  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, whilst 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.
