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:

Microwave amplification with nanomechanical resonators

Nature volume 480, pages 351–354 (2011)Cite this article

Subjects

Abstract

The sensitive measurement of electrical signals is at the heart of modern technology. According to the principles of quantum mechanics, any detector or amplifier necessarily adds a certain amount of noise to the signal, equal to at least the noise added by quantum fluctuations1,2. This quantum limit of added noise has nearly been reached in superconducting devices that take advantage of nonlinearities in Josephson junctions3,4. Here we introduce the concept of the amplification of microwave signals using mechanical oscillation, which seems likely to enable quantum-limited operation. We drive a nanomechanical resonator with a radiation pressure force5,6,7, and provide an experimental demonstration and an analytical description of how a signal input to a microwave cavity induces coherent stimulated emission and, consequently, signal amplification. This generic scheme, which is based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices. In our device, we achieve signal amplification of 25 decibels with the addition of 20 quanta of noise, which is consistent with the expected amount of added noise. The generality of the model allows for realization in other physical systems as well, and we anticipate that near-quantum-limited mechanical microwave amplification will soon be feasible in various applications involving integrated electrical circuits.

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: Electromechanical microwave amplification.
Figure 2: Amplification mechanism.
Figure 3: Amplifier gain.

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. Haus, H. A. Electromagnetic Noise and Quantum Optical Measurements 267–277 (Advanced Texts in Physics, Springer, 2000)

    Book  Google Scholar 

  3. Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008)

    Article  ADS  Google Scholar 

  4. Bergeal, N. et al. Phase-preserving amplification near the quantum limit with a Josephson ring modulator. Nature 465, 64–68 (2010)

    Article  ADS  CAS  Google Scholar 

  5. Braginsky, V. B., Strigin, S. E. & Vyatchanin, S. P. Parametric oscillatory instability in Fabry-Perot interferometer. Phys. Lett. A 287, 331–338 (2001)

    Article  ADS  CAS  Google Scholar 

  6. Metzger, C. H. & Karrai, K. Cavity cooling of a microlever. Nature 432, 1002–1005 (2004)

    Article  ADS  CAS  Google Scholar 

  7. Kippenberg, T. J., Rokhsari, H., Carmon, T., Scherer, A. & Vahala, K. J. Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett. 95, 033901 (2005)

    Article  ADS  CAS  Google Scholar 

  8. Yurke, B. et al. Observation of 4.2-K equilibrium-noise squeezing via a Josephson-parametric amplifier. Phys. Rev. Lett. 60, 764–767 (1988)

    Article  ADS  CAS  Google Scholar 

  9. André, M. O., Mück, M., Clarke, J., Gail, J. & Heiden, C. Radio-frequency amplifier with tenth-kelvin noise temperature based on a microstrip direct current superconducting quantum interference device. Appl. Phys. Lett. 75, 698–700 (1999)

    Article  ADS  Google Scholar 

  10. Raskin, J. P., Brown, A. R., Khuri-Yakub, B. T. & Rebeiz, G. M. A novel parametric-effect MEMS amplifier. J. Microelectromech. Syst. 9, 528–537 (2000)

    Article  CAS  Google Scholar 

  11. Leggett, A. J. Testing the limits of quantum mechanics: motivation, state of play, prospects. J. Phys. Condens. Matter 14, R415–R451 (2002)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008)

    Article  CAS  Google Scholar 

  15. Sillanpää, M. A., Sarkar, J., Sulkko, J., Muhonen, J. & Hakonen, P. J. Accessing nanomechanical resonators via a fast microwave circuit. Appl. Phys. Lett. 95, 011909 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  17. Marquardt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007)

    Article  ADS  Google Scholar 

  18. Wilson-Rae, I., Nooshi, N., Zwerger, W. & Kippenberg, T. J. Theory of ground state cooling of a mechanical oscillator using dynamical backaction. Phys. Rev. Lett. 99, 093901 (2007)

    Article  ADS  CAS  Google Scholar 

  19. Sulkko, J. et al. Strong gate coupling of high-Q nanomechanical resonators. Nano Lett. 10, 4884–4889 (2010)

    Article  ADS  CAS  Google Scholar 

  20. Mancini, S. & Tombesi, P. Quantum-noise reduction by radiation pressure. Phys. Rev. A 49, 4055–4065 (1994)

    Article  ADS  CAS  Google Scholar 

  21. Genes, C., Vitali, D., Tombesi, P., Gigan, S. & Aspelmeyer, M. Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes. Phys. Rev. A 77, 033804 (2008)

    Article  ADS  Google Scholar 

  22. Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  23. Rugar, D. & Grütter, P. Mechanical parametric amplification and thermomechanical noise squeezing. Phys. Rev. Lett. 67, 699–702 (1991)

    Article  ADS  CAS  Google Scholar 

  24. Woolley, M. J., Doherty, A. C., Milburn, G. J. & Schwab, K. C. Nanomechanical squeezing with detection via a microwave cavity. Phys. Rev. A 78, 062303 (2008)

    Article  ADS  Google Scholar 

  25. Carr, D. W., Evoy, S., Sekaric, L., Craighead, H. G. & Parpia, J. M. Parametric amplification in a torsional microresonator. Appl. Phys. Lett. 77, 1545–1547 (2000)

    Article  ADS  CAS  Google Scholar 

  26. Arcizet, O., Cohadon, P. F., Briant, T., Pinard, M. & Heidmann, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 71–74 (2006)

    Article  ADS  CAS  Google Scholar 

  27. Safavi-Naeini, A. H. et al. Electromagnetically induced transparency and slow light with optomechanics. Nature 472, 69–73 (2011)

    Article  ADS  CAS  Google Scholar 

  28. Weis, S. et al. Optomechanically induced transparency. Science 330, 1520–1523 (2010)

    Article  ADS  CAS  Google Scholar 

  29. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011)

    Article  ADS  CAS  Google Scholar 

  30. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We would like to thank S. Paraoanu and H. Seppä for discussions. This work was supported by the Academy of Finland and by the European Research Council (grant numbers 240362-Heattronics and 240387-NEMSQED) and EU-FP7-NMP-246026.

Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Aalto University, PO Box 15100, FI-00076 Aalto, Finland,

    F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, P. J. Hakonen & M. A. Sillanpää

  2. Microsystems and Nanoelectronics, VTT Technical Research Centre of Finland, PO Box 1000, FI-02044 VTT, Finland,

    H. Saloniemi

Authors
  1. F. Massel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. T. Heikkilä
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J.-M. Pirkkalainen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. U. Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. H. Saloniemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. P. J. Hakonen
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. M. A. Sillanpää
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.M. and T.T.H. developed the theory. J.-M.P. and S.U.C. contributed to the design and fabrication of the samples and to the cryogenic set-up. H.S. made the samples. P.J.H. and M.A.S. designed the experimental set-up. M.A.S. initiated the work and carried out the measurements.

Corresponding author

Correspondence to F. Massel.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Text and Data 1-2, Supplementary Figures 1-6 with legends and additional references. (PDF 1555 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Massel, F., Heikkilä, T., Pirkkalainen, JM. et al. Microwave amplification with nanomechanical resonators. Nature 480, 351–354 (2011). https://doi.org/10.1038/nature10628

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature10628

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