Fourier synthesis and timbre tuning of radio frequency nanomechanical pulses

The concept of Fourier synthesis provides the foundation for both everyday consumer electronic products and fundamental research. In the latter, so called pulse shaping is nowadays key to dynamically initialize, probe and manipulate the state of classical or quantum systems. In nuclear magnetic resonance, for instance, shaped pulses have a long-standing tradition and the underlying fundamental concepts have subsequently been successfully extended to optical frequencies and even to implement quantum gate operations. Transfer of these paradigms to nanomechanical systems, requires tailored nanomechanical waveforms (NMWFs) for mechanically mediated coherent control schemes. Here, we report on a novel additive Fourier synthesizer for NMWFs based on monochromatic surface acoustic waves (SAWs). As a proof of concept, we electrically synthesize four different elementary NMWFs from a fundamental SAW at $ f_1 \sim 150$ MHz using a superposition of up to three discrete harmonics $f_n$. We employ these shaped pulses to interact with an individual sensor quantum dot (QD) and detect their deliberately and temporally modulated strain component via the opto-mechanical QD response. As a very attractive feature and in contrast to the commonly applied direct mechanical actuation by bulk piezoactuators, SAWs provide more than two orders of magnitude larger frequencies > 20 GHz to resonantly drive mechanical motion. Thus, our technique uniquely allows coherent mechanical control of localized vibronic modes of optomechanical and phoXonic crystals, most tantalizing even in the quantum limit when cooled to the vibrational ground state.