Nonclassical millihertz linewidth light source with Rydberg polaritons

A superradiant laser could be used to generate light with extremely high spectral purity, with important applications to quantum information and precision measurements. These applications can be further extended when the photon statistics becomes nonclassical. Here we propose a practical way to generate arbitrarily strong nonlinearity in a superradiant laser by introducing a Rydberg gas into the cavity. The output photons can be made perfectly anti-bunched, while inheriting the millihertz linewidth of the lasing atoms. Our method can also be used to generate a photon blockade in various cavity QED setups, and has implications for the simulation of quantum many body physics with photons.