  We present experiments in which self-assembled InAs quantum dots are coupled
to a thin, suspended-beam GaAs resonator. The quantum dots are driven
resonantly and the resonance fluorescence is detected. The narrow quantum-dot
linewidths, just a factor of three larger than the transform limit, result in a
high sensitivity to the mechanical motion. We show that one quantum dot couples
to eight mechanical modes spanning a frequency range from $30$ to
$600~\mathrm{MHz}$: one quantum dot provides an extensive characterisation of
the mechanical resonator. The coupling spans the unresolved-sideband to the
resolved-sideband regimes. Finally, we present the first detection of
thermally-driven phonon sidebands (at $4.2~\mathrm{K}$) in the
resonance-fluoresence spectrum.
