Significance The weak-measurement (WM) theory was proposed by Aharonov et al. in 1988. We can obtain the measurement value that is much larger than the eigenvalue using the WM theory by appropriately adjusting the pre-and post-selection states and maintaining a small interaction intensity between the system under test and the detector. The small interaction maintained here is what referred to as “weak” in the WM. In the process of weak interaction, an important parameter, named “weak value,” contained in the pointer state has always played an important role. Therefore, we call this process of significantly amplifying the actual parameters as the weak value amplification. However, because it is impossible to prove the existence of this “weak value” at the beginning, the WM theory has been questioned by the scientific community to the extent that some believed that the WM theory was an absurd idea. In 1989, Duck et al. re-explained the concept of WM, and then in 1991, Ritchie et al. verified the existence of weak values of key parameters in WM through experiments. Consequently, the WM theory is widely accepted.
Progress The WM theory provides a deeper explanation for quantum physics and shows potential for the precision measurement. However, in the next decade, WM development mainly revolved around the theoretical study, such as WM realization in some specific systems, related study on the pointer states in the WM systems, and the “weak value”. In this paper, we discussed important parameters, the WM techniques in classical and quantum physics, the prospect of applying WM techniques to the fields of high-precision measurement, and some other theoretical studies. After the first five years of the 21 st century, the WM techniques have gradually showed their own unique properties in the measurement field. In 2005 and 2007, Pryde and Jozsa, respectively, implemented the WM experiments in polarization detection and measured the complex weak value. They explained in detail the physical meaning of the real and imaginary parts of the weak value in the actual measurement. The WM has been improved to the stage of high-precision measurement. In 2008, Hosten et al. reported a related WM work that studies the spin Hall effect of observing light in Science, which refocused the spotlight on the WM, the promising techniques. Owing to the high measurement accuracy and potential, the amplification mechanism of the WM can be used to observe the physical phenomena and detect the physical parameters.
Furthermore, several related theories since 2010 have shown that the WM performance in the frequency domain has more obvious detection advantages than other fields. Particularly, in 2011, Li group from the University of Science and Technology, China, proposed that white light could be used to achieve high-sensitivity detection of optical phase in the WM system. Two years later, they verified the WM through experiments, which laid the foundation for the WM applications in frequency domain optics. In 2016, He Yonghong group used broadband high-brightness super-luminescent diode as a light source and realized an optical frequency domain WM system with a wide range of general values. Compared with the traditional optical interference detection, the WM system is 1--2 orders of magnitude higher in detection accuracy.
Currently, the WM techniques are widely implemented in four fields including the time domain, frequency domain, spatial domain, and polarization angle distribution based on the requirement of different applications. Relevant study results show that the WM technique has good applicability and high measurement accuracy in these four fields. The representative work in each field is as follows:
(1) Time-domain WM: single-photon tunneling time and observing the spin Hall effect of light.
(2) WM in frequency domain: subpulse width time delay, temperature measurement, and phase shift.
(3) WM in the spatial domain: ultrasensitive beam deflection measurement, Goos-H?nchen displacement, WM techniques to improve the SPR resolution.
(4) Weak-polarization angle measurement: polarization rotation, beam deflection angle measurement, light polarization measurement, chiral molecule measurement, and deviation of the beam angle in reflection or refraction.
Conclusions and Prospects In this paper, we introduce two types of measurement methods combining weak-value amplification based on practical applications of the weak-value amplification in high-precision measurement. These methods are used to measure changes in physical quantities by analyzing the lateral offset and frequency shift of the beam. Based on these systems, the weak-value amplification can be combined with many traditional measurement methods to improve the resolution of the system. Finally, we discuss the development trend of weak-value amplification. Combining the traditional detection methods and weak-value amplification techniques to achieve higher system resolution, indicators are a direct application of the WM in high-precision measurement. Because the weak-value amplification techniques can excellently suppress technical noise, the existing WM system has a resolution of ~1--2 orders of magnitude improvement compared with that of the traditional system. The WM techniques have potential applications in the fields of biology and chemistry.
