  Recently, Grange et al. [Phys. Rev. Lett. 114, 193601 (2015)] showed the
possibility of single photon generation with high indistinguishability from a
quantum emitter, despite strong pure dephasing, by `funneling' emission into a
photonic cavity. Here, we show that cascaded two-cavity system can further
improve the photon characteristics and greatly reduce the Q-factor requirement
to levels achievable with present-day technology. Our approach leverages recent
advances in nanocavities with ultrasmall mode volume and does not require
ultrafast excitation of the emitter. These results were obtained by numerical
and closed-form analytical models with strong emitter dephasing, representing
room-temperature quantum emitters.
