Multiphonon transitions in a quantum electromechanical system

We investigate and measure the multiphonon transitions of a system comprised of a superconducting qubit coupled to a high overtone bulk acoustic resonator (HBAR). The measured spectrums are found to show distinctly non-classical features, providing additional evidence for the quantization of GHz sound. These multiphonon peaks are found to shift with higher driving amplitude which is explained by the dressing of many multiphonon transitions, and a model is derived to calculate these shifts.