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arXiv:2208.10755 · Applied Optics

Robustness of optic-fiber-based weak-value amplification against amplitude-type noise

Han Wang, Jingzheng Huang, Chaozheng Huang, Hongjing Li, Guihua Zeng

Published Jul 29, 2022• 4 citations
arXivHTMLPDF

Abstract

Experiments based on a free-space platform have demonstrated that the weak-value amplification (WVA) technique can provide high sensitivity and precision for optical sensing and metrology. To promote this technique for real-world applications, it is more suitable to implement WVA based on an optical-fiber platform due to the lower cost, smaller scale, and higher stability. In contrast to the free-space platform, the birefringence in optical fiber is strong enough to cause polarization cross talk, and the amplitude-type noise must be taken into account. By theoretical analysis and experimental demonstration, we show that the optic-fiber-based WVA is robust in the presence of amplitude-type noise. In our experiment, even the angular misalignment on optical axes at the interface reaches 0.08 rad, and the sensitivity loss can be maintained at less than 3 dB. Moreover, the main results are valid to a simplified detection scheme that was recently proposed that is more compatible with the future design of optical-fiber-based WVA. Our results indicate the feasibility of implementing WVA based on optical fiber, which provides a possible way for designing optical sensors with higher sensitivity and stability in the future.

DOI
10.1364/ao.467660

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Experiments based on a free-space platform have demonstrated that the weak-value amplification (WVA) technique can provide high sensitivity and precision for optical sensing and metrology. To promote this technique for real-world applications, it is more suitable to implement WVA based on an optical-fiber platform due to the lower cost, smaller scale, and higher stability. In contrast to the free-space platform, the birefringence in optical fiber is strong enough to cause polarization cross talk, and the amplitude-type noise must be taken into account. By theoretical analysis and experimental demonstration, we show that the optic-fiber-based WVA is robust in the presence of amplitude-type noise. In our experiment, even the angular misalignment on optical axes at the interface reaches 0.08 rad, and the sensitivity loss can be maintained at less than 3 dB. Moreover, the main results are valid to a simplified detection scheme that was recently proposed that is more compatible with the future design of optical-fiber-based WVA. Our results indicate the feasibility of implementing WVA based on optical fiber, which provides a possible way for designing optical sensors with higher sensitivity and stability in the future.
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).
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 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 study the amplification of a weak magnetic field with the weak-value amplification (WVA) technique based on the Faraday magneto-optic effect. By using a different scheme to perform the Mach–Zehnder interferometer with the probe in momentum space, we have demonstrated a new, to the best of our knowledge, weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of the Faraday magneto-optic effect. Our numerical results show that our scheme with the WVA technique has a higher signal-to-noise ratio than the traditional optical fiber scheme with the open-loop modulation technique. Besides, considering the instrument limitations of our scheme, we have demonstrated the magnetic field resolution at the 10 − 13 T level.
Weak value amplification (WVA) has emerged as a powerful technique that enhances measurement precision. However, traditional table-top WVA setups and on-chip demonstrations have not achieved an amplification over 20 dB. The practical limit of the amplification is the fidelity of photon post-selection. To address this limit, we design a weak value device with an over 30 dB interferometer extinction ratio, where the stray light in the dark port is minimized with thermally tunable phase shifters. As a result, the device successfully shows 30 dB WVA, termed ultra-high WVA. This WVA optimization strategy by improving interferometer extinction is extensible to a wide range of WVA-based detections, paving the way for their broader application in practical precision measurements.
In this paper, we propose a scheme for angular rotation Ω measurement in an optic-fiber-based Sagnac interferometer based on cascaded weak-value amplification (CWVA). CWVA is a modified standard weak-value amplification (SWVA) technique for further enhancing temporal shifts based on the principle of the Vernier effect. By choosing the appropriate CWVA parameters and the repetition time intervals of the Vernier scale, the temporal shifts in SWVA can be further amplified by measuring the envelope shifts in CWVA. Our comprehensive simulations demonstrate that CWVA enables the detection of minuscule rotations in the range of 1.0×10 −9 rad/s≤Ω≤10×10 −9 rad/s, with significantly improved sensitivity and superior signal-to-noise ratios compared to SWVA. The enhancement with a larger detection band may have great influence on physics and related sciences, such as rotational seismology and gravitational sensing.