Bright Heralded Single-Photon Source Saturating Theoretical Single-photon Purity

Single-photon source is the cornerstone for modern quantum information processing. The present work derives the theoretical limit of single-photon purity for general parametric heralded single-photon sources, and subsequently demonstrates a bright, gigahertz-pulsed heralded source with the purity saturating the limit. By stimulating spontaneous four-wave mixing effect in the silicon spiral waveguide, this on-chip source is measured to have a coincidence rate exceeding 1.5 MHz at a coincidence-to-accidental ratio (CAR) of 16.77 in the photon pair correlation experiment. The single-photon purity of this source, quantified by the heralded auto-correlation function gh(2)(0)$g<^>{(2)}_{\text{h}}(0)$, is measured by a heralded Hanbury Brown-Twiss setup to reach the theoretical limit with the lowest value of 0.00094 +/- 0.00002$0.00094 \pm 0.00002$ obtained at a coincidence rate of 0.8 kHz and a CAR of 2220. The performance improvements are attributed to effective spectral filtering suppressing the noise as well as the coherent pump condition helped by optical injection locking. The reported results provide a reliable standard for benchmarking heralded single-photon sources and present a state-of-the-art heralded source for quantum information processing.