Improving the precision of weak-value-amplification with two cascaded Michelson interferometers based on Vernier-effect

TL;DR

This paper introduces a modified weak-value amplification method utilizing two cascaded Michelson interferometers based on the Vernier effect, achieving enhanced sensitivity and signal-to-noise ratio for velocity measurements.

Contribution

The paper proposes a novel MWVA technique with cascaded interferometers exploiting the Vernier effect, demonstrating improved sensitivity and SNR over traditional methods.

Findings

Enhanced sensitivity and SNR using cascaded interferometers

The envelope shift is significantly larger than single interferometers

MWVA outperforms traditional weak-value amplification in SNR within measurement window

Abstract

A modified-weak-value-amplification(MWVA) technique of measuring the mirror's velocity based on the Vernier-effect has been proposed. We have demonstrated with sensitivity-enhanced and the higher signal-to-noise ratio(${\rm SNR}$) by using two cascaded Michelson interferometers. These two interferometers are composed of similar optical structures. One interferometer with a fixed mirror acts as a fixed part of the Vernier-scale, while the other with a moving mirror acts as a sliding part of the Vernier-scale for velocity sensing. The envelope of the cascaded interferometers shifts much more than a single one with a certain enhancement factor, which is related to the free space range difference between these two interferometers. In addition, we calculate the ${\rm SNR}$ based on the Fisher information with both the MWVA technique and the traditional-weak-value-amplification(TMVA) technique. The results show that the ${\rm SNR}$ with our MWVA technique is larger than the the ${\rm SNR}$ with the TWVA technique within the range of our time measurement window. Our numerical analysis proved that our MWVA technique is more efficient than the TWVA technique. And by using the principles of the Vernier-effect, it is applicative and convenient to ulteriorly improving the sensitivity and ${\rm SNR}$ in measuring other quantities with the MWVA technique.