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

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.

Weak-value-amplification enhancement of the magneto-optical Kerr effect in nanoscale layered structures

“…The most sensitivity relationship between Kerr signals and the pointer shift depends on finding the most appropriate post-selection state. It is very important to go beyond this and design a new scheme based on the weak-value-amplification technique [73,30,74,36]. Particularly, the article [73] experimentally verified that biased weak measurement significant improves the precision of optical metrology with a scheme to measure a small optical delay, where the estimated parameter (corresponding to the small optical delay) was amplified as the parameter in the "weak-coupling" progress in the standard weak-value-amplification technique.…”

Cascaded weak-value amplification for optic-fiber-based Sagnac interferometers

“…First, if we set the same intensity of the Laser in the two schemes, naturally the value of 𝜅 equals 2 due to the beam split of the OC1. However, the value of 𝜅 could be one when the PD is dominated by the saturation effect [43]. Note that the different values of 𝜅 will not influence the pointer shifts (corresponding to the sensitivity) but have an effect on the calculation of SNR.…”

Demonstration of a New Characterization Method for Weak Measurement

“…In 2005 and 2007, the teams of Pryde and Jozsa realized and measured complex weak values in polarization detection based on the weak measurement theory and explained in detail the physical significance of the weak values in both the real and imaginary parts of the actual measurement ( Pryde et al, 2005 ; Jozsa, 2007 ). With this approach, it was possible to achieve high precision measurement with weak measurement technology ( Xu et al, 2013 ; Vella et al, 2019 ; Xu et al, 2020 ; Yin et al, 2021 ). Since 2010, relevant theories have shown that the weak measurement technology exhibits more obvious detection advantages in the frequency domain than the other fields ( Brunner and Simon, 2010 ; Xu et al, 2013 ).…”