Repulsive photons via interaction engineering in a quantum nonlinear medium

Being able to manipulate interactions between single photons is significant for both fundamental studies and applications in quantum information and metrology. Photons do not typically interact with each other; however, special optical media can be engineered to achieve large non-linearity at the single photon level. Here, we control photon-photon interactions and demonstrate both repulsion and attraction between photons. We achieve this by coupling photons to two distinct atomic states in a cold atomic gas with one of the states being a strongly interacting Rydberg state. We demonstrate both repulsive and attractive interactions as characterized by the measured two- and three-photon correlation functions. These observations of repulsion between single photons and the ability to control the nature of interactions open a route to creating quantum matter composed of light such as a crystal of photons.