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Journal of Physics B Atomic Molecular and Optical Physics

Effects of nonlinearity and technical noise on weak-value amplified phase measurement

Hao Wu, Zhengchun Luo, Li-Ping Xu, Peng Wu, Haofei Shi, Tianying Chang, Chunlei Du, Yang Liu, Yueguang Lü, Hong‐Liang Cui

Published Mar 20, 2020• 3 citations
Publisher

Abstract

Abstract An exact nonlinear model for pointer shift estimation in phase measurement with weak-value amplification is presented, and the necessary assumptions for the linear approximations are discussed. A realistic experimental weak measurement system with pure imaginary weak-value is demonstrated to verify the nonlinear model, and it is shown that our model is effective over a wide dynamic range. In addition, the influence of several common-type technical noise on the uncertainty of pointer shift estimation in momentum space is analyzed theoretically and verified experimentally, in connection with the relationship between the working condition and the signal-to-noise ratio of the system. This close examination of the impact and ramifications of nonlinearity and technical noise in a realistic experimental phase measurement setting employing weak value amplification provides helpful guidance for its invocation in optical interferometric sensor design.

DOI
10.1088/1361-6455/ab81e8

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Abstract An exact nonlinear model for pointer shift estimation in phase measurement with weak-value amplification is presented, and the necessary assumptions for the linear approximations are discussed. A realistic experimental weak measurement system with pure imaginary weak-value is demonstrated to verify the nonlinear model, and it is shown that our model is effective over a wide dynamic range. In addition, the influence of several common-type technical noise on the uncertainty of pointer shift estimation in momentum space is analyzed theoretically and verified experimentally, in connection with the relationship between the working condition and the signal-to-noise ratio of the system. This close examination of the impact and ramifications of nonlinearity and technical noise in a realistic experimental phase measurement setting employing weak value amplification provides helpful guidance for its invocation in optical interferometric sensor design.
We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields the difference in estimating the noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss the signal-to-noise ratio and its optimization in the presence of the shot noise.
An effective approach for general measurement based on weak value amplification using non-Gaussian broadband light sources is demonstrated. This scheme can reduce the difficulty of preparing the measurement apparatus and correcting the systematic error caused by the imperfection of device's wave function, thus making the weak-value amplification scheme more convenient and robust for practical field applications. The influence of several common noise sources in a general application based on weak value amplification is analyzed theoretically and examined experimentally. A purely imaginary weak-value phase measurement system is considered for the noise model verification experimentally. In this we show how to optimize the precision of measurement in a unique solution that takes into account the interplay between precision and uncertainty, and explicate the ramifications of such a compromising and pragmatic approach.
In this paper, we theoretically and experimentally present a precision method to simultaneously estimate the phase and amplitude variations of light based on the weak-value amplification. We demonstrate that the imaginary and real components of the weak-value correspond to the amplification of the phase and amplitude variations, respectively. If both the phase and the amplitude are varied, the phase measurement using the imaginary weak-value is not influenced by the amplitude shift and the amplitude measurement using the real weak value is not influenced by the phase shift. Thus, the tiny changes of the phase and amplitude of light can be obtained simultaneously with different post-selections, and the measurement precision reaches ∼10−6 rad. These findings may be favorable for highly sensitive optical polarization-dependent effects, including optical activity and magneto-optic effects.
We show that weak measurement can be used to "amplify" optical nonlinearities at the single-photon level, such that the effect of one properly postselected photon on a classical beam may be as large as that of many unpostselected photons. We find that "weak-value amplification" offers a marked improvement in the signal-to-noise ratio in the presence of technical noise with long correlation times. Unlike previous weak-measurement experiments, our proposed scheme has no classical equivalent.
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.