  A promising route towards the heralded creation and annihilation of
single-phonons is to couple a single-photon emitter to a mechanical resonator.
The challenge lies in reaching the resolved-sideband regime with a large
coupling rate and a high mechanical quality factor. We achieve all of this by
coupling self-assembled InAs quantum dots to a small-mode-volume
phononic-crystal resonator with mechanical frequency $\Omega_\mathrm{m}/2\pi =
1.466~\mathrm{GHz}$ and quality factor $Q_\mathrm{m} = 2.1\times10^3$. Thanks
to the high coupling rate of $g_\mathrm{ep}/2\pi = 2.9~\mathrm{MHz}$, and by
exploiting a matching condition between the effective Rabi and mechanical
frequencies, we are able to observe the interaction between the two systems.
Our results represent a major step towards quantum control of the mechanical
resonator via a single-photon emitter.
