Polarisation 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 analysing 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 polarisation plane of linearly polarised light. To extract a pure rotational phase shift, we suggest to measure a difference in the angle of the polarisation plane rotation by two consecutive light beams with opposite OAM. The differential angle $\mathrm{\Delta }{\alpha }_{\mathrm{\ell }}$ is proportional to the rotation frequency of the medium ${\omega }_{\mathrm{r}\mathrm{o}\mathrm{t}}$ and the winding number $\mathrm{\ell }$ of light, and is inversely proportional to the group velocity of light. For slow light the angle $\mathrm{\Delta }{\alpha }_{\mathrm{\ell }}$ should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency ${\omega }_{\mathrm{r}\mathrm{o}\mathrm{t}}$ of the medium.