Linear and angular momenta of photons in the context of "which path" experiments of quantum mechanics

TL;DR

This paper explores how the linear and angular momenta of photons relate to the 'which path' information in quantum interference experiments, highlighting the trade-off between path knowledge and interference visibility.

Contribution

It analyzes the connection between photon momenta and path information, demonstrating how momentum exchanges can reveal paths at the cost of destroying interference.

Findings

Photon momentum exchanges can indicate the photon's path.

Path information acquisition destroys interference fringes.

Angular momentum transfer can provide 'which path' information without explicit uncertainty principle involvement.

Abstract

In optical experiments involving a single photon that takes alternative paths through an optical system and ultimately interferes with itself (e.g., Young's double-slit experiment, Mach-Zehnder interferometer, Sagnac interferometer), there exist fundamental connections between the linear and angular momenta of the photon on the one hand, and the ability of an observer to determine the photon's path through the system on the other hand. This paper examines the arguments that relate the photon momenta (through the Heisenberg uncertainty principle) to the "which path" (German: welcher Weg) question at the heart of quantum mechanics. We show that the linear momenta imparted to apertures or mirrors, or the angular momenta picked up by strategically placed wave-plates in a system, could lead to an identification of the photon's path only at the expense of destroying the corresponding interference effects. We also describe a thought experiment involving the scattering of a circularly-polarized photon from a pair of small particles kept at a fixed distance from one another. The exchange of angular momentum between the photon and the scattering particle in this instance appears to provide the "which path" information that must, of necessity, wipe out the corresponding interference fringes, although the fringe-wipe-out mechanism does not seem to involve the uncertainty principle in any obvious way.