Majorana fermions coupled to electromagnetic radiation

We consider a voltage-biased Josephson junction between two nanowires hosting Majorana zero modes which occur as topological protected zero-energy excitations at the junction. We show that two Majorana fermions localized at the junction, even though being neutral particles, interact with the electromagnetic field and generate coherent radiation similar to the conventional Josephson radiation. Within a semiclassical analysis of the radiation field, we find that the optical phase gets locked to the superconducting phase difference and that the radiation is emitted at half the Josephson frequency. In order to confirm the coherence of the radiation, we study correlations of the radiation emitted by two spatially-separated junctions in a d.c.-SQUID geometry taking into account decoherence due to spontaneous state-switches as well as due to quasi-particle poisoning.