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arXiv:2610.10714 · Science

Quantum jumps of sound

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

quant-phSubmitted Oct 7, 2026• Announced Oct 9, 2026• 0 citations
arXivHTMLPDF

Abstract

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 $T_1 = 2.1$ milliseconds and a dispersive shift of $2χ/2π= 328$ 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.

Journal reference
Takuma Makihara et al., Quantum jumps of sound. Science 393, 1217-1220 (2026)
DOI
10.1126/science.aeh7535
Comments
12 pages, 11 figures

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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 T1=2.1T_1 = 2.1T1​=2.1 milliseconds and a dispersive shift of 2χ/2π=3282χ/2π= 3282χ/2π=328 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.
Atoms, ions, and superconducting qubits are all examples of quantum objects, capable of producing and processing individual quanta of light, known as photons. Mechanical movement can be quantized in the same way as light, into particles of vibration known as phonons. Recent experiments have shown that quantum information generated in qubits can be converted to vibrations in mechanical resonators, which resemble miniature drum skins or piano strings. Such resonators restrict motion to their discrete and stationary modes, and thus serve as \emph{local storage units} for phonons. Here, we demonstrate the use of phonons as \emph{propagating carriers} of quantum information, by coupling them strongly to a superconducting qubit. The phonons thus serve the same role as itinerant photons have in the field of quantum optics. Due to the low speed of sound and a potential for very strong coupling, the use of propagating phonons as quantum carriers allows regimes to be explored which are difficult or impossible to reach with photons.
We use the strong intrinsic nonlinearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micromechanical oscillator vibrating at 25 MHz. The qubit and the oscillator are coupled electrostatically at a rate of approximately 2π×22 MHz. In this far off-resonant regime, the qubit frequency is shifted by 0.52 MHz per oscillator phonon, or about 14% of the 3.7 MHz qubit linewidth. The qubit behaves as a vibrational energy detector and from its line shape we extract the phonon number distribution of the oscillator. We manipulate this distribution by driving number state sensitive sideband transitions and creating profoundly nonthermal states. Finally, by driving the lower frequency sideband transition, we cool the oscillator and increase its ground state population up to 0.48±0.13, close to a factor of 8 above its value at thermal equilibrium. These results demonstrate a new class of electromechanics experiments that are a promising strategy for quantum nondemolition measurements and nonclassical state preparation.
The coupled dynamics of a nanomechanical resonator and superconducting quantum circuits are studied in three experiments, in the context of studying the quantum limit for force detection and quantum physics of macroscopic objects. In the first experiment, the dispersive mechanical resonance shift from the interaction with a Cooper-pair box qubit is studied. The measured coupling strength is large enough to satisfy one of the conditions required to perform many of the proposed quantum nanomechanical measurements. The resonance shift also probes the microwave-driven response of the qubit, showing Rabi oscillation and Landau-Zener tunneling, proving the coherent dynamics of the qubit. Second, the parametric excitation of nanomechanical motion is studied via experiments with a driven qubit. Degenerate parametric amplification and oscillation are demonstrated, with a new observation of nonlinear dissipation. The squeezing of the back-action noise from the detection amplifier is also observed, up to 4dB. It is the first demonstration using a qubit as an auxiliary system to modify the nanomechanical dynamics, showing a possible route for generation of nanomechanical quantum states. Finally, back-action cooling of nanomechanical motion has been investigated, which is implemented by capacitively coupling a high-Q coplanar waveguide microwave resonator to a nanomechanical resonator. The thermal state with 7.5 mechanical quanta on average is reached, a result that is ultimately limited due to increased bath heating with microwave power. The heating is consistent with a model based on two-level systems resonantly coupled to the nanomechanical mode. This additional heating suggests future efforts to improve coupling and for reducing two-level system density in materials employed to reach the motional ground state via back-action cooling.
Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit-oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit-oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.
Mechanical objects have important practical applications in the fields of quantum information and metrology as quantum memories or transducers for measuring and connecting different types of quantum systems. The field of electromechanics is in pursuit of a robust and highly coherent device that couples motion to nonlinear quantum objects such as superconducting qubits. Here, we experimentally demonstrate a high-frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction with a cooperativity of 260. We measure qubit and mechanical coherence times on the order of 10 microseconds. Our device requires only simple fabrication methods and provides controllable access to a multitude of phonon modes. We demonstrate quantum control and measurement on gigahertz phonons at the single-quantum level.
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