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Quantum ground state and single-phonon control of a mechanical resonator

Nature volume 464, pages 697703 (01 April 2010) | Download Citation

Abstract

Quantum mechanics provides a highly accurate description of a wide variety of physical systems. However, a demonstration that quantum mechanics applies equally to macroscopic mechanical systems has been a long-standing challenge, hindered by the difficulty of cooling a mechanical mode to its quantum ground state. The temperatures required are typically far below those attainable with standard cryogenic methods, so significant effort has been devoted to developing alternative cooling techniques. Once in the ground state, quantum-limited measurements must then be demonstrated. Here, using conventional cryogenic refrigeration, we show that we can cool a mechanical mode to its quantum ground state by using a microwave-frequency mechanical oscillator—a ‘quantum drum’—coupled to a quantum bit, which is used to measure the quantum state of the resonator. We further show that we can controllably create single quantum excitations (phonons) in the resonator, thus taking the first steps to complete quantum control of a mechanical system.

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References

  1. 1.

    & Quantum Measurement (Cambridge Univ. Press, 1992)

  2. 2.

    , & Quantum limits of cold damping with optomechanical coupling. Eur. Phys. J. D 17, 399–408 (2001)

  3. 3.

    , & Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)

  4. 4.

    & Nanometre-scale displacement sensing using a single electron transistor. Nature 424, 291–293 (2003)

  5. 5.

    & Superconducting qubit storage and entanglement with nanomechanical resonators. Phys. Rev. Lett. 93, 070501 (2004)

  6. 6.

    , , & Approaching the quantum limit of a nanomechanical resonator. Science 304, 74–77 (2004)

  7. 7.

    Quantum electromechanical systems. Phys. Rep. 395, 159–222 (2004)

  8. 8.

    , , & Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)

  9. 9.

    & Sub-kelvin optical cooling of a micromechanical resonator. Nature 444, 75–78 (2006)

  10. 10.

    & Quantum analysis of a linear dc SQUID mechanical displacement detector. Phys. Rev. B 76, 014511 (2007)

  11. 11.

    , , , & Resolved-sideband cooling of a micromechanical oscillator. Nature Phys. 4, 415–419 (2008)

  12. 12.

    , & Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008)

  13. 13.

    , , , & Nanomechanical measurements of a superconducting qubit. Nature 459, 960–964 (2009)

  14. 14.

    et al. Self-cooling of a micromirror by radiation pressure. Nature 444, 67–70 (2006)

  15. 15.

    , , , & Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 71–74 (2006)

  16. 16.

    , , & Theory of ground-state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett. 99, 093901 (2007)

  17. 17.

    , , & Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007)

  18. 18.

    et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008)

  19. 19.

    et al. Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity. Nature Phys. 5, 485–488 (2009)

  20. 20.

    & Resolved-sideband and cryogenic cooling of an optomechanical resonator. Nature Phys. 5, 489–493 (2009)

  21. 21.

    , , , & Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit. Nature Phys. 5, 509–514 (2009)

  22. 22.

    et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 72–75 (2010)

  23. 23.

    et al. State tomography of capacitively shunted phase qubits with high fidelity. Phys. Rev. Lett. 97, 050502 (2006)

  24. 24.

    Superconducting phase qubits. Quantum Inf. Process. 8, 81–103 (2009)

  25. 25.

    , , , & in Proc. 2001 IEEE Ultrasonics Symp. (eds Yuhas, D. E. & Schneider, S. C.) 813–821 (IEEE, 2001)

  26. 26.

    et al. Piezoelectric properties of aluminum nitride for thin film bulk acoustic wave resonator. J. Korean Phys. Soc. 47, S309–S312 (2005)

  27. 27.

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

  28. 28.

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

  29. 29.

    Growth and applications of group-III nitrides. J. Phys. D 31, 2653–2710 (1998)

  30. 30.

    , , , & Quantum mechanics of a macroscopic variable: the phase difference of a Josephson junction. Science 239, 992–997 (1988)

  31. 31.

    et al. Violation of Bell’s inequality in Josephson phase qubits. Nature 461, 504–506 (2009)

  32. 32.

    & Exploring the Quantum: Atoms, Cavities and Photons (Oxford Univ. Press, 2006)

  33. 33.

    , , & Observation of strong coupling between a micromechanical resonator and an optical cavity field. Nature 460, 724–727 (2009)

  34. 34.

    et al. Microwave dielectric loss at single photon energies and millikelvin temperatures. Appl. Phys. Lett. 92, 112903 (2008)

  35. 35.

    , & Landau-Zener interferometry for qubits. Eur. Phys. J. B 36, 263–269 (2003)

  36. 36.

    et al. Mach-Zehnder interferometry in a strongly driven superconducting qubit. Science 310, 1653–1657 (2005)

  37. 37.

    et al. Nonlinear spectroscopy of photons bound to one atom. Nature Phys. 4, 382–385 (2008)

  38. 38.

    , , & in Proc. 2000 IEEE Ultrasonics Symp. (eds Schneider, S. C., Levy, M. & McAvoy, B. R.) 863–868 (IEEE, 2000)

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Acknowledgements

We would like to thank M. Geller for numerous conversations and A. Berube for assistance with resonator fabrication and measurements. This work was supported by the US National Science Foundation (NSF) under grant DMR-0605818 and by the Intelligence Advanced Research Projects Activity under grant W911NF-04-1-0204. Devices were made at the University of California, Santa Barbara, Nanofabrication Facility, which is part of the NSF-funded US National Nanotechnology Infrastructure Network.

Author Contributions A.D.O’C. fabricated the devices and performed the measurements, M.H. providing measurement assistance. A.N.C., A.D.O’C. and J.M.M. conceived and designed the experiment. All authors contributed to providing experimental support and writing the manuscript.

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Affiliations

  1. Department of Physics, University of California, Santa Barbara, California 93106, USA

    • A. D. O’Connell
    • , M. Hofheinz
    • , M. Ansmann
    • , Radoslaw C. Bialczak
    • , M. Lenander
    • , Erik Lucero
    • , M. Neeley
    • , D. Sank
    • , H. Wang
    • , M. Weides
    • , J. Wenner
    • , John M. Martinis
    •  & A. N. Cleland

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The authors declare no competing financial interests.

Corresponding author

Correspondence to A. N. Cleland.

Supplementary information

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  1. 1.

    Supplementary Information

    This Supplementary Information file comprises: (I) Methods - Mechanical Resonator Fabrication; (II) Methods - Qubit-Mechancial Resonator Fabrication; (III) Verification of Mechancial Nature of Resonance; (IV) Qubit Measurement; (V) Qubit Characterization; (VI) Simulations; (VII) Classical Circuit Analyses; and includes Supplementary Figures 1-3 with Legends and Supplementary References.

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https://doi.org/10.1038/nature08967

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