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 $\Delta\alpha_{\ell}$ is proportional to the rotation frequency of the medium $\omega_{\mathrm{rot}}$ and the winding number $\ell$ of light, and is inversely proportional to the group velocity of light. For slow light the angle $\Delta\alpha_{\ell}$ should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency $\omega_{\mathrm{rot}}$ of the medium.