Spatio-spectral characteristics of parametric down-conversion in waveguide arrays

High dimensional quantum states are of fundamental interest for quantum information processing. They give access to large Hilbert spaces and, in turn, enable the encoding of quantum information on multiple modes. One method to create such quantum states is parametric down-conversion (PDC) in waveguide arrays (WGAs) which allows for the creation of highly entangled photon pairs in controlled, easily accessible spatial modes, with unique spectral properties. In this paper we examine both theoretically and experimentally the PDC process in a lithium niobate WGA. We measure the spatial and spectral properties of the emitted photon pairs, revealing correlations between spectral and spatial degrees of freedom of the created photons. Our measurements show that, in contrast to prior theoretical approaches, spectrally dependent coupling effects have to be taken into account in the theory of PDC in WGAs. To interpret the results, we developed a theoretical model specifically taking into account spectrally dependent coupling effects, which further enables us to explore the capabilities and limitations for engineering the spatial correlations of the generated quantum states.