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Quantum states of mechanical motion can be important resources for quantuminformation, metrology, and studies of fundamental physics. Recentdemonstrations of superconducting qubits coupled to acoustic resonators haveopened up the possibility of performing quantum operations on macroscopicmotional modes, which can act as long-lived quantum memories or transducers. Inaddition, they can potentially be used to test for novel decoherence mechanismsin macroscopic objects and other modifications to standard quantum theory. Manyof these applications call for the ability to create and characterize complexquantum states, putting demanding requirements on the speed of quantumoperations and the coherence of the mechanical mode. In this work, wedemonstrate the controlled generation of multi-phonon Fock states in amacroscopic bulk-acoustic wave resonator. We also perform Wigner tomography andstate reconstruction to highlight the quantum nature of the prepared states.These demonstrations are made possible by the long coherence times of ouracoustic resonator and our ability to selectively couple to individual phononmodes. Our work shows that circuit quantum acousto-dynamics (circuit QAD)enables sophisticated quantum control of macroscopic mechanical objects andopens the door to using acoustic modes as novel quantum resources.

Creation and control of multi-phonon Fock states in a bulk acoustic wave resonator