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.
@article{arxiv.1304.0029,
title = {Weak Values Technique for Velocity Measurements},
author = {Gerardo I. Viza and Julián Martínez-Rincón and Gregory A. Howland and Hadas Frostig and Itay Shomroni and Barak Dayan and John C. Howell},
journal= {arXiv preprint arXiv:1304.0029},
year = {2013}
}