  Polaritons are an emerging platform for exploration of synthetic materials
[1] and quantum information processing [2] that draw properties from two
disparate particles: a photon and an atom. Cavity polaritons are particularly
promising, as they are long-lived and their dispersion and mass are
controllable through cavity geometry [3]. To date, studies of cavity polaritons
have operated in the mean-field regime, using short-range interactions between
their matter components [4]. Rydberg excitations have recently been
demonstrated as a promising matter-component of polaritons [5], due to their
strong interactions over distances large compared to an optical wavelength. In
this work we explore, for the first time, the cavity quantum electrodynamics of
Rydberg polaritons, combining the non-linearity of polaritonic quantum wires
with the zero-dimensional strong coupling of an optical resonator. We assemble
a quantum dot composed of $\sim 150$ strongly interacting, Rydberg-dressed
$^{87}$Rb atoms in a cavity, and observe blockaded polariton transport as well
as coherent quantum dynamics of a single polaritonic super-atom. This work
establishes a new generation of photonic quantum information processors and
quantum materials, along with a clear path to topological quantum matter [6].
