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Strong coupling between a local quantum system and extended bosonic states has recently become experimentally feasible in a variety of plasmonic, photonic, superconducting qubit, and cold-atom contexts. This has opened up a new field dubbed ``waveguide QED''. I first introduce several of the experimental systems and the basic quantum non-linear optics problems they can address. Then, turning to our own work, I present results for scattering of photons in a waveguide strongly coupled to a two- or four- level system, or to several qubits. We explore the dramatic quantum optics effects in these systems. In particular, multi-photon correlated states emerge in the scattering of two or more photons, which then have a large impact on the transport of coherent-state wave-packets such as causing photon blockade. For several qubits, we observe quantum interference effects in the correlations of the photons and a high degree of long-distance entanglement between the qubits. Such nonlinear phenomena in open quantum systems can play a critical role in the manipulation of individual, mobile quanta, which is a key goal of quantum information processing and communication. Host: Dibyendu Roy |