Coherent nonlinear optics of quantum emitters in nanophotonic waveguides

Coherent quantum optics, where the phase of a photon is not scrambled as it interacts with an emitter, 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 element can be integrated into complex photonic chips. Yet, preserving the full coherence properties of the coupled emitter-waveguide system is challenging because of the complex and dynamic electromagnetic landscape found in the solid state. Here, we review progress toward 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 discuss higher order nonlinearities that arise as a result of 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 toward their realization, and the challenges that remain to be overcome.