  The desire to produce high-quality single photons for applications in quantum
information science has lead to renewed interest in exploring solid-state
emitters in the weak excitation regime. Under these conditions it is expected
that photons are coherently scattered, and so benefit from a substantial
suppression of detrimental interactions between the source and its surrounding
environment. Nevertheless, we demonstrate here that this reasoning is
incomplete, as phonon interactions continue to play a crucial role in
determining solid-state emission characteristics even for very weak excitation.
We find that the sideband resulting from non-Markovian relaxation of the phonon
environment is excitation strength independent. It thus leads to an intrinsic
limit to the fraction of coherently scattered light and to the visibility of
two-photon coalescence at weak driving, both of which are absent for atomic
systems or within simpler Markovian treatments.
