Fundamental limit on the heralded single photons' spectral brightness

Abstract: The heralded single photons' (HSPs) spectral brightness (SB) is defined as the generation rate per linewidth. As the generation rate of HSPs gets larger or the photons' linewidth becomes narrower, both of which are desirable in quantum information processing using HSPs, does the SB have a limit? We systematically studied the SB and the cross-correlation function, or equivalently, the signal-to-background ratio. The results in this study provide an answer applicable to all types of HSP sources. The answer relies on a newly defined quantity, the quality factor, which reveals how a HSP source approaches the ideal noise-free one. Furthermore, employing the HSP source based on hot atomic vapor, we achieved an SB of (7.0$\pm$0.3)$\times10^5$ pairs/s/MHz and a quality factor of 0.68$\pm$0.02 under the single-photon criterion. Both values are the highest records to date among all kinds of HSP sources.