Measuring small longitudinal phase shifts via weak measurement amplification

Abstract

Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimations. Since many physical quantities can be converted into phase signals, it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference. Besides, we analyze the effect of magnification error which is never considered in the previous works, and find the constraint on the magnification. Our results may find important applications in high-precision measurements, e.g., gravitational wave detection.