Photons in a cold axion background and strong magnetic fields: polarimetric consequences

In this work we analyze the propagation of photons in an environment where a strong magnetic field (perpendicular to the photon momenta) coexists with an oscillating cold axion background with the characteristics expected from dark matter in the galactic halo. Qualitatively, the main effect of the combined background is to produce a three-way mixing among the two photon polarizations and the axion. It is interesting to note that in spite of the extremely weak interaction of photons with the cold axion background, its effects compete with those coming from the magnetic field in some regions of the parameter space. We determine (with one plausible simplification) the proper frequencies and eigenvectors as well as the corresponding photon ellipticity and induced rotation of the polarization plane that depend both on the magnetic field and the local density of axions. We also comment on the possibility that some of the predicted effects could be measured in optical table-top experiments.