Polarization rotation of slow light with orbital angular momentum in ultracold atomic gases

We consider the propagation of slow light with an orbital angular momentum (OAM) in a moving atomic medium. We have derived a general equation of motion and applied it in analyzing propagation of slow light with an OAM in a rotating medium, such as a vortex lattice. We have shown that the OAM of slow light manifests itself in a rotation of the polarization plane of linearly polarized light. To extract a pure rotational phase shift, we suggest to measure a difference in the angle of the polarization plane rotation by two consecutive light beams with opposite OAM. The differential angle Deltaalphal is proportional to the rotation frequency of the medium omegarot and the winding number l of light, and is inversely proportional to the group velocity of light. For slow light the angle Deltaalphal should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency omegarot of the medium.