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Physical Review A

Real-time and high-precision optical time-delay estimation via weak measurement with double-edge filter

Zhiqiang Liu, Hongjing Li, Qi Song, Jingzheng Huang, Guihua Zeng

Published Aug 4, 2025• 0 citations
Publisher

Abstract

Optical time delays play a pivotal role in modern physics and practical applications. We propose and experimentally validate a weak measurement system with a double-edge filter, which enables the real-time, high-precision estimation of varying time delays, and the effective suppression of technical noise. In the experiment, the postselected probe light is processed by the double-edge filter, which is formed by a pair of fiber Bragg gratings positioned symmetrically about the center frequency of the probe light, and subsequently detected by photodetectors. The experimental results demonstrate a time-delay precision of 1.66 attoseconds (as) and real-time estimation capability. With a postselection angle of ${10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}$ and the system operating within the most sensitive linear dynamic range, the precision can be further improved to ${10}^{\ensuremath{-}4}$ as. The approach benefits from its high sensitivity and rapid detection, which shows great potential applications in real-time and high-precision time-delay measurements.

DOI
10.1103/6nlm-lj76

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Optical time delays play a pivotal role in modern physics and practical applications. We propose and experimentally validate a weak measurement system with a double-edge filter, which enables the real-time, high-precision estimation of varying time delays, and the effective suppression of technical noise. In the experiment, the postselected probe light is processed by the double-edge filter, which is formed by a pair of fiber Bragg gratings positioned symmetrically about the center frequency of the probe light, and subsequently detected by photodetectors. The experimental results demonstrate a time-delay precision of 1.66 attoseconds (as) and real-time estimation capability. With a postselection angle of 10\ensuremath−3rad{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{rad}10\ensuremath−3rad and the system operating within the most sensitive linear dynamic range, the precision can be further improved to 10\ensuremath−4{10}^{\ensuremath{-}4}10\ensuremath−4 as. The approach benefits from its high sensitivity and rapid detection, which shows great potential applications in real-time and high-precision time-delay measurements.
In fiber-optic sensing, time delays induced by polarization mode dispersion can distort signals in systems relying on phase or intensity variations for measurement, degrading performance, especially in long distance, high-precision applications. To address this challenge, we propose a weak measurement-based scheme using intensity contrast ratio for high-precision, high-sensitivity fiber-optic time delay estimation under large inherent time delays. We demonstrate that a narrower light source bandwidth enhances the effective sensing distance for high-sensitivity measurements. Our results show that, even with large inherent time delays, the measurement precision and sensitivity remain comparable to those of biased weak measurement, enabling detection of time delay variations at the attosecond level, corresponding to a 25.5 Pa water pressure change. The scheme is also robust against fiber misalignment errors, offering a novel solution for long-distance distributed fiber-optic sensing and broadening the applications of weak measurement techniques.
In fiber optic sensing, time delays induced by polarization mode dispersion can distort signals in systems relying on phase or intensity variations for measurement, degrading performance, especially in long distance, high-precision applications. To address this challenge, we propose a weak measurement-based scheme using intensity contrast ratio for high-precision, high-sensitivity fiber optic delay estimation under large inherent time delays. We demonstrate that a narrower light source bandwidth enhances the effective sensing distance for high-sensitivity measurements. Our results show that, even with large inherent time delays, the measurement precision and sensitivity remain comparable to those of biased weak measurement, enabling detection of time delay variations at the attosecond level, corresponding to a 25.5 Pa water pressure change. The scheme is also robust against fiber misalignment errors, offering a novel solution for long-distance distributed fiber-optic sensing and broadening the applications of weak measurement techniques.
We propose a scheme called the weak measurement with two pointers to measure time delays in a large dynamic range with high precision. One pointer with the light frequency and the other pointer with the postselected probability play a complementary role in the dynamic range of the time-delay estimation. By inserting the main systematic errors, we study the antierror capability and the amplification behavior of two types of pointers, where the pointer with the postselected probability shows stronger robustness against systematic errors and larger working range in general. The proof-of-principle experiments together with the Fisher information metric analysis show that high precision can be effectively retained in a large dynamic range of the time-delay estimation. Further implementation strategy of this scheme is also provided, which may promote the precise estimation of other parameters in a large dynamic range.
Abstract Optical phase tracking is an important technique for use in high-precision measurement applications, including optical frequency metrology and ground- or space-based gravitational wave observation, and coherent optical communications. When measuring fast-varying real-time signals, the response time limitations of the measurement system’s phase-locked loop cause the best operating point to be mismatched, and the measurement then becomes nonlinear. To make these measurements possible, this work proposes a time delay loop that theoretically enables optimal homodyne detection. When the time delay loop is combined with an extended Kalman filter, the estimated measurement accuracy is improved by 2.4 dB when tracking a fast-varying random signal with a velocity of 107 rad/s. This phase estimation improvement also increases as the interference angle deviates further from the optimal measurement point. The proposed method shows potential for use in real-time sensing and measurement applications.
In the standard weak measurement, the imaginary part of the weak value is usually constructed with a specific pre- or postselection state to cause a large shift of the frequency-domain pointer. In this paper we demonstrate that the purely real weak value can also shift the frequency-domain pointer when using a broad-spectrum light source. The reason for the deflection of the frequency-domain pointer in this scheme is that the postselection probability of different frequency is different, which causes the rearrangement of the amplitudes of the spectrum. The weak measurement with real weak value can be used for the estimation of time delay, and it is found that it can reach the same high resolution as the standard weak measurement in some sensitive regions.
Abstract High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.