  Quantum states of mechanical motion can be important resources for quantum
information, metrology, and studies of fundamental physics. Recent
demonstrations of superconducting qubits coupled to acoustic resonators have
opened up the possibility of performing quantum operations on macroscopic
motional modes, which can act as long-lived quantum memories or transducers. In
addition, they can potentially be used to test for novel decoherence mechanisms
in macroscopic objects and other modifications to standard quantum theory. Many
of these applications call for the ability to create and characterize complex
quantum states, putting demanding requirements on the speed of quantum
operations and the coherence of the mechanical mode. In this work, we
demonstrate the controlled generation of multi-phonon Fock states in a
macroscopic bulk-acoustic wave resonator. We also perform Wigner tomography and
state reconstruction to highlight the quantum nature of the prepared states.
These demonstrations are made possible by the long coherence times of our
acoustic resonator and our ability to selectively couple to individual phonon
modes. Our work shows that circuit quantum acousto-dynamics (circuit QAD)
enables sophisticated quantum control of macroscopic mechanical objects and
opens the door to using acoustic modes as novel quantum resources.
