Multiphonon transitions in a quantum electromechanical system

We investigate a superconducting qubit coupled to a quantum acoustic system in a near resonant configuration. In our system we measure multiphonon transitions, whose spectrum reveals distinctly nonclassical features and thus provides direct evidence of quantization of GHz sound, enabling phonon counting. Additionally, at a high driving amplitude comparable to the qubit-oscillator coupling, we observe a shift of the multiphonon spectral lines owing to dressing of many multiphonon transitions.