Experimentally quantifying the advantages of weak-value-based metrology

TL;DR

This paper experimentally compares weak-value-based metrology with standard methods, demonstrating that the weak-value approach can achieve equal or better precision, up to two orders of magnitude, by mitigating external disturbances and maintaining high statistical efficiency.

Contribution

The study provides the first experimental quantification of the advantages of weak-value-based metrology over standard techniques, including robustness to external noise and high Fisher information retention.

Findings

Weak-value technique matches or exceeds standard method precision by up to two orders of magnitude.

Postselection on 1% of photons retains 99% of Fisher information.

Weak-value approach effectively mitigates external transverse modulations.

Abstract

We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-values technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-values-based technique. By postselecting on $1\%$ of the photons, we obtain $99\%$ of the available Fisher information of the beam deflection parameter.