Skip to main content

Thank you for visiting 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:

Phonon counting and intensity interferometry of a nanomechanical resonator


In optics, the ability to measure individual quanta of light (photons) enables a great many applications, ranging from dynamic imaging within living organisms1 to secure quantum communication2. Pioneering photon counting experiments, such as the intensity interferometry performed by Hanbury Brown and Twiss3 to measure the angular width of visible stars, have played a critical role in our understanding of the full quantum nature of light4. As with matter at the atomic scale, the laws of quantum mechanics also govern the properties of macroscopic mechanical objects, providing fundamental quantum limits to the sensitivity of mechanical sensors and transducers. Current research in cavity optomechanics seeks to use light to explore the quantum properties of mechanical systems ranging in size from kilogram-mass mirrors to nanoscale membranes5, as well as to develop technologies for precision sensing6 and quantum information processing7,8. Here we use an optical probe and single-photon detection to study the acoustic emission and absorption processes in a silicon nanomechanical resonator, and perform a measurement similar to that used by Hanbury Brown and Twiss to measure correlations in the emitted phonons as the resonator undergoes a parametric instability formally equivalent to that of a laser9. Owing to the cavity-enhanced coupling of light with mechanical motion, this effective phonon counting technique has a noise equivalent phonon sensitivity of 0.89 ± 0.05. With straightforward improvements to this method, a variety of quantum state engineering tasks using mesoscopic mechanical resonators would be enabled10, including the generation and heralding of single-phonon Fock states11 and the quantum entanglement of remote mechanical elements12,13.

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

Access options

Buy this article

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

Figure 1: Phonon counting and device characterization.
Figure 2: Phonon counting sensitivity.
Figure 3: Phonon lasing.
Figure 4: Phonon intensity correlations.

Similar content being viewed by others


  1. Hoover, E. E. & Squier, J. A. Advances in multiphoton microscopy technology. Nature Photon. 7, 93–101 (2013)

    Article  ADS  CAS  Google Scholar 

  2. Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nature Photon. 3, 696–705 (2009)

    Article  ADS  CAS  Google Scholar 

  3. Hanbury Brown, R. & Twiss, R. Q. A test of a new type of stellar interferometer on Sirius. Nature 178, 1046–1048 (1956)

    Article  ADS  Google Scholar 

  4. Glauber, R. J. The quantum theory of optical coherence. Phys. Rev. 130, 2529–2539 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  5. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014)

    Article  ADS  Google Scholar 

  6. Suh, J. et al. Mechanically detecting and avoiding the quantum fluctuations of a microwave field. Science 344, 1262–1265 (2014)

    Article  ADS  CAS  Google Scholar 

  7. Stannigel, K., Rabl, P., Sørensen, A. S., Lukin, M. D. & Zoller, P. Optomechanical transducers for quantum-information processing. Phys. Rev. A 84, 042341 (2011)

    Article  ADS  Google Scholar 

  8. Stannigel, K. et al. Optomechanical quantum information processing with photons and phonons. Phys. Rev. Lett. 109, 013603 (2012)

    Article  ADS  CAS  Google Scholar 

  9. Grudinin, I. S., Lee, H., Painter, O. & Vahala, K. J. Phonon laser action in a tunable two-level system. Phys. Rev. Lett. 104, 083901 (2010)

    Article  ADS  Google Scholar 

  10. Vanner, M. R., Aspelmeyer, M. & Kim, M. S. Quantum state orthogonalization and a toolset for quantum optomechanical phonon control. Phys. Rev. Lett. 110, 010504 (2013)

    Article  ADS  CAS  Google Scholar 

  11. Galland, C., Sangouard, N., Piro, N., Gisin, N. & Kippenberg, T. J. Heralded single-phonon preparation, storage, and readout in cavity optomechanics. Phys. Rev. Lett. 112, 143602 (2014)

    Article  ADS  Google Scholar 

  12. Børkje, K., Nunnenkamp, A. & Girvin, S. M. Proposal for entangling remote micromechanical oscillators via optical measurements. Phys. Rev. Lett. 107, 123601 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  14. 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 

  15. Qian, J., Clerk, A. A., Hammerer, K. & Marquardt, F. Quantum signatures of the optomechanical instability. Phys. Rev. Lett. 109, 253601 (2012)

    Article  ADS  Google Scholar 

  16. Kronwald, A., Ludwig, M. & Marquardt, F. Full photon statistics of a light beam transmitted through an optomechanical system. Phys. Rev. A 87, 013847 (2013)

    Article  ADS  Google Scholar 

  17. Kimble, H. J., Dagenais, M. & Mandel, L. Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1977)

    Article  ADS  CAS  Google Scholar 

  18. Pike, R. 50th anniversary of the laser. J. Eur. Opt. Soc. Rapid Publ. 5, 10047s (2010)

    Article  Google Scholar 

  19. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011)

    Article  ADS  CAS  Google Scholar 

  20. Chan, J., Safavi-Naeini, A. H., Hill, J. T., Meenehan, S. & Painter, O. Optimized optomechanical crystal cavity with acoustic radiation shield. Appl. Phys. Lett. 101, 081115 (2012)

    Article  ADS  Google Scholar 

  21. Safavi-Naeini, A. H. et al. Laser noise in cavity-optomechanical cooling and thermometry. New J. Phys. 15, 035007 (2013)

    Article  ADS  Google Scholar 

  22. Fetter, A. L. Intensity correlations in Raman scattering. Phys. Rev. 139, A1616–A1623 (1965)

    Article  ADS  Google Scholar 

  23. Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nature Photon. 7, 210–214 (2013)

    Article  ADS  CAS  Google Scholar 

  24. Rodrigues, D. A. & Armour, A. D. Amplitude noise suppression in cavity-driven oscillations of a mechanical resonator. Phys. Rev. Lett. 104, 053601 (2010)

    Article  ADS  CAS  Google Scholar 

  25. Lax, M. Classical noise. V. Noise in self-sustained oscillators. Phys. Rev. 160, 290–307 (1967)

    Article  ADS  CAS  Google Scholar 

  26. Rice, P. R. & Carmichael, H. J. Photon statistics of a cavity-QED laser: a comment on the laser-phase-transition analogy. Phys. Rev. A 50, 4318–4329 (1994)

    Article  ADS  CAS  Google Scholar 

  27. Lörch, N., Qian, J., Clerk, A., Marquardt, F. & Hammerer, K. Laser theory for optomechanics: limit cycles in the quantum regime. Phys. Rev. X 4, 011015 (2014)

    Google Scholar 

  28. Meenehan, S. M. et al. Silicon optomechanical crystal resonator at millikelvin temperatures. Phys. Rev. A 90, 011803 (2014)

    Article  ADS  Google Scholar 

Download references


We thank F. Marquardt and A. G. Krause for discussions, and V. B. Verma, R. P. Miriam and S. W. Nam for their help with the single-photon detectors used in this work. This work was supported by the DARPA ORCHID and MESO programmes, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation, and the Kavli Nanoscience Institute at Caltech. Part of the research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. A.H.S.-N. acknowledges support from NSERC. S.G. was supported by a Marie Curie International Out-going Fellowship within the 7th European Community Framework Programme.

Author information

Authors and Affiliations



O.P., S.M.M., J.D.C., S.G. and A.H.S.-N. planned the experiment. J.D.C., S.G., G.S.M., S.M.M. and A.H.S.-N. performed the device design and fabrication. F.M. and M.D.S. provided the single-photon detectors along with technical support for their installation and running. J.D.C., S.M.M., G.S.M. and O.P. performed the measurements, analysed the data and wrote the manuscript.

Corresponding author

Correspondence to Oskar Painter.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-8, Supplementary Figures 1-4 and additional references. (PDF 752 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cohen, J., Meenehan, S., MacCabe, G. et al. Phonon counting and intensity interferometry of a nanomechanical resonator. Nature 520, 522–525 (2015).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


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.


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