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

友紀 須佐, Yuki Susa, Saki Tanaka

Yuki Susa

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.

Yuki Susa, Saki Tanaka

We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the large weak value has the advantage to increase the detection power and to reduce the possibility of missing the presence of interaction. We enhance the physical understanding of the weak value and mathematically establish the significance of the weak-value amplification. Our present work overcomes the critical dilemma of the weak-value amplification that the larger the amplification is, the smaller the number of data becomes, because the statistical hypothesis testing works even for a small number of data. This is contrasted with the parameter estimation by the weak-value amplification in the literature which requires a large number of data.

Ladislav Mišta, Jan Peřina

Garrett K. Josemans, Benjamin Baldwin, John Edward Gray +2 more

We present an investigation into the tilt sensitivity of the canonical, optical, weak-value amplification device (COWVAD), introduced by Duck, Stevenson, and Sudarshan in 1989, for potential application in a Coriolis vibratory gyroscope (CVG). We model the breakdown of the weak-value amplification effect in this device with respect to angle of incidence between the laser beam and the surface of the birefringent crystal. Additionally, we model the effect of beam divergence due to misalignment of the crystals optic axis. We found that the presence of beam divergence allows the architecture to be placed in an inverse weak-value amplification configuration. We found that weak-value amplification occurs at angles other than those reported in Duck 1989. We also present laboratory measurements that support the validity of the mathematical model. The maximum tilt sensitivity measured was ~.58 m/rad, which, while 390 times greater than it would be without weak-value amplification, does not represent the maximum possible sensitivity of the device through weak-value amplification.

O. P. Varnavskiǐ, Valerie V. Golovlev, A. N. Kirkin +2 more