Optical Josephson radiation from a Majorana Josephson junction

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