Strongly Correlated Photons in Nonlinear Nanophotonic Platforms

Modern nano-fabrication technologies allow to realize photonic propagation and confinement to unprecedented degree of compactness, and very close to lossless conditions. Such figures of merit are inherently driving the possibility to reach a strong enhancement of optical nonlinearities in ordinary semiconductor platforms, which have been mainly used for opto-electronics purposes so far. After reviewing the basic nanophotonic platforms that are used in integrated quantum photonics nowadays, with a focus on photonic crystal cavities and cavity arrays, we will give an overview of the application of strongly correlated photonic concepts to such systems. The focus will be on small-scale systems, compatible with modern nanofabrication capabilities, and on physical quantities of direct experimental access, such as field intensity and second-order correlations in time. A few topical cases that will be reviewed include novel quantum photonic devices of increasing system size and complexity, from the quantum optical Josephson interferometer in a three-cavity system, to the out-of-equilibrium phase crossover from delocalized to strongly interacting manybody states in cavity arrays.