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Light Science & Applications

Improving the precision of optical metrology by detecting fewer photons with biased weak measurement

Peng Yin, Wen-Hao Zhang, Liang Xu, Ze-Gang Liu, Wei-Feng Zhuang, Lei Chen, Ming Gong, Yu Ma, Xing-Xiang Peng, Gongchu Li, Jin‐Shi Xu, Zong‐Quan Zhou, Lijian Zhang, Geng Chen, Chuan‐Feng Li, Guang‐Can Guo

Published May 17, 2021• 43 citations
Publisher

Abstract

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.

DOI
10.1038/s41377-021-00543-4

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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.
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.
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.
Weak measurements have been under intensive investigation in both experiment and theory. Numerous experiments have indicated that the amplified meter shift is produced by the post-selection, yielding an improved precision compared to conventional methods. However, this amplification effect comes at the cost of a reduced rate of acquiring data, which leads to an increasing uncertainty to determine the level of meter shift. From this point of view, a number of theoretical works have suggested that weak measurements cannot improve the precision, or even damage the metrology information due to the post-selection. In this review, we give a comprehensive analysis of the weak measurements to justify their positive effect on prompting measurement precision. As a further step, we introduce two modified weak measurement protocols to boost the precision beyond the standard quantum limit. Compared to previous works beating the standard quantum limit, these protocols are free of using entangled or squeezed states. The achieved precision outperforms that of the conventional method by two orders of magnitude and attains a practical Heisenberg scaling up to n=106 photons.
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.
A modified weak measurement scheme, rotatory biased weak measurement, is proposed to significantly improve the sensitivity and resolution of the refractive index sensor on a total reflection structure. This method introduces an additional phase in the post-selected procedure and generates an extinction point in the spectrum distribution. The biased post-selection makes smaller coupling strength available, which leads to an enhancement of phase sensitivity and refractive index sensitivity. In rotatory biased weak measurement, we achieve an enhanced refractive index sensitivity of 13605 nm/RIU compared to 1644 nm/RIU in standard weak measurement. The performance of sensors with different sensitivity is analyzed, and we find the optimal refractive index resolution of sensors increases with sensitivity. In this work, we demonstrate an optimal refractive index resolution of 4×10−74\times10^{-7}4×10−7 RIU on a total reflection structure. The rabbit anti-mouse IgG and mouse IgG binding reaction experiments demonstrate that our system has a high response to the concentration of IgG in a wide range and the limit of detection is 15 ng/mL. The improvements in this work are helpful to the optimizations of other optical sensors with weak measurement.
In quantum metrology researching, weak measurement has been widely applied in many aspects, providing weak-value amplification and noise suppressing ability. Recently, several modified schemes of weak measurement have been proposed, such as inverse, almost-balanced, and biased weak measurement. In this study, we enhance a spin-exchange relaxation-free (SERF) magnetometer using the biased weak measurement metrology technique. We establish and simulate a biased weak measurement (BWM)-enhanced SERF magnetometer model. By adjusting the pre-coupling process and analysing the Fisher information, higher sensitivity to magnetic fields is verified in this study. 0.003 fT can be achieved through adjusting pre-coupling process and extinction ratio, which is higher than the best sensitivity of SERF magnetometer in existence. Our work paves the way for embedding weak measurement techniques into atomic magnetometer sensors and greatly improving their sensitivity.