Recoil-induced optical Faraday rotation

It is shown that, as a result of recoil during spontaneous emission, optical activity in a vapor can be induced under the action of resonant pump and probe fields. For field geometries that exclude other mechanisms for rotation of the probe field's plane of polarization, the recoil accompanying spontaneous emission provides the needed coupling between the spatial and internal atomic degrees of freedom to produce an optically active medium. A transition between ground and excited states, each having angular momentum $J=\frac{1}{2}$, is analyzed in detail. The effect can be interpreted as the result of pump field scattering off a spatial polarization grating of ground-state Zeeman coherence.