  Single photons coupled to atomic systems have shown to be a promising
platform for developing quantum technologies. Yet a bright on-demand, highly
pure and highly indistinguishable single-photon source compatible with atomic
platforms is lacking. In this work, we demonstrate such a source based on a
strongly interacting Rydberg system. The large optical nonlinearities in a
blockaded Rydberg ensemble convert coherent light into a single-collective
excitation that can be coherently retrieved as a quantum field. We observe a
single-transverse-mode efficiency up to 0.18(2),
$g^{(2)}=2.0(1.5)\times10^{-4}$, and indistinguishability of 0.982(7), making
this system promising for scalable quantum information applications. Accounting
for losses, we infer a generation probability up to 0.40(4). Furthermore, we
investigate the effects of contaminant Rydberg excitations on the source
efficiency. Finally, we introduce metrics to benchmark the performance of
on-demand single-photon sources.
