Towards interferometry of neutrino electromagnetism

It is predicted within the Standard Model of elementary particles that asymmetric neutrino environments cause rotation of linear polarization of electromagnetic wave -- the birefringence. We demonstrate that this effect is strongly enhanced if additionally the photon is propagating through refractive medium, which effectively increases the photon exposure to the neutrino medium. Our estimate for infrared laser beam in $1\,\mathrm{m}$ long optical fiber exposed to reactor anti-neutrino flux results in linear polarization rotation by the angle $\sim4.6\times10^{-39}\,\mathrm{rad}$. We also derive the proper dependence of the effect on the angle between the directions of photon and neutrino propagation in the laboratory frame. For that purpose we derive the correct form of the basis of polarization four-vectors, which differs from the one widely used in literature. We also estimate the sub-leading optical effect of the neutrino medium due to the neutrino dipole magnetic moment, in terms of a variation of the refractive index and its angular dependence. A rough monochromatic approximation points towards the existence of a resonant enhancement of the effect.