  Surface acoustic waves (SAWs) coupled to quantum dots (QDs), trapped atoms
and ions, and point defects have been proposed as quantum transduction
platforms, yet the requisite coupling rates and cavity lifetimes have not been
experimentally established. Although the interaction mechanism varies, small
acoustic cavities with large zero-point motion are required for high
efficiencies. We experimentally establish the feasibility of this platform
through electro- and opto-mechanical characterization of tightly focusing,
single-mode Gaussian SAW cavities at $\sim$3.6 GHz on GaAs. We explore the
performance limits of the platform by fabricating SAW cavities with mode
volumes approaching 6$\lambda^3$ and linewidths $\leq$1 MHz. Employing
strain-coupled single InAs QDs as optomechanical intermediaries, we measure
single-phonon optomechanical coupling rates $g_0 \approx 2\pi \times 1.2$ MHz.
Sideband scattering rates thus exceed intrinsic phonon loss, indicating the
potential for quantum optical readout and transduction of cavity phonon states.
To demonstrate the feasibility of this platform for low-noise ground-state
quantum transduction, we develop a fiber-based confocal microscope in a
dilution refrigerator and perform single-QD resonance fluorescence sideband
spectroscopy at mK temperatures. These measurements show conversion between
microwave phonons and optical photons with sub-natural linewidths.
