  Hybrid systems consisting of a quantum emitter coupled to a mechanical
oscillator are receiving increasing attention for fundamental science and
potential applications in quantum technologies. In contrast to most of the
presented works, in which the oscillator eigenfrequencies are irreversibly
determined by the fabrication process, we present here a simple approach to
obtain frequency-tunable mechanical resonators based on suspended
nanomembranes. The method relies on a micromachined piezoelectric actuator,
which we use both to drive resonant oscillations of a suspended Ga(Al)As
membrane with embedded quantum dots and to fine tune their mechanical
eigenfrequencies. Specifically, we excite oscillations with frequencies of at
least 60 MHz by applying an AC voltage to the actuator and tune the
eigenfrequencies by at least 25 times their linewidth by continuously varying
the elastic stress state in the membranes through a DC voltage. The light
emitted by optically excited quantum dots is used as sensitive local strain
gauge to monitor the oscillation frequency and amplitude. We expect that our
method has the potential to be applicable to other optomechanical systems based
on dielectric and semiconductor membranes possibly operating in the quantum
regime.
