Photon trajectories, anomalous velocities, and weak measurements: A classical interpretation

TL;DR

This paper provides a classical optics interpretation of weak measurements of photon trajectories, explaining anomalous velocities and related phenomena through classical field concepts like the Poynting vector, vortices, and evanescent waves.

Contribution

It offers a novel classical optics perspective on weak measurements of photon momentum, connecting quantum weak measurement results with classical field phenomena.

Findings

Weak measurements correspond to classical Poynting vector measurements.

Anomalous velocities relate to vortices and evanescent waves.

Classical optics can explain photon trajectory observations.

Abstract

Recently, Kocsis et al. reported the observation of "average trajectories of single photons" in a two-slit interference experiment [Science 332, 1170 (2011)]. This was possible by using the quantum weak-measurements method, which implies averaging over many events, i.e., in fact, a multi-photon limit of classical linear optics. We give a classical-optics interpretation to this experiment and other related problems. It appears that weak measurements of the local momentum of photons made by Kocsis et al. represent measurements of the Poynting vector in an optical field. We consider both the real and imaginary parts of the local momentum, and show that their measurements have been realized in classical optics using small probe particles. We also examine the appearance of "anomalous" values of the local momentum: either negative (backflow) or exceeding the wavenumber (superluminal propagation). These features appear to be closely related to vortices and evanescent waves. Finally, we revisit a number of older works and find examples of photon-trajectories and anomalous-momentum measurements in various optical experiments.