  We demonstrate that, even when employing above-band excitation, photons
emitted from semiconductor quantum dots can have linewidths that approach their
transform-limited values. This is accomplished by using quantum dots embedded
in bottom-up photonic nanowires, an approach which mitigates several potential
mechanisms that can result in linewidth broadening: (i) only a single quantum
dot is present in each device, (ii) dot nucleation proceeds without the
formation of a wetting layer, and (iii) the sidewalls of the photonic nanowire
are comprised not of etched facets, but of epitaxially grown crystal planes.
Using these structures we achieve linewidths of 2x the transform limit,
unprecedented for above-band excitation. We also demonstrate a highly nonlinear
dependence of the linewidth on both excitation power and temperature which can
be described by an independent Boson model that considers both deformation and
piezoelectric exciton-phonon coupling. We find that for sufficiently low
excitation powers and temperatures, the observed excess broadening is not
dominated by phonon dephasing, a surprising result considering the high phonon
occupation that occurs with above-band excitation.
