We investigate the effect of slow light propagating in a degenerate atomic Fermi gas. In particular we use slow light with an orbital angular momentum. We present a microscopic theory for the interplay between light and matter and show how the slow light can provide an effective magnetic field acting on the electrically neutral fermions, a direct analogy of the free electron gas in an uniform magnetic field. As an example we illustrate how the corresponding de Haas-van Alphen effect can be seen in a gas of neutral atomic fermions.
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 $\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}$ is proportional to the rotation frequency of the medium ${\ensuremath{\omega}}_{\text{rot}}$ and the winding number
l of light, and is inversely proportional to the group velocity of light. For slow light the angle $\ensuremath{\Delta}{\ensuremath{\alpha}}_{l}$ should be large enough to be detectable. The effect can be used as a tool for measuring the rotation frequency ${\ensuremath{\omega}}_{\text{rot}}$ of the medium.