Metrology with Weak Value Amplification and Related Topics.

摘要

This report summarizes our accomplishments in the past 3+1 years concerning our investigation into the advantages of weak value approaches to precision measurements, as well as other investigations into weak measurements and weak values. The report is divided into two sections: The first focuses on a detailed discussion of results concerning applications and advantages of weak value amplification techniques to precision measurement. Here, we discuss four separate but connected projects. The first concerns the possibility of reusing the rejected photons in the post-selection portion of the weak value amplification. The second project concerns the technical merits of weak value amplification. We also discuss a third project using our interferometric weak value technique to make precision frequency measurements on an optical beam, reporting a resolution of 129 +/- 7 kHz per root Hz with only 2 mW of continuous-wave power. The fourth project deals with a weak value inspired phase amplification technique. The second main part of the report concerns results related to weak measurements and weak values, but not directly related to the amplification issue. We give a brief survey of our results in this area. We have investigated weak measurements as a test of quantum mechanics, by deriving generalized Leggett-Garg inequalities for multiple parties and violating them with entangled photons. We have extensively investigated a new approach to generalized measurement we call contextual values, which gives a precise connection between an indirectly measured system and the outcomes of the detector by assigning a set of generalized eigenvalues to each detector outcome. This assignment permits a principled definition of a conditioned average, which limits to the weak value under certain conditions that are usually satisfied in the laboratory. We have also discussed the significance of the imaginary part of the weak value.