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Physical Review Applied

High-sensitivity and wide-dynamic-range parameter estimation via weak-value amplification

Zhongyuan Luo, Jingzheng Huang, Qi Song, Binke Xia, Hongjing Li, Guihua Zeng

Published Dec 18, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physrevapplied.22.064070

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Applied Physics Letters•Mar 18, 2024•5 citations
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.
Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In this paper, we propose an adaptive WVA scheme to achieve the highest Fisher information when using an unbalanced pointer. Different from previous schemes, the adaptive WVA scheme is associated with a real-time update on the postselection states with the help of feedback information from the outcomes, and the ``extremely small'' condition set on the parameter of interest is relaxed. By applying this scheme to a time-delay measurement scenario, we show by numerical simulation that the precision achieved in our scheme is several times higher than the standard WVA scheme. Our result might open a path for improving the WVA technique in a more flexible and robust way.
Achieving higher sensitivity is an earnest purpose for precision metrology. As a response to this goal, the weak-value amplification approach has been developed for measuring ultrasmall physical effects, realizing sensitivity that had never been reached before. Encouraged by the successes, many efforts have been devoted to obtain ultimate sensitivity of weak-value amplification. However, the benefit would be easily compromised in practice, because the cost of significant reduction on signal intensity leads to an ultralow signal-to-noise ratio. In this work, we bridge this gap by proposing an alternative weak-value amplification approach, which provides sensitivity several orders of magnitude higher than the standard approach while being compatible with practical imperfections. In the proof-of-principle experiment of measuring longitudinal phase change in time domain, sensitivity up to $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ attosecond is exemplified. Our approach can be applied to measure other small parameters with extremely high sensitivity, providing a method for future precision metrology.
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.
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.
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.