Weak Values Technique for Velocity Measurements

TL;DR

This paper introduces a novel interferometric method using weak values and time-domain analysis to measure extremely small velocities with high precision, surpassing traditional techniques.

Contribution

It presents a new interferometric scheme combining weak value amplification with time-domain analysis for precise velocity measurements.

Findings

Achieved velocity measurement of 400 fm/s.

Estimator reaches the Cramér-Rao bound, indicating optimal efficiency.

Demonstrated superiority over standard interferometry methods.

Abstract

In a recent letter, Brunner and Simon propose an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [N. Brunner and C. Simon, Phys. Rev. Lett {\bf105} (2010)]. Here we demonstrate an interferometric scheme combined with a time-domain analysis to measure longitudinal velocities. The technique employs the near-destructive interference of non-Fourier limited pulses, one Doppler shifted due to a moving mirror, in a Michelson interferometer. We achieve a velocity measurement of 400 fm/s and show our estimator to be efficient by reaching its Cram\'{e}r-Rao bound.