We present a scheme to generate nonlocal optical Kerr nonlinearity and polaritonic solitons via matter-wave superradiance in a Rydberg-dressed Bose-Einstein condensate (BEC). We show that the polariton spectrum of the scattered field generated by the superradiance is changed significantly due to the existence of the long-range Rydberg-Rydberg interaction between atoms, i.e. it has a roton-maxon form; moreover, the BEC structure factor displays a strong dependence on the Rydberg-dressing, which can be tuned in a controllable way. We also show that such a Rydberg-dressed BEC system can support a giant nonlocal optical Kerr nonlinearity, and hence allow the formation and stable propagation of polaritonic solitons, which have ultraslow propagation velocity and ultralow generation power. The results reported here are useful to understand the unique properties of Rydberg-dressing in BECs and have potential applications in optical information processing and transmission.
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