Transport through a dissipative superfluid contact

In superconducting contacts, the coherent tunneling of a single quasiparticle together with Cooper pairs leads to a sub-gap current structure. This phenomenon, also called multiple Andreev reflections, is well-known in condensed-matter superconducting junctions. Current-voltage characteristics consistent with multiple Andreev reflections have also been measured in a cold-atom setup where two superfluids are coupled by a quantum point contact. Furthermore, cold-atom experiments have probed transport in the presence of local particle losses. Motivated by these experiments, we theoretically investigate the effect of a local particle loss on the multiple Andreev reflection process. To quantify this effect, we use the Keldysh formalism to calculate current-voltage characteristics of a superconducting contact. We compare the effect of dissipation by particle loss to that of a finite temperature and find that the two effects are qualitatively different.