Self-Ordering of Individual Photons in Waveguide QED and Rydberg-Atom Arrays

The scattering between light and individual saturable quantum emitters can induce strong optical nonlinearities and correlations between individual light quanta. Typically, this leads to an effective attraction that can generate exotic bound states of photons, which form quantum mechanical precursors of optical solitons, as found in many optical media. Here, we study the propagation of light through an optical waveguide that is chirally coupled to three-level quantum emitters. We show that the additional laser-coupling to a third emitter state not only permits to control the properties of the bound state but can even eliminate it entirely. This makes it possible to turn an otherwise focussing nonlinearity into a repulsive photon-photon interaction. We demonstrate this emerging photon-photon repulsion by analysing the quantum dynamics of multiple photons in large emitter arrays and reveal a dynamical fragmentation of incident uncorrelated light fields and self-ordering into regular trains of single photons. These striking effects expand the rich physics of waveguide quantum electrodynamics into the domain of repulsive photons and establish a conceptually simple platform to explore optical self-organization phenomena at the quantum level. We discuss implementations of this setting in cold-atom experiments and propose a new approach based on arrays of mesoscopic Rydberg-atom ensembles.