Physical description of statistical hypothesis testing for a weak-value amplification experiment using a birefringent crystal

TL;DR

This paper provides a physical interpretation of statistical hypothesis testing in weak-value amplification experiments using birefringent crystals, demonstrating its advantages over traditional methods in specific polarizer configurations.

Contribution

It offers a physical explanation and validation of weak-value amplification's effectiveness in detecting birefringence, enhancing understanding of its practical utility.

Findings

Weak-value amplification outperforms non-postselected measurement in birefringence detection.

The method is particularly effective when polarizer angles are nearly orthogonal.

Supports the experimental usefulness of weak-value amplification in optical measurements.

Abstract

We investigate the weak measurement experiment demonstrated by Ritchie et al. [N. W. M. Ritchie, J. G. Story, and R. G. Hulet, Phys. Rev. Lett. 66, 1107 (1991)] from the viewpoint of the statistical hypothesis testing for the weak-value amplification proposed by Susa and Tanaka [Y. Susa and S. Tanaka, Phys. Rev. A 92, 012112 (2015)]. We conclude that the weak-value amplification is a better method to determine whether the crystal used in the experiment is birefringent than the measurement without postselection, when the angles of two polarizers are almost orthogonal. This result gives a physical description and intuition of the hypothesis testing and supports the experimental usefulness of the weak-value amplification.