Weak value amplification in a shot-noise limited interferometer

TL;DR

This paper investigates the effectiveness of weak-value amplification in optical interferometers limited by shot noise, analyzing the noise contributions and optimizing the signal-to-noise ratio for practical phase measurements.

Contribution

It provides a comprehensive analysis of shot noise effects in WVA, including full-order interaction terms, and discusses optimization strategies for real-world applications.

Findings

Shot noise contribution exceeds the final pointer variance by up to 1.5 times.

WVA's advantage depends on signal-to-noise ratio optimization.

Full-order interaction terms are crucial for accurate noise analysis.

Abstract

We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA, and show that the shot-noise contribution to a phase shift in a pointer variable is always larger than the final variance of the pointer variable. This yields difference in estimating noise level up to a factor of 1.5. To clarify an advantage for practical uses of the WVA, we discuss signal-to-noise ratio and its optimization in the presence of the shot noise.