We investigate a tradeoff relation between the internal generation efficiency and the escape efficiency for single-photon generation based on cavity quantum electrodynamics, where cavity internal loss is treated explicitly. Consequently, we analytically derive an upper bound on the overall efficiency. The bound is expressed only with an internal cooperativity, introduced here as the cooperativity parameter with respect to the cavity internal loss rate. This result means that the internal cooperativity is a figure of merit for single-photon generation based on cavity QED. The bound is derived by optimizing the cavity external loss rate, which can be experimentally controlled by designing or tuning the transmissivity of the output coupler. The model here is general enough to treat various cavity-QED effects, such as the Purcell effect, on-resonant or off-resonant cavity-enhanced Raman scattering, and vacuum-stimulated Raman adiabatic passage. For typical optical systems, we additionally take into account a "reexcitation" process, where the atom is reexcited after its decay to the initial ground state.
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