Detection prospects for the Cosmic Neutrino Background using matter interferometers

In this paper we discuss how the Cosmic Neutrino Background can affect the measured phase difference in a matter interferometer. This phase is proportional to a difference in potential energies along the two interferometer paths. The relevant potentials here are the well-known neutrino matter potential and a potential related to the Stodolsky effect. We show how they can be rewritten in terms of scalar potentials, pseudo magnetic fields and spin-spin interactions. Unfortunately, current technology is unlikely to detect this effect and we discuss prospects for the future. We also briefly comment on fermionic Dark Matter which can give rise to very similar effects which can easily be larger than the neutrino case.