Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?

Abstract

We consider forces on an atom due to a plane-wave light pulse. The standard view of the optical dipole force indicates that red-detuned light should attract the atom towards high intensity. While the atom is inside the pulse, this would increase the average momentum per photon from p_{0} to p_{0}n, where n is the average refractive index due to the presence of the atom. We show, however, that this is the wrong conclusion and that the dispersive forces repel the atom from the light in this particular case, giving the photons a momentum 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.