  We fabricated an acousto-optic semiconductor hybrid device for strong
optomechanical coupling of individual quantum emitters and a surface acoustic
wave. Our device comprises a surface acoustic wave chip made from highly
piezoelectric LiNbO$_3$ and a GaAs-based semiconductor membrane with an
embedded layer of quantum dots. Employing multi-harmonic transducers, we
generated sound waves on LiNbO$_3$ over a wide range of radio frequencies. We
monitored their coupling to and propagation across the semiconductor membrane
both in the electrical and optical domain. We demonstrate enhanced
optomechanical tuning of the embedded quantum dots with increasing frequencies.
This effect was verified by finite element modelling of our device geometry and
attributed to an increased localization of the acoustic field within the
semiconductor membrane. For moderately high acoustic frequencies, our
simulations predict strong optomechanical coupling making our hybrid device
ideally suited for applications in semiconductor based quantum acoustics.
