Full two-photon down-conversion of a single photon

We demonstrate, both numerically and analytically, that it is possible to deterministically generate two photons from one and only one photon. We characterize the output two-photon field and make our calculations close to reality by including losses. Our proposal relies on real or artificial three-level atoms with a cyclic transition strongly coupled to a one-dimensional waveguide. We show that almost perfect down-conversion, with efficiency over 99%, is reachable using state-of-the-art waveguide QED architectures such as photonic crystals or superconducting circuits. In particular, we sketch an implementation in circuit QED, where the three-level atom is a transmon.