Takuma Makihara, Erik Szakiel, Matthew P Maksymowych, Oliver A Hitchcock, Kaveh Pezeshki, Rachel G Gruenke-Freudenstein, Mihir Pendharkar, Shannon P Harvey, David I Schuster, Amir H Safavi-Naeini
Quantum mechanics predicts that a vibrating object's energy comes in discrete packets, yet no measurement of its position reveals this discreteness. Resolving individual energy levels requires a qualitatively different measurement, one coupling to the resonator's energy rather than its displacement. We use a superconducting qubit dispersively coupled to a nanomechanical resonator to perform repeated quantum nondemolition measurements of the phonon number. An aligned transfer-print technique integrating the qubit and resonator yields a mechanical lifetime of [Formula: see text] milliseconds and a dispersive shift of [Formula: see text] kilohertz per phonon. We heralded single-phonon states with 85% fidelity and observed quantum jumps between the resonator's first excited state and ground state. These discontinuous transitions are a striking manifestation of quantum mechanics in a massive, vibrating object.