Fourier synthesis of radiofrequency nanomechanical pulses with different shapes

The concept of Fourier synthesis1 is heavily used in both consumer electronic products2 and fundamental research3. In the latter, pulse shaping is key to dynamically initializing, probing and manipulating the state of classical or quantum systems. In NMR, for instance, shaped pulses have a long-standing tradition4 and the underlying fundamental concepts have subsequently been successfully extended to optical frequencies3, 5 and even to the implementation of quantum gate operations6. Transferring these paradigms to nanomechanical systems requires tailored nanomechanical waveforms. Here, we report on an additive Fourier synthesizer for nanomechanical waveforms based on monochromatic surface acoustic waves. As a proof of concept, we electrically synthesize four different elementary nanomechanical waveforms from a fundamental surface acoustic wave at f1 ≈ 150 MHz using a superposition of up to three discrete harmonics. We use these shaped pulses to interact with an individual sensor quantum dot and detect their deliberately and temporally modulated strain component via the optomechanical quantum dot response7, 8, 9. Importantly, and in contrast to direct mechanical actuation by bulk piezoactuators7, surface acoustic waves provide much higher frequencies (>20 GHz; ref. 10) to resonantly drive mechanical motion11. Thus, our technique uniquely allows coherent mechanical control12 of localized vibronic modes of optomechanical crystals13, 14, even in the quantum limit when cooled to the vibrational ground state15.