Pragmatic Implementation With Non-Gaussian Devices of Noise-Limited Weak Value Amplification

Abstract

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.

Auto-correlative weak-value amplification under strong noise background

“…It has been pointed out that technique noise [20,21,23] has a great influence on the weak measurement. To simulate the WVA and AWVA schemes with the temporal pointer on Simulink in a realistic situation, the effects of Gaussian white noises with different SNR on the two schemes are investigated firstly.…”

“…Though the Fisher information [23,32,37,38] is widely used to estimate the SNR in the standard weak measurement, it only represents the statistical error. Herein, we use a more general definition of SNR in the WVA scheme:…”

“…Meanwhile, the determination of the pointer shift would inevitably be influenced by technique noise and the surrounding environment. Numerous studies [20,21,23] have been done to investigate the advantage of WVA in presence of noise. In particular, Knee et al [21] argued that the amplified displacement offered no fundamental metrological advantage, due to the necessarily reduced probability of success.…”

“…Using statistically rigorous arguments, Christopher et al [20] showed that the technique of WVA does not perform better than standard statistical techniques for single parameter estimation or signal detection. Considering the measured system cannot be completely isolated from the surrounding environment and the instability of the element itself, the determination of the pointer shift will inevitably be influenced by many sources [23]: instability of the light source's spectrum and intensity, interference in the light path, thermal noise and shot noise of the detection, and other noise sources. A natural thought is to equate these noises with Gaussian white noises.…”

“…Therefore, the WVA scheme based on the imaginary weak value is currently used in the field of biosensors, such as a new chiral sensor based on weak measurement for estimation of a trace amount of chiral molecule [34], a tunable and high-sensitivity temperature-sensing method via WVA of Goos-änchen (GH) shifts in a graphene-coated system [35], even an optical system based on optical rotation via weak measurement for detection of single-and double-strand state of DNA [36]. Furthermore, there have been several optimization schemes to improve the WVA scheme based on analysis of its Fisher information [23,32,37,38].…”