Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Cooling a nanomechanical resonator with quantum back-action

Nature volume 443, pages 193–196 (2006)Cite this article

Abstract

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action1,2,3. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK—an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Nanodevice and measurement diagram.
Figure 2: Resonator temperature versus bath temperature and coupling voltage.
Figure 3: Resonator damping rate and frequency shift versus coupling voltage.
Figure 4: Back-action effects versus SSET bias point.

Similar content being viewed by others

References

  1. Caves, C. M. Quantum limits on noise in linear amplifiers. Phys. Rev. D 26, 1817–1839 (1982)

    Article  ADS  Google Scholar 

  2. Braginsky, V. B. & Khalili, F. Ya. Quantum Measurement (Cambridge Univ. Press, Cambridge, 1995)

    MATH  Google Scholar 

  3. Clerk, A. A. Quantum-limited position detection and amplification: A linear response perspective. Phys. Rev. B 70, 245306 (2004)

    Article  ADS  Google Scholar 

  4. Abbott, B. et al. Upper limits on gravitational wave bursts in LIGO's second science run. Phys. Rev. D 72, 062001 (2005)

    Article  ADS  Google Scholar 

  5. Rugar, D., Budakian, R., Mamin, H. J. & Chui, B. W. Single spin detection by magnetic resonance force microscopy. Nature 430, 329–332 (2004)

    Article  CAS  ADS  Google Scholar 

  6. Tittonen, I. et al. Interferometric measurements of the position of a macroscopic body: Towards observations of quantum limits. Phys. Rev. A 59, 1038–1044 (1999)

    Article  CAS  ADS  Google Scholar 

  7. LaHaye, M. D., Buu, O., Camarota, B. & Schwab, K. C. Approaching the quantum limit of a nanomechanical resonator. Science 304, 74–77 (2004)

    Article  CAS  ADS  Google Scholar 

  8. Schoelkopf, R. J., Wahlgren, P., Kozhevnikov, A. A., Delsing, P. & Prober, D. The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer. Science 280, 1238–1242 (1998)

    Article  CAS  ADS  Google Scholar 

  9. Fulton, T. A., Gammel, P. L., Bishop, D. J., Dunkleberger, L. N. & Dolan, G. J. Observation of combined Josephson and charging effects in small tunnel junction circuits. Phys. Rev. Lett. 63, 1307–1310 (1989)

    Article  CAS  ADS  Google Scholar 

  10. Clerk, A. A. & Bennett, S. Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects. N. J. Phys. 7, 238 (2005)

    Article  Google Scholar 

  11. Blencowe, M. P., Imbers, J. & Armour, A. D. Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor. N. J. Phys. 7, 236 (2005)

    Article  Google Scholar 

  12. Mozyrsky, D., Martin, I. & Hastings, M. B. Quantum-limited sensitivity of single-electron-transistor-based displacement detectors. Phys. Rev. Lett. 92, 018303 (2004)

    Article  CAS  ADS  Google Scholar 

  13. Armour, A. D., Blencowe, M. P. & Zhang, Y. Classical dynamics of a nanomechanical resonator coupled to a single-electron transistor. Phys. Rev. B 69, 125313 (2004)

    Article  ADS  Google Scholar 

  14. Mozyrsky, D. & Martin, I. Quantum-classical transition induced by electrical measurement. Phys. Rev. Lett. 89, 018301 (2002)

    Article  CAS  ADS  Google Scholar 

  15. Ojha, R. P., Lemieux, P.-A., Dixon, P. K., Liu, A. J. & Durian, D. J. Statistical mechanics of a gas-fluidized particle. Nature 427, 521–523 (2004)

    Article  CAS  ADS  Google Scholar 

  16. Clerk, A. A., Girvin, S. M., Nguyen, A. K. & Stone, A. D. Resonant Cooper-pair tunneling: quantum noise and measurement characteristics. Phys. Rev. Lett. 89, 176804 (2002)

    Article  CAS  ADS  Google Scholar 

  17. Gavish, U., Levinson, Y. & Imry, Y. Detection of quantum noise. Phys. Rev. B 62, R10637 (2000)

    Article  CAS  ADS  Google Scholar 

  18. Schoelkopf, R. J., Clerk, A. A., Girvin, S. M., Lehnert, K. W. & Devoret, M. H. in Quantum Noise is Mesoscopic Physics (Kluwer Academic, Norwell, Massachusetts, 2003)

    Google Scholar 

  19. Deblock, R., Onac, E., Gurevich, L. & Kouwenhoven, L. P. Detection of quantum noise from an electrically driven two-level system. Science 301, 203–206 (2003)

    Article  CAS  ADS  Google Scholar 

  20. Braginsky, V. B. & Vyatchanin, S. P. Low quantum noise tranquilizer for Fabry-Perot interferometer. Phys. Lett. A 293, 228–234 (2002)

    Article  CAS  ADS  Google Scholar 

  21. Lett, P. D. et al. Optical molasses. J. Opt. Soc. Am. B 6, 2084–2107 (1989)

    Article  CAS  ADS  Google Scholar 

  22. Pohlen, S. L., Fitzgerald, R. J. & Tinkham, M. The Josephson-quasiparticle (JQP) current cycle in the superconducting single-electron transistor. Physica B 284–288, 1812–1813 (2000)

    Article  ADS  Google Scholar 

  23. Choi, M.-S., Plastina, F. & Fazio, R. Charge and current fluctuations in a superconducting single-electron transistor near a Cooper pair resonance. Phys. Rev. B 67, 045105 (2003)

    Article  ADS  Google Scholar 

  24. Ruskov, R., Schwab, K. & Korotkov, A. N. Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback. Phys. Rev. B 71, 235407 (2005)

    Article  ADS  Google Scholar 

  25. Armour, A. D., Blencowe, M. P. & Schwab, K. C. Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)

    Article  CAS  ADS  Google Scholar 

  26. Irish, E. K. & Schwab, K. Quantum measurement of a coupled nanomechanical resonator-Cooper-pair box system. Phys. Rev. B 68, 155311 (2003)

    Article  ADS  Google Scholar 

  27. Martin, I., Shnirman, A., Tian, L. & Zoller, P. Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)

    Article  ADS  Google Scholar 

  28. Wilson-Rae, I., Zoller, P. & Imamoglu, A. Laser cooling of a nanomechanical resonator mode to its quantum ground state. Phys. Rev. Lett. 92, 075507 (2004)

    Article  CAS  ADS  Google Scholar 

  29. Lundin, U. Localized heating or cooling in mesocopic devices by electron transport. Phys. Lett. A 332, 127–130 (2004)

    Article  CAS  ADS  Google Scholar 

  30. Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

We thank A. Rimberg and A. Vandaley for discussions, and B. Camarota for assistance with the fabrication of the samples. M.P.B. is supported by the NSF through an NIRT grant, A.D.A. is supported by the EPSRC, and A.A.C. is supported by NSERC. Author Contributions A.N. and O.B. contributed equally to this work.

Author information

Authors and Affiliations

  1. Laboratory for Physical Sciences,

    A. Naik, O. Buu, M. D. LaHaye & K. C. Schwab

  2. Department of Electrical and Computer Engineering,

    A. Naik

  3. Department of Physics, University of Maryland, Maryland, 20740, College Park, USA

    O. Buu & M. D. LaHaye

  4. School of Physics and Astronomy, University of Nottingham, NG7 2RD, Nottingham, UK

    A. D. Armour

  5. Department of Physics, McGill University, QC H3A 2T8, Montreal, Canada

    A. A. Clerk

  6. Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, 03755, USA

    M. P. Blencowe

Authors
  1. A. Naik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Buu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. D. LaHaye
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. D. Armour
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. A. Clerk
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. P. Blencowe
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. K. C. Schwab
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. C. Schwab.

Ethics declarations

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Notes

This file contains details of the nanoelectromechanical device, both electronic and mechanical properties and describes the calibration procedure, noise thermometry, data analysis, and the analysis of the backaction and comparison to the quantum limit. This file also contains figures that show the SSET bias points used and typical noise spectra. (DOC 689 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Naik, A., Buu, O., LaHaye, M. et al. Cooling a nanomechanical resonator with quantum back-action. Nature 443, 193–196 (2006). https://doi.org/10.1038/nature05027

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature05027

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing