Transverse Momentum Transfer in Atom-Light Scattering

Light scattering exchanges momentum between matter and radiation, and thus induces a force on the matter. Classical light scattering is well known to be affected by a magnetic field. A specific feature, the photon Hall effect (PHE), was first predicted in multiple light scattering [1], and observed shortly afterwards [2] with typical changes in the magneto-transverse photon flux of order 10 −5 per Tesla of applied magnetic field. A Mie theory for the PHE [4] agreed quantitatively with the experiments. Given the wave number k of the incident photon flux and the magnetic field B , the PHE induces an exchange of momentum between scatterer and radiation in the magnetotransverse (”upward”) direction along B×k. A light flux of 10 4 W/m 2 incident on a micron-sized particle with a relative PHE of 10 −5 per Tesla experiences a transverse force of 10 −19 N/T, roughly equivalent to the Lorentz force on a charge e moving with a velocity of 1 m/s. The magneto-transverse acceleration for a 10µm TiO2 particle would be as small as 10 −11 m/s 2 in a field of 10 Tesla.