  The development, characterization and control of $N$-photon sources are
instrumental for quantum technological applications. This work constitutes a
step forward in this direction, where we propose a cavity quantum
electrodynamics setup designed for the generation of photon pairs. We analyze
it both via the scattering and master equation formalisms. From the connection
between these two frameworks it naturally arises a physical criterion
characterizing when weakly-driven systems behave as continuous antibunched
two-photon sources. We find the optimal parameters for which our setup works as
an efficient photon-pair source, showing also that it becomes a deterministic
down-converter of single photons. We provide a specific implementation based on
state-of-the-art superconducting circuits, showing how our proposal is within
the reach of current technologies.
