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The two-level system (TLS) creates a non-linearity, causing an interaction between the photons (a repulsion).
By adding photons to a two-dimensional array of coupled optical cavities, each containing a single two-level atom in the photon-blockade regime, they form atom-photon `molecules' termed dressed states or polaritons.
The coupling between the atom and the photons leads to optical nonlinearities and an effective photon-photon repulsion.