Quantum optics in combination with integrated optical devices shows great promise for efficient manipulation of single photons. New physical concepts, however, can only be found when these fields truly merge and reciprocally enhance each other. Here
we work at the merging point and investigate the physical concept behind a two-coupled-waveguide system with an integrated parametric down-conversion process. We use the eigenmode description of the linear system and the resulting modification in momentum conservation to derive the state generation protocol for this type of device. With this new concept of state engineering, we are able to effectively implement a two-in-one waveguide source that produces the useful two-photon NOON state without extra overhead such as phase stabilization or narrow-band filtering. Experimentally, we benchmark our device by measuring a two-photon NOON state fidelity of $mathcal{F} = (84.2 pm 2.6) %$ and observe the characteristic interferometric pattern directly given by the doubled phase dependence with a visibility of $V_{mathrm{NOON}} = (93.3 pm 3.7) %$.
