Quantum propagation of light: from photon molecules to many-body physics
Recent experiments have demonstrated that light propagation through ensembles of Rydberg atoms is highly non-linear at the level of individual photons. Other developing platforms, such as circuit QED and atoms coupled to nanophotonic waveguides, also promise the ability to engineer the quantum state of propagating light at the few and many-body limit. Coupled to these experimental advances, effective theoretical descriptions have been produced, modeling the physics in specific instances. However, general numerical techniques are currently limited. Here, we describe an approach to this problem by using a "spin model" that maps the light propagation problem to a system of interacting spins, where all of the photon correlations are obtained from those of the spins. In the few-body limit we use this method to show that in systems of atoms coupled to photonic-crystal waveguides photons can bind together forming molecules. Going beyond this limit, we can use the powerful toolbox of matrix product states to solve the spin problem and study multi photon effects, where as an example we simulate the number dependent pulse velocity in vacuum induced transparency.