Coherent nonlinear optics of quantum emitters in nanophotonic waveguides

Coherent quantum optics, where the interaction of a photon with an emitter does not scramble phase coherence, lies at the heart of many quantum optical effects and emerging technologies. Solid-state emitters coupled to nanophotonic waveguides are a promising platform for quantum devices, as this combination is scalable. Yet, reaching full coherence in these systems is challenging due to the dynamics of the solid-state environment of the emitters. Here, we review progress towards coherent light-matter interactions with solid-state quantum emitters coupled to nanophotonic waveguides. We first lay down the theoretical foundation for coherent and nonlinear light-matter interactions of a two-level system in a quasi-one-dimensional system, and then benchmark experimental realizations. We then discuss higher-order nonlinearities that arise due to the addition of photons of different frequencies, more complex energy-level schemes of the emitters, and the coupling of multiple emitters via a shared photonic mode. Throughout, we highlight protocols for applications and novel effects that are based on these coherent interactions, the steps taken towards their realization, and the challenges that remain to be overcome.