  A quantum dot coupled to an optical cavity has recently proven to be an
excellent source of on-demand single photons. Typically, applications require
simultaneous high efficiency of the source and quantum indistinguishability of
the extracted photons. While much progress has been made both in suppressing
background sources of decoherence and utilizing cavity-quantum electrodynamics
to overcome fundamental limitations set by the intrinsic exciton-phonon
scattering inherent in the solid-state platform, the role of the excitation
pulse has been often neglected. We investigate quantitatively the factors
associated with pulsed excitation that can limit simultaneous efficiency and
indistinguishability, including excitation of multiple excitons, multi-photons,
and pump-induced dephasing, and find for realistic single photon sources that
these effects cause degradation of the source figures-of-merit comparable to
that of phonon scattering. We also develop rigorous open quantum system polaron
master equation models of quantum dot dynamics under a time-dependent drive
which incorporate non-Markovian effects of both photon and phonon reservoirs,
and explicitly show how coupling to a high Q-factor cavity suppresses
multi-photon emission in a way not predicted by commonly employed models. We
then use our findings to summarize the criteria that can be used for single
photon source optimization.
