Theory of double Cooper-pair tunneling and light emission mediated by a resonator

Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tunneling of two Cooper pairs, while also uncovering a regime of coherent double Cooper-pair tunneling. We show that the system can also display an unusual form of photon blockade and hence could serve as a single-photon source.