From few to many strongly interacting Rydberg polaritons

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This project aims to experimentally realize and study in detail systems of strongly interacting Rydberg polaritons inside a highly nonlinear medium. It thus falls into the "Rydberg Quantum Optics" category of this programme, addressing the experimental implementation of novel many-body states.We will approach the challenge of realizing many-body Rydberg polariton systems from two sides. On the one hand we will realize systems on the scale of two to ten concurrently interacting polaritons inside a highly elongated ultra-cold atomic cloud. This enables a controlled transition from two- to many-body physics of strongly correlated (quasi-)particles, where all interaction parameters are highly controlled and tunable and measurement of the full quantum statistics and correlations through time-resolved photon counting is possible.With this system we will study in detail the two-body interaction between Rydberg polaritons, with the goal of observing polariton scattering resonances and novel bound states of photons of increasing size. We will also investigate the case of repulsive interactions, which, at sufficient strength, leads to the fermionization of the bosonic polaritons, resulting in the crystallization of the many-body photon state.Complementary to the effectively one-dimensional strongly interacting system, we will realize larger three-dimensional polariton liquids with weaker interaction. We will extend our investigation to the effect of interactions on the transverse mode of propagating polaritons, which we will directly image with a high-sensitivity camera after the photons have propagated through the medium. In this larger system, we will investigate the formation of spatial solitons mediated by Rydberg interaction. One of the main questions we hope to address is to what extend mean-field treatments of the Rydberg polariton system is justified and under which condition beyond mean-field effect become relevant.Ultimately, we plan to combine the two approaches and to realize strongly correlated polariton systems of moderate size (>10), from which we can still extract the full photon statistics and correlations. This gives unprecedented access to the microscopic details of a strongly correlated system.