We consider the free-carrier dispersion effect in a semiconductor nanocavity in the limit of discrete photoexcited electron-hole pairs. This analysis reveals the possibility of ultrafast, incoherent transduction and gain from a single photon signal to a strong coherent probe field. Homodyne detection of the displaced probe field enables an all-optical method for room-temperature, photon-number-resolving single photon detection. In particular, we estimate that a single photon absorbed within a silicon nanocavity can, within tens of picoseconds, be detected with ∼99% efficiency and a dark count rate on the order of kilohertz assuming a mode volume Veff∼10−2 (λ/nSi)3 for a 4.5-μm probe wavelength and a loaded quality factor Q on the order of 104.
Panuski, C., Pant, M., Heuck, M., Hamerly, R., & Englund, D. (2019). Single photon detection by cavity-assisted all-optical gain. Physical Review B, 99(20), . https://doi.org/10.1103/PhysRevB.99.205303