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 this field, 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 a 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.

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