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

## Abstract

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 macroscale motional modes1,2,3, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test decoherence mechanisms in macroscale objects and other modifications to standard quantum theory4,5. Many of these applications call for the ability to create and characterize complex quantum states, such as states with a well defined phonon number, also known as phonon Fock states. Such capabilities require fast quantum operations and long coherence times of the mechanical mode. Here we demonstrate the controlled generation of multi-phonon Fock states in a macroscale bulk acoustic-wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states6. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple a superconducting qubit to individual phonon modes. Our work shows that circuit quantum acoustodynamics7 enables sophisticated quantum control of macroscale mechanical objects and opens up the possibility of using acoustic modes as quantum resources.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We thank M. Devoret, S. Girvin, Y. Zhang, K. Chou and V. Jain for discussions. We thank K. Silwa for providing the Josephson parametric converter amplifier. This research was supported by the US Army Research Office (W911NF-14-1-0011), ONR YIP (N00014-17-1-2514), NSF MRSEC (DMR-1119826) and the Packard Fellowship for Science and Engineering. Facility use was provided by the Yale SEAS cleanroom, the Yale West Campus Cleanroom and the Yale Institute for Nanoscience and Quantum Engineering (YINQE).

### Reviewer information

Nature thanks S. Deleglise and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

Y.C. performed the experiment and analysed the data under the supervision of P.T.R. and R.J.S. Y.C., P.K. and L.F. designed and fabricated the device. P.K. and T.Y. provided experimental suggestions and theory support. Y.C., P.K., P.T.R. and R.J.S. wrote the manuscript with contributions from all authors.

### Corresponding authors

Correspondence to Yiwen Chu or Robert J. Schoelkopf.

## Ethics declarations

### Competing interests

R.J.S. and L.F. are founders and equity shareholders of Quantum Circuits, Inc.

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## Supplementary information

### Supplementary Information

The SI is in PDF format and contains the following sections: 1. Fabrication procedures, 2. Acoustic mode simulations, 3. Coherent displacement calibration, 4. Wigner tomography and state reconstruction. There are 4 figures: S1. Fabrication of acoustic resonator chip, S2. Acoustic resonator simulations, S3. Coherent displacements of the phonon mode, S4. Density matricies. The SI also includes 10 references.

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Reprints and Permissions

Chu, Y., Kharel, P., Yoon, T. et al. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666–670 (2018). https://doi.org/10.1038/s41586-018-0717-7

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### Keywords

• Bulk Acoustic Wave Resonators
• Fock State
• Superconducting Qubit
• Complex Quantum States
• Perform Quantum Operations

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