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Journal of the Optical Society of America B

Overcoming residual timing jitter in pump–probe–reference interferometry via weak value amplification and deep learning

Jing-Hui Huang, Hu Xiang-Yun

Published Apr 29, 2026• 1 citation
Publisher

Abstract

We introduce a hybrid methodology that synergistically combines weak value amplification (WVA) and deep learning to suppress the limiting effects of residual timing jitter in pump–probe–reference interferometry, achieved through simulations of pump-induced time delays at a few-attosecond resolution. The WVA protocol, employing real weak values, amplifies the minute delay induced by sample perturbation, thereby translating it into a measurable shift of interference fringes between the probe and the reference. However, this amplification introduces significant fringe distortion. To address this, we deploy deep learning architectures as high-precision parameter estimators: a convolutional neural network regressor (CNN-regressor) for direct delay estimation and a classifier (CNN-classifier) for discrete delay categorization. These are systematically benchmarked against traditional Fourier-transform-based analysis. Two key conclusions are drawn: (i) the WVA technique consistently enhances measurement precision across all estimators by effectively increasing the signal-to-noise ratio (SNR); (ii) both deep learning models surpass the traditional FFT approach: the CNN-regressor achieves a higher SNR at small weak values, while the CNN-classifier enables accurate estimation even under a challenging “ π phase shift” condition where conventional analysis fails.

DOI
10.1364/josab.591436

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We introduce a hybrid methodology that synergistically combines weak value amplification (WVA) and deep learning to suppress the limiting effects of residual timing jitter in pump–probe–reference interferometry, achieved through simulations of pump-induced time delays at a few-attosecond resolution. The WVA protocol, employing real weak values, amplifies the minute delay induced by sample perturbation, thereby translating it into a measurable shift of interference fringes between the probe and the reference. However, this amplification introduces significant fringe distortion. To address this, we deploy deep learning architectures as high-precision parameter estimators: a convolutional neural network regressor (CNN-regressor) for direct delay estimation and a classifier (CNN-classifier) for discrete delay categorization. These are systematically benchmarked against traditional Fourier-transform-based analysis. Two key conclusions are drawn: (i) the WVA technique consistently enhances measurement precision across all estimators by effectively increasing the signal-to-noise ratio (SNR); (ii) both deep learning models surpass the traditional FFT approach: the CNN-regressor achieves a higher SNR at small weak values, while the CNN-classifier enables accurate estimation even under a challenging “ π phase shift” condition where conventional analysis fails.
We introduce a hybrid methodology that synergistically combines weak value amplification (WVA) and deep learning to suppress the limiting effects of residual timing jitter in pump-probe interferometry, achieved through simulations of pump-induced time delays at a few-attosecond resolution. The WVA protocol, employing real weak values, amplifies the minute delay induced by sample perturbation, thereby translating it into a measurable shift of interference fringes. However, this amplification introduces significant fringe distortion. To address this, we deploy deep learning architectures as high-precision parameter estimators: a convolutional neural network regressor (CNN-Regressor) for direct delay estimation and a classifier (CNN-Classifier) for discrete delay categorization. These are systematically benchmarked against traditional Fourier-transform-based analysis. Two key conclusions are drawn: (i) The WVA technique consistently enhances measurement precision across all estimators by effectively increasing the signal-to-noise ratio (SNR). (ii) Both deep learning models surpass the traditional FFT approach; the CNN-Regressor achieves a higher SNR at small weak values, while the CNN-Classifier enables accurate estimation even under a challenging "πππ phase shift" condition where conventional analysis fails. This synergistic combination of WVA and deep learning establishes a powerful framework for attosecond metrology, paving the way for enhanced precision in ultrafast spectroscopy.
We introduce an ultrasensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA+interferometry uses weak value amplification of the relative delay between two paths to enhance interferometric sensitivity. As an example, we demonstrate a proof-of-principle experiment that achieves few-attosecond timing resolution (few nanometer path length resolution) with a double-slit interferometer using only common optical components. Since our example uses only the spatial shift of double-slit interference fringes, its precision is not limited by the timing resolution of the detectors but is instead limited by the fundamental shot noise associated with classical light and the diminished technical noise. We experimentally demonstrate that the signal-to-noise ratio can be improved by one to two orders of magnitude relative to a measurement that does not use WVA. Two key conclusions are drawn: (i) Most conventional interferometric techniques primarily rely on determining the path difference (time delay or longitudinal phase), with their precision constrained by technical noise. Our protocol offers a robust solution for minimizing the technical noise in traditional interferometry, with precision in principle approaching the shot-noise limit. (ii) Although WVA has achieved significant advancements in ultrasensitive longitudinal phase measurement, its applicability is constrained by the need for broad spectral bandwidths and high-resolution spectrometers. Contrary to previous assumptions, we demonstrate that quantum-limited WVA time delay measurements are achievable with narrow band light using real weak values. Thus, the cost-effectiveness and practicality of the proposed WVA+interferometry protocol using narrow band light broaden the scope of WVA applications. This protocol holds potential for broad applications in optical metrology, quantum optics and quantum information, biomedical imaging, and interferometric telescopes for astrophysics.
We report a quantitative evaluation of weak-value amplification (WVA) for longitudinal phase measurements using Allan variance analysis. Building on a recent double-slit interferometry experiment with real weak values [Phys. Rev. Lett. 134, 080802 (2025)], our Allan variance analysis demonstrates measurement of a few attosecond time delay approaching the shot noise limit at short averaging intervals of TTT = 0.01−0.10.01-0.10.01−0.1 s, representing two orders of magnitude variance reduction compared to the T=300T=300T=300 s operating point in prior implementations. We demonstrate that the Allan-variance noise floor scales with the inverse of the detected photon number 1/Nr1/N_r1/Nr​, confirming shot-noise-limited operation with WVA. Furthermore, this 1/Nr1/N_r1/Nr​ scaling experimentally validates that WVA can outperform conventional measurement under fixed detected photon number and detector saturation, in the presence of technical noise, as theoretically predicted [Phys. Rev. Lett. 118, 070802 (2017)]. Our results provide rigorous, quantitative evidence of the near-optimal noise performance achievable with WVA, establishing a new benchmark for precision optical metrology. This advancement is particularly relevant to applications such as gravitational-wave detection, where signals predominantly occupy the high-frequency regime (>10>10>10 Hz).
By choosing more orthogonality between preselection and postselection states, one can significantly improve the sensitivity in general optical quantum metrology based on the weak-value amplification (WVA) approach. However, increasing the orthogonality decreases the probability of detecting photons and makes the weak measurement difficult, especially when the weak measurement is disturbed by strong noise and the pointer is drowned in noise with a negative-decibel signal-to-noise ratio (SNR). In this article we introduce and numerically evaluate a modified weak-measurement protocol with a temporal pointer, namely, the autocorrelative weak-value amplification (AWVA) approach. Specifically, a small longitudinal time delay (tiny phase shift) $\ensuremath{\tau}$ of a Gaussian pulse is measured by implementing two simultaneous autocorrelative weak measurements under Gaussian white noise with different SNRs. The small quantities $\ensuremath{\tau}$ are obtained by measuring the autocorrelation coefficient of the pulses instead of fitting the shift of the mean value of the probe in the standard WVA technique. Simulation results show that the AWVA approach outperforms the standard WVA technique in the time domain with smaller statistical errors, remarkably increasing the precision of weak measurement under a strong noise background.
In sensing technologies, the efforts for increasing sensitivity are usually at the cost of restraining the dynamic range. Here, we propose a closed-loop-control-based weak-value amplification (WVA) method to address this trade-off problem. Different from the previous adaptive WVA schemes, our method can significantly increase the dynamic range without sacrificing sensitivity, and hence improve the sensing dynamic factor by several orders of magnitude, in principle. Moreover, by employing the small weak value in the feedback process, the phase-modulation uncertainty can be effectively suppressed and provide much higher SNR in practice. Additionally, our approach achieves high-sensitivity detection and high-precision closed-loop control on two distinct dimensions within the same weak-measurement system. Our method can find broad applications on sensing technologies that require both high sensitivity and wide dynamic range, such as the sensing of temperature, magnetic fields, pressure, angular velocity, and so on.
In this letter, we propose a precision method for phase estimation based on the weak-value amplification (WVA) technique using a monochromatic light source. The anomalous WVA significantly suppresses the technical noise with respect to the intensity difference signal induced by the phase delay when the post-selection procedure comes into play. The phase measured precision of this method is proportional to the weak-value of a polarization operator in the experimental range. Our results compete well with the wide spectrum light phase weak measurements and outperform the standard homodyne phase detection technique.