice, time-varying errors induced by noises significantly compromise its advantages. While prolonging the measurement time can reduce the effect of short-term correlated noises (e.g. white noise), it will on the other hand increase the estimation errors in the presence of long-term correlated noises(e.g. 1/ f and 1/ f 2 noises). The main obstacle of compensating these kind of errors is to precisely predict the time-varying trend of error, where the disturbances that causing error are highly unpredictable. In this work, we propose a weak measurement scheme with assistance of machine learning algorithm, which can ‘learn’ the time-varying trend of errors from data without an explicit model. In order to verify the feasibility of this scheme, we carry out a time-delay measurement experiment and achieve the noise compensation via machine learning algorithm. Experimental results demonstrate a 6 dB reduction of mean-square error comparing to the setup without machine learning, which suggest that our scheme can effectively improve the performance of weak measurement in the presence of long-time correlated noises.
Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.