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Microwave amplification with nanomechanical resonators

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.

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Figure 1: Electromechanical microwave amplification.
Figure 2: Amplification mechanism.
Figure 3: Amplifier gain.

References

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

    ADS  Article  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)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  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)

    ADS  Article  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)

    CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

  12. 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 

  13. 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 

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

    CAS  Article  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)

    ADS  Article  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)

    ADS  CAS  Article  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)

    ADS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  Article  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)

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  CAS  Article  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)

    ADS  Article  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)

    ADS  CAS  Article  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)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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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.

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Authors and Affiliations

Authors

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.

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Correspondence to F. Massel.

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The authors declare no competing financial interests.

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

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

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