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 $V_{\mathrm{NOON}} = (93.3 \pm 3.7) \%$.Comment: 6 pages, 3 figure
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