Abstract

Optical nonlinearities at the few-photon level bring together the fields of quantum optics and nonlinear optics. This regime, so-called quantum nonlinear optics, is described by effective strong interactions between individual photons. I will introduce the basic concepts and the original experiments realizing this regime using ultracold Rydberg atoms. I will overview recent achievements and outstanding proposals, including photon crystallization and the generation of photonic cluster states.