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arXiv:2110.11060

Enhancing the sensitivity of amplification of rotation velocity in Sagnac's interferometer with biased weak measurement

Jing-Hui Huang, Xiangyun Hu, Xue-Ying Duan, Guang-Jun Wan

Published Oct 21, 2021• 1 citation
arXivHTMLPDF

Abstract

Recently, biased weak measurement(BWM) has shown higher precision than both conventional measurement and standard weak measurement(SWM) in optical metrology. In this paper, we propose a scheme of detecting rotation velocity in Sagnac's interferometer with BWM. In particular, BWM employs an additional reduction of photons in the post-selection by introducing a pre-coupling, and the remaining photons have been shown to be extremely sensitive to the estimated parameter. In addition, our numerical results show that the scheme with BWM can obtain a higher sensitivity than the scheme with SWM.

DOI
10.48550/arxiv.2110.11060

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Recently, biased weak measurement(BWM) has shown higher precision than both conventional measurement and standard weak measurement(SWM) in optical metrology. In this paper, we propose a scheme of detecting rotation velocity in Sagnac's interferometer with BWM. In particular, BWM employs an additional reduction of photons in the post-selection by introducing a pre-coupling, and the remaining photons have been shown to be extremely sensitive to the estimated parameter. In addition, our numerical results show that the scheme with BWM can obtain a higher sensitivity than the scheme with SWM.
Recently, biased quantum weak measurement has shown higher precision than both conventional measurement and standard quantum weak measurement in optical metrology. In this work, a scheme of detecting the ultrasmall rotation velocity in Sagnac's interferometer with biased quantum weak measurement is proposed. In biased quantum weak measurement, additional progress of pre-coupling is introduced in standard quantum weak measurement to enhance the sensitivity for the estimated parameter, and the cost of the reduction of photons in the post-selection by pre-coupling may not impact the measurement because eliminating the saturation effect of the detector response. In addition, our numerical results show that the scheme with biased quantum weak measurement can obtain a higher sensitivity for rotation velocity measurement than the scheme with standard quantum weak measurement.
In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number n to improve measurement precision. However, practical constraints prevent the arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by the saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains a considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to remarkably mitigate the detector saturation effect with low-cost apparatuses.
We experimentally demonstrate a sub-nanometer optical path difference (OPD) metrology scheme based on biased weak measurement (BWM) with real weak values using a classical coherent light source. By introducing a controlled bias phase in a Mach-Zehnder interferometric configuration, the proposed approach enables enhanced detection of sub-nanometer OPD variations while maintaining compatibility with common optical components and narrowband light sources. We systematically compare the measurement response, sensitivity, and signal-to-noise ratio (SNR) of BWM with those of standard weak measurement (SWM) and conventional interferometric measurement (CM) under identical experimental conditions. Relative to SWM, BWM provides an approximately fourfold enhancement in measurement response within the linear operating range, while achieving a (94 ± 10)-fold signal amplification compared with CM. Furthermore, the measured SNR exhibits an order-of-magnitude improvement over CM under detector-saturation-limited measurement conditions. Experimentally, the BWM scheme achieves a minimum detectable OPD of (5.6 ± 0.36) × 10 −4 nm, obtained from Allan deviation analysis. These results highlight the potential of weak measurement as a practical strategy for high-precision optical path metrology and precision interferometric sensing.
Abstract Quantum metrology has emerged as a crucial paradigm for enhancing measurement sensitivity beyond classical limits. While standard weak measurement and static biased phase methods can effectively amplify extremely small signals, they fundamentally suffer from a trade-off between postselection probability and linear response range, leaving them vulnerable to parameter drift. Motivated by realistic experimental applications such as measuring optical birefringence or thickness using a polarization-frequency Sagnac interferometer, we propose an adaptive biased weak measurement (ABWM) scheme that combines the sensitivity enhancement of biased weak measurement with a feedback-assisted adjustment of the bias phase. By dynamically updating the bias phase in response to measurement outcomes, the system can track slow parameter variations and maintain nearoptimal estimation precision. Numerical simulations under technical noise demonstrate reliable convergence from multiple random initial bias phases and show that the proposed adaptive- β strategy achieves more accurate dynamic tracking than standard weak measurement and static biased weak measurement. Our results suggest that ABWM provides a flexible and resource-efficient strategy for high-precision quantum metrology in realistic experimental scenarios.
In optical metrological protocols to measure physical quantities, it is, in principle, always beneficial to increase photon number to improve measurement precision. However, practical constraints prevent arbitrary increase of n due to the imperfections of a practical detector, especially when the detector response is dominated by saturation effect. In this work, we show that a modified weak measurement protocol, namely, biased weak measurement significantly improves the precision of optical metrology in the presence of saturation effect. This method detects an ultra-small fraction of photons while maintains considerable amount of metrological information. The biased pre-coupling leads to an additional reduction of photons in the post-selection and generates an extinction point in the spectrum distribution, which is extremely sensitive to the estimated parameter and difficult to be saturated. Therefore, the Fisher information can be persistently enhanced by increasing the photon number. In our magnetic-sensing experiment, biased weak measurement achieves precision approximately one order of magnitude better than those of previously used methods. The proposed method can be applied in various optical measurement schemes to circumvent detector saturation effect with low-cost apparatuses.