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Applied Optics

Optimization of a quantum weak measurement system with digital filtering technology

Yang Xu, Lixuan Shi, Tian Guan, Dongmei Li, Yuxuan Yang, Xiangnan Wang, Zhangyan Li, Luyuan Xie, Xuesi Zhou, Yonghong He, Wenyue Xie

Published Sep 16, 2018• 15 citations
Publisher

Abstract

In this paper, we propose a post-Gaussian filtering theory for weak measurement in the frequency domain, and propose a highly deformed digital filtering technique that can be used to optimize sensors based on weak-frequency measurement techniques. We completed the experimental verification based on the weak measurement total internal reflection sensor. The experimental results show that digital filtering technology can optimize the system in the working range, sensitivity, and resolution of the frequency domain weak measurement system, so that it can reach 0.210 rad, 3210.9 nm/RIU, and 7.12×10−7 RIU, respectively.

DOI
10.1364/ao.57.007956

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In this paper, we propose a post-Gaussian filtering theory for weak measurement in the frequency domain, and propose a highly deformed digital filtering technique that can be used to optimize sensors based on weak-frequency measurement techniques. We completed the experimental verification based on the weak measurement total internal reflection sensor. The experimental results show that digital filtering technology can optimize the system in the working range, sensitivity, and resolution of the frequency domain weak measurement system, so that it can reach 0.210 rad, 3210.9 nm/RIU, and 7.12×10−7 RIU, respectively.
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 the field of sensing technology, there is a trade-off between sensitivity and dynamic range. This paper proposes a high-precision weak measurement sensing method with flexible sensitivity adjustment to achieve matching between sensitivity and dynamic range. We demonstrate that precise control over sensitivity can be achieved by adjusting the bandwidth and coupling strength of the probe in frequency domain. In the experiment, the sensitivity ranges from 104 to 105RIU−1, and the precision ranges from 10−7 to 10−8 RIU. Additionally, the decomposition of hydrogen peroxide was precisely measured. Our measurement scheme can facilitate broader application of weak measurement technology in precision sensing.
Abstract High-precision temperature measurement with adjustable operating range is investigated and experimentally demonstrated based on weak measurement in the frequency domain. The operating range of measurement is precisely modulated by introducing a dynamic extra time delay to the post-selection pumped by a femtosecond laser. By choosing appropriate nonlinear materials and the attenuation, the resolution of the optimized extra time delay can be improved by two orders of magnitude over that of a traditional phase delay compensator. Considering the influence of noise in the experiment, the highest precision of 8.03 × 10 −7 °C can be achieved by using a currently available spectrometer. Moreover, the average sensitivity can reach to 38 nm/°C. Taking advantage of the high precision and adjustable operating range, the proposed method has great potential applications in high-precision temperature measurements.
Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using nonclassical states and quantum filters, which modify both the noise and signal response. We find an approach to realizing quantum filters directly from their frequency-domain transfer functions, utilizing techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show an optical realization of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.
In the standard weak measurement, the imaginary part of the weak value is usually constructed with a specific pre- or postselection state to cause a large shift of the frequency-domain pointer. In this paper we demonstrate that the purely real weak value can also shift the frequency-domain pointer when using a broad-spectrum light source. The reason for the deflection of the frequency-domain pointer in this scheme is that the postselection probability of different frequency is different, which causes the rearrangement of the amplitudes of the spectrum. The weak measurement with real weak value can be used for the estimation of time delay, and it is found that it can reach the same high resolution as the standard weak measurement in some sensitive regions.
In this study, we investigate whether the weak measurement can enhance the estimation precision, when coupling between system and measurement apparatus is extremely weak. Our result shows that the weak measurement could enhance the estimation precision, when the noise is introduced during interaction process. By calculating and comparing the Fisher information under weak measurement and traditional quantum measurement scheme, we quantify the precision-improvement by the weak measurement and find the optimal post-selection protocol. Furthermore, we argue that there exists a threshold for the noise strength that the quantum weak measurement renders a higher precision compared to the traditional measurement.