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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Fig. 1: The ħBAR device and strong qubit–phonon coupling.
Fig. 2: Mode structure of the ħBAR.
Fig. 3: Climbing the phonon Fock state ladder.
Fig. 4: Wigner tomography of non-classical states of motion.

Data availability

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

References

  1. 1.

    O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).

    ADS  Article  Google Scholar 

  2. 2.

    Moores, B. A., Sletten, L. R., Viennot, J. J. & Lehnert, K. W. Cavity quantum acoustic device in the multimode strong coupling regime. Phys. Rev. Lett. 120, 227701 (2018).

    ADS  Article  Google Scholar 

  3. 3.

    Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).

    ADS  MathSciNet  CAS  Article  Google Scholar 

  4. 4.

    Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nat. Phys. 10, 271–277 (2014).

    CAS  Article  Google Scholar 

  5. 5.

    Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996).

    ADS  CAS  Article  Google Scholar 

  7. 7.

    Manenti, R. et al. Circuit quantum acoustodynamics with surface acoustic waves. Nat. Commun. 8, 975 (2017).

    ADS  Article  Google Scholar 

  8. 8.

    Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Lee, K. C. et al. Entangling macroscopic diamonds at room temperature. Science 334, 1253–1256 (2011).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Riedinger, R. et al. Remote quantum entanglement between two micromechanical oscillators. Nature 556, 473–477 (2018).

    ADS  CAS  Article  Google Scholar 

  12. 12.

    Ockeloen-Korppi, C. F. et al. Stabilized entanglement of massive mechanical oscillators. Nature 556, 478–482 (2018).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Gustafsson, M. V. et al. Propagating phonons coupled to an artificial atom. Science 346, 207–211 (2014).

    ADS  CAS  Article  Google Scholar 

  14. 14.

    Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014).

    CAS  Article  Google Scholar 

  15. 15.

    Schuetz, M. J. A. et al. Universal quantum transducers based on surface acoustic waves. Phys. Rev. X 5, 031031 (2015).

    Google Scholar 

  16. 16.

    Naik, R. K. et al. Random access quantum information processors using multimode circuit quantum electrodynamics. Nat. Commun. 8, 1904 (2017); publisher correction 9, 172 (2018).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Leghtas, Z. et al. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett. 111, 120501 (2013).

    ADS  Article  Google Scholar 

  18. 18.

    Chou, K. S. et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 368–373 (2018).

    CAS  Article  Google Scholar 

  19. 19.

    Satzinger, K. J. et al. Quantum control of surface acoustic-wave phonons. Nature https://doi.org/10.1038/s41586-018-0719-5 (2018).

    Google Scholar 

  20. 20.

    Hofheinz, M. et al. Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Royer, A. Wigner function as the expectation value of a parity operator. Phys. Rev. A 15, 449–450 (1977).

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

    Gambetta, J. et al. Qubit-photon interactions in a cavity: measurement-induced dephasing and number splitting. Phys. Rev. A 74, 042318 (2006).

    ADS  Article  Google Scholar 

  24. 24.

    Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007).

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Heeres, R. W. et al. Implementing a universal gate set on a logical qubit encoded in an oscillator. Nat. Commun. 8, 94 (2017).

    ADS  Article  Google Scholar 

  26. 26.

    Kharel, P. et al. Ultra-high-Q phononic resonators on-chip at cryogenic temperatures. APL Photonics 3, 066101 (2018).

    ADS  Article  Google Scholar 

  27. 27.

    Penrose, R. On gravity’s role in quantum state reduction. Gen. Relativ. Gravit. 28, 581–600 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  28. 28.

    Pikovski, I., Vanner, M. R., Aspelmeyer, M., Kim, M. S. & Brukner, V. Probing planck-scale physics with quantum optics. Nat. Physics 8, 393–397 (2012).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Marin, F. et al. Gravitational bar detectors set limits to Planck-scale physics on macroscopic variables. Nat. Phys. 9, 71–73 (2013).

    CAS  Article  Google Scholar 

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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).

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

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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.

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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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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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