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

TL;DR

This paper investigates how slow light with orbital angular momentum propagates in a rotating ultracold atomic medium, revealing a measurable polarization rotation that can be used to determine the medium's rotation frequency.

Contribution

It derives a general equation of motion for slow light with OAM in moving media and proposes a method to measure medium rotation via polarization rotation differences.

Findings

Polarization plane rotation is proportional to medium's rotation frequency and light's winding number.

The differential polarization rotation can be used to measure the medium's rotation frequency.

The effect is significant for slow light, enabling practical rotation sensing.

Abstract

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.