Momentum exchange between light and a single atom: Abraham or Minkowski?

Abstract

We consider the forces exerted by a pulse of plane-wave light on a single atom. The leading edge of the pulse exerts a dispersive force on the atom, and this modifies the atomic momentum while the atom is enveloped in the light. The standard view of the optical dipole force indicates that red-detuned light should attract the atom towards high intensity. This should increase the average momentum per photon to $\textbf{p}_{0} n$, where $\textbf{p}_{0}$ is the photon momentum in free space and $n$ is the average refractive index due to the presence of the atom in the light. We show, however, that this is the wrong conclusion and that the atom is in fact repelled from the light by the dispersive forces, giving the photons a momentum $\textbf{p}_{0} /n$. This leads us to identify Abraham's optical momentum with the kinetic momentum transfer. The form due to Minkowski is similarly associated with the canonical momentum. We consider the possibility of demonstrating this in the laboratory, and we note an unexpected connection with the Aharonov-Casher effect.Comment: 4 pages, 1 figur