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arXiv:2404.00531 · Physical Review Letters

Enhancing Interferometry Using Weak Value Amplification with Real Weak Values

Jing-Hui Huang, Kyle M. Jordan, Adetunmise C. Dada, Xiangyun Hu, Jeff S. Lundeen

Published Feb 27, 2025• 11 citations
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Abstract

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.

DOI
10.1103/physrevlett.134.080802

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Journal of the Optical Society of America B•Apr 29, 2026•1 citation
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).
We experimentally demonstrate an ultra-sensitive technique for measuring sub-nanometer optical path differences (OPDs) using the biased weak measurement (BWM) protocol. By employing real weak values with a classical coherent light source and introducing a bias phase procedure, this method directly amplifies small OPDs in interferometry, achieving significantly enhanced amplification compared to conventional measurement (CM) and standard weak measurement (SWM). In a proof-of-principle experiment of sub-nanometer OPD measurement, BWM achieves nearly 4× signal improvement within the linear response range relative to SWM, and an 85× improvement over CM. The signal-to-noise ratio of BWM and SWM exhibits an order-of-magnitude enhancement on average compared to CM. Furthermore, we experimentally determine a minimum OPD resolution of 3.1×10-4nm, corresponding to a time delay of 1 ×10-3attoseconds and a phase shift of 3.0× 10-6rad. These results highlight the potential of weak measurement protocols for high-precision longitudinal phase estimation using narrow-band sources and common optical components.
We experimentally demonstrate an ultra-sensitive technique for measuring sub-nanometer optical path differences (OPDs) using the biased weak measurement (BWM) protocol. By employing real weak values with a classical coherent light source and introducing a bias phase procedure, this method directly amplifies small OPDs in interferometry, achieving significantly enhanced amplification compared to conventional measurement (CM) and standard weak measurement (SWM). In a proof-of-principle experiment of sub-nanometer OPD measurement, BWM achieves nearly 4× signal improvement within the linear response range relative to SWM, and an 85× improvement over CM. The signal-to-noise ratio of BWM and SWM exhibits an order-of-magnitude enhancement on average compared to CM. Furthermore, we experimentally determine a minimum OPD resolution of 3.1×10-4nm, corresponding to a time delay of 1 ×10-3attoseconds and a phase shift of 3.0× 10-6rad. These results highlight the potential of weak measurement protocols for high-precision longitudinal phase estimation using narrow-band sources and common optical components.
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.
Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.
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.