Optical angular momentum in atomic transitions: a paradox

TL;DR

This paper examines the paradox of how Gaussian beams with zero orbital angular momentum can induce quadrupole atomic transitions requiring angular momentum transfer, challenging conventional understanding of light-matter interactions.

Contribution

It clarifies the apparent paradox by analyzing the angular momentum properties of Gaussian beams and their interaction with atomic transitions.

Findings

Gaussian beams with zero orbital angular momentum can drive quadrupole transitions.

The angular momentum transfer involves subtleties in the beam's field structure.

The study resolves the paradox by examining the local and global angular momentum properties.

Abstract

Stated simply the paradox is as follows: it is clear that the orbital angular momentum of a light beam in its direction of propagation is an intrinsic quantity, and therefore has the same value everywhere in the beam. How then can a Gaussian beam, with precisely zero orbital angular momentum, drive a (single-photon) quadrupole transition which requires the transfer of angular momentum 2$\hbar$ to an absorbing atom?