  We study the crucial role played by the solid-state environment in
determining the photon emission characteristics of a driven quantum dot. For
resonant driving, we predict a phonon-enhancement of the coherently emitted
radiation field with increasing driving strength, in stark contrast to the
conventional expectation of a rapidly decreasing fraction of coherent emission
with stronger driving. This surprising behaviour results from thermalisation of
the dot with respect to the phonon bath, and leads to a nonstandard regime of
resonance fluorescence in which significant coherent scattering and the Mollow
triplet coexist. Off-resonance, we show that despite the phonon influence,
narrowing of dot spectral sideband widths can occur in certain regimes,
consistent with an experimental trend.
