Probing Cosmic Neutrino Background Charge via Unconventional Interferometer

If neutrinos carry non-zero electric charge, they would interact directly with photons. This would induce a phase shift along the photon path in the optical experiment. We propose a novel idea to detect this phase shift induced by cosmic neutrino background (CNB) and the photon interaction using laser interferometry experiment. We show that our setup can probe the CNB neutrino charge in the order of $10^{-18} \,e- 10^{-17}\, e$. This is quite competitive with the existing upper bound on neutrino charge from both laboratory experiments and astrophysical observations.