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Incoherent pumping in quantum dots (QDs) can create a biexciton state throughtwo paths: via the formation of bright or dark exciton states. The latter,dark-pumping, path is shown to enhance the probability of two-photonsimultaneous emission, and hence increase $g^{(2)}(0)$ by a factor $\propto1/\gamma_S$, due to the slow spin relaxation rate $\gamma_S$ in QDs. Theexistence of the dark path is shown to impose a limitation on the single photon(SP) emission process, especially in nanocavities which exhibit a largeexciton-cavity coupling and a Purcell enhancement for fast quantumtelecommunications.

Impact of the dark path on quantum dot single photon emitters in small cavities