On-demand generation of background--free single photons from a solid-state source

True on–demand high–repetition–rate single–photon sources are highly sought after for quantum information processing applications. However, any coherently driven two-level quantum system suffers from a finite re-excitation probability under pulsed excitation, causing undesirable multi–photon emission. Here, we present a solid–state source of on–demand single photons yielding a raw second–order coherence of $g^{(2)}(0)=(7.5\pm 1.6)\times {10}^{-5}$ without any background subtraction nor data processing. To this date, this is the lowest value of $g^{(2)}(0)$ reported for any single–photon source even compared to the previously best background subtracted values. We achieve this result on GaAs/AlGaAs quantum dots embedded in a low–Q planar cavity by employing (i) a two–photon excitation process and (ii) a filtering and detection setup featuring two superconducting single–photon detectors with ultralow dark-count rates of $(0.0056\pm 0.0007)s^{-1}$ and $(0.017\pm0.001) s^{-1}$, respectively. Re–excitation processes are dramatically suppressed by (i), while (ii) removes false coincidences resulting in a negligibly low noise floor.