Protecting Heralded Single Photons Generated from Double-$\Lambda$ Biphoton Sources with Doppler-Broadened Atomic Media

Biphoton sources that use room-temperature or hot atoms are valuable for real-world applications in long-distance quantum communication and photonic quantum computation. The heralded single photons produced by biphoton sources using the double-$\Lambda$ spontaneous four-wave mixing (SFWM) process offer advantages of narrow linewidth, stable frequency, and tunable linewidth -- qualities not found in other types of biphoton sources. In this study, we investigated a hot-atom SFWM double-$\Lambda$ biphoton source. We discovered that, under the condition counterintuitive to the present theory, heralded single photons of the source enhanced their generation rate by a factor of 3.6, heralding probability by a factor of 3.0, temporal width by 2.1, and spectral brightness by a factor of 10. These unexpected findings led us to propose a new theoretical framework for a previously unexplored physical mechanism. Our proposed theory effectively explains the observed results. Traditionally, similar spectral brightness (SB) from atom-based sources resulted in a lower signal-to-background ratio (SBR) than crystal- or chip-based biphoton sources, mainly due to poorer heralding probabilities. In our work, we experimentally demonstrated that the SBR improved by a factor of 4.8 while maintaining a comparable SB. As a result, the SBR performance of the atom-based biphoton source is now on par with that of crystal- or chip-based sources. This research introduces a new tuning parameter for double-$\Lambda$ SFWM biphoton sources, enhances our understanding of biphoton generation, and opens new avenues for improving the performance of these sources.