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arXiv:1803.08637 · Physical Review A

Weak-value-amplification metrology without spectral analysis

Jingzheng Huang, Chen Fang, Guihua Zeng

Published Jun 26, 2018• 15 citations
arXivHTMLPDF

Abstract

We propose a scheme called difference weak measurement, and we illustrate its advantages for measuring a small longitude phase shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has a much higher resolution in the presence of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing a complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose a closed-loop scenario to solve the narrow dynamic range problem that exists in the current weak measurement schemes. The difference weak measurement scheme simultaneously fulfills the requirements of high precision, wide dynamic range, and strong robustness, which makes it a powerfully practical tool for phase-shift measurement and other metrological tasks.

DOI
10.1103/physreva.97.063853

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We propose a scheme called difference weak measurement, and we illustrate its advantages for measuring a small longitude phase shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has a much higher resolution in the presence of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing a complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose a closed-loop scenario to solve the narrow dynamic range problem that exists in the current weak measurement schemes. The difference weak measurement scheme simultaneously fulfills the requirements of high precision, wide dynamic range, and strong robustness, which makes it a powerfully practical tool for phase-shift measurement and other metrological tasks.
Weak measurement enables the amplification of weak physical effects via post-selection and has become an important tool in precision optical metrology; however, conventional schemes based on mean-pointer shifts suffer from response saturation, limited linear range, and stringent stability requirements. Here, we propose and experimentally demonstrate a weak-measurement scheme based on spectral-interference trough shifts, where the zero-intensity points of the post-selected spectrum act as the measurement pointer, establishing an analytical mapping between the trough displacement and the target phase or time delay. Theoretical analysis shows that, under detector resolution limits, the measurement resolution depends solely on the frequency of extinction point and is independent of weak-value singular amplification or bias-phase modulation, thereby maintaining high sensitivity while avoiding pointer saturation. Experiments demonstrate that the trough-shift scheme achieves significantly better agreement between measured and theoretical sensitivities than biased weak measurement and provides a stable linear response without additional bias-compensation structures, reaching a minimum resolvable phase variation at the 10−7 level. Moreover, the approach intrinsically supports multi-period traceable measurements and exhibits strong robustness against intensity fluctuations and spectral distortions, offering a promising route toward high-sensitivity, large-dynamic-range, and stable weak measurement-based optical sensing.
Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here, we propose and experimentally demonstrate a weak measurement scheme to considerably suppress the phase uncertainties by the direct amplification of the phase shift in optical interferometry. Given an initial ultrasmall phase shift between orthogonal polarization states, we observe a phase amplification effect with a factor of 388. Our weak measurement scheme provides a practical approach to significantly improve the interferometric phase resolution, which is favorable for precision measurement applications.
Optical interferometry has been widely used in various high-precision applications. Usually, the minimum precision of an interferometry is limited by various technical noises in practice. To suppress such kinds of noises, we propose a scheme which combines the weak measurement with the standard interferometry. The proposed scheme dramatically outperforms the standard interferometry in the signal-to-noise ratio and the robustness against noises caused by the optical elements' reflections and the offset fluctuation between two paths. A proof-of-principle experiment is demonstrated to validate the amplification theory.
High-precision surface-roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and can only achieve a precision of 0.1 nm with a white-light interferometer. Here, we propose two weak-measurement schemes to estimate surface roughness through a spectrum analysis and intensity analysis. The estimating precision with the spectrum analysis is about ${10}^{\ensuremath{-}5}$ nm by using a currently available spectrometer with a resolution of $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}=0.04$ pm and the corresponding sensitivity is better than 0.1 THz/nm. The precision and sensitivity of the light intensity analysis scheme achieved is as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of a surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and a wide measurement range, making it a promising practical tool.
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative precision of the measurement. Thus, they do not set a limit on the smallest measurable phase shift, contrary to standard interferometry and weak-value-based measurement techniques. Our idea is not restricted to phase-shift measurements and could be used to measure other small effects using a similar protocol.
Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.