  The emergence of photonic quantum correlations is typically associated with
emitters strongly coupled to a photonic mode. Here, we show that semiconductor
Rydberg excitons, which are only weakly coupled to a free-space light mode can
produce strongly antibunched fields, i.e. quantum light. This effect is fueled
by micron-scale excitation blockade between Rydberg excitons inducing pair-wise
polariton scattering events. Photons incident on an exciton resonance are
scatted into blue- and red-detuned pairs, which enjoy relative protection from
absorption and thus dominate the transmitted light. We demonstrate that this
effect persists in the presence of additional phonon coupling, strong
non-radiative decay and across a wide range of experimental parameters. Our
results pave the way for the observation of quantum statistics from weakly
coupled semiconductor excitons.
