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.

  • Article
  • Published:

Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution

Abstract

The small mass and high coherence of nanomechanical resonators render them the ultimate mechanical probe, with applications that range from protein mass spectrometry and magnetic resonance force microscopy to quantum optomechanics. A notorious challenge in these experiments is the thermomechanical noise related to the dissipation through internal or external loss channels. Here we introduce a novel approach to define the nanomechanical modes, which simultaneously provides a strong spatial confinement, full isolation from the substrate and dilution of the resonator material's intrinsic dissipation by five orders of magnitude. It is based on a phononic bandgap structure that localizes the mode but does not impose the boundary conditions of a rigid clamp. The reduced curvature in the highly tensioned silicon nitride resonator enables a mechanical Q > 108 at 1 MHz to yield the highest mechanical Qf products (>1014 Hz) yet reported at room temperature.

The corresponding coherence times approach those of optically trapped dielectric particles. Extrapolation to 4.2 K predicts quanta per milliseconds heating rates, similar to those of trapped ions.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Device characterization.
Figure 2: Quality factor statistics.
Figure 3: Scaling of quality factors.
Figure 4: Enhancing the dissipation dilution.
Figure 5: Alternative structures.

Similar content being viewed by others

References

  1. 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  Google Scholar 

  2. Hanay, M. S. et al. Single-protein nanomechanical mass spectrometry in real time. Nat. Nanotechnol. 7, 602–608 (2012).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  4. Ekinci, K. L. & Roukes, M. L. Nanoelectromechanical systems. Rev. Sci. Instrum. 76, 061101 (2005).

    Article  Google Scholar 

  5. Verbridge, S. S., Craighead, H. G. & Parpia, J. M. A megahertz nanomechanical resonator with room temperature quality factor over a million. Appl. Phys. Lett. 92, 013112 (2008).

    Article  Google Scholar 

  6. Zwickl, B. M. et al. High quality mechanical and optical properties of commercial silicon nitride membranes. Appl. Phys. Lett. 92, 103125 (2008).

    Article  Google Scholar 

  7. Unterreithmeier, Q. P., Faust, T. & Kotthaus, J. P. Damping of nanomechanical resonators. Phys. Rev. Lett. 105, 027205 (2010).

    Article  Google Scholar 

  8. Schmid, S., Jensen, K. D., Nielsen, K. H. & Boisen, A. Damping mechanisms in high-Q micro and nanomechanical string resonators. Phys. Rev. B 84, 165307 (2011).

    Article  Google Scholar 

  9. Yu, P.-L., Purdy, T. P. & Regal, C. A. Control of material damping in high-Q membrane microresonators. Phys. Rev. Lett. 108, 083603 (2012).

    Article  Google Scholar 

  10. González, G. I. & Saulson, P. R. Brownian motion of a mass suspended by an anelastic wire. J. Acoust. Soc. Am. 96, 207–212 (1994).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).

    Article  CAS  Google Scholar 

  13. Wilson, D. J. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015).

    Article  CAS  Google Scholar 

  14. Nielsen, W. H. P., Tsaturyan, Y., Møller, C. B., Polzik, E. S. & Schliesser, A. Multimode optomechanical system in the quantum regime. Proc. Natl Acad. Sci. USA 144, 62–66 (2017).

    Article  Google Scholar 

  15. Villanueva, L. G. & Schmid, S. Evidence of surface loss as ubiquitous limiting damping mechanism in SiN micro- and nanomechanical resonators. Phys. Rev. Lett. 113, 227201 (2014).

    Article  CAS  Google Scholar 

  16. Wilson, D. J., Regal, C. A., Papp, S. B. & Kimble, H. J. Cavity optomechanics with stoichiometric SiN films. Phys. Rev. Lett. 103, 207204 (2009).

    Article  CAS  Google Scholar 

  17. Chakram, S., Patil, Y. S., Chang, L. & Vengalattore, M. Dissipation in ultrahigh quality factor SiN membrane resonators. Phys. Rev. Lett. 112, 127201 (2014).

    Article  CAS  Google Scholar 

  18. Kleckner, D. et al. Optomechanical trampoline resonators. Opt. Express 19, 19708–19716 (2011).

    Article  CAS  Google Scholar 

  19. Reinhardt, C., Müller, T., Bourassa, A. & Sankey, J. C . Ultralow-noise sin trampoline resonators for sensing and optomechanics. Phys. Rev. X 6, 021001 (2016).

    Google Scholar 

  20. Norte, R., Moura, J. P. & Gröblacher, S. Mechanical resonators for quantum optomechanics experiments at room temperature. Phys. Rev. Lett. 116, 147202 (2016).

    Article  CAS  Google Scholar 

  21. Maldovan, M. Sound and heat revolutions in phononics. Nature 503, 209–217 (2013).

    Article  CAS  Google Scholar 

  22. Wilson-Rae, I. Intrinsic dissipation in nanomechanical resonators due to phonon tunneling. Phys. Rev. B 77, 245418 (2008).

    Article  Google Scholar 

  23. Schliesser, A., Tsaturyan, Y., Polzik, E. S. & Barg, A. Periodic structuring of two-dimensional membrane and string resonators under high tensile stress to shield localised oscillation modes. US patent pending.

  24. Braginsky, V. B., Mitrofanov, V. P. & Panov, V. I. Systems with Small Dissipation (Univ. Chicago Press, 1985).

    Google Scholar 

  25. Ballato, A. & Gualtieri, J. G. Advances in high-Q piezoelectric resonator materials and devices. IEEE Trans. Ultrason. Ferroelec. Freq. Control 41, 834–844 (1994).

    Article  CAS  Google Scholar 

  26. Lee, J. E.-Y. & Seshia, A. A. 5.4-MHz single-crystal silicon wine glass mode disk resonator with quality factor of 2 million. Sensor Actuat. A 156, 28–35 (2009).

    Article  CAS  Google Scholar 

  27. Cumming, A. V. et al. Design and development of the advanced LIGO monolithic fused silica suspension. Class. Quant. Grav. 29, 035003 (2012).

    Article  Google Scholar 

  28. Ghaffari, S. et al. Quantum limit of quality factor in silicon micro and nano mechanical resonators. Sci. Rep. 3, 1 (2013).

    Google Scholar 

  29. Mayer Alegre, T. P., Safavi-Naeini, A., Winger, M & Painter, O. Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap. Opt. Express 19, 5658–5669 (2011).

    Article  Google Scholar 

  30. Tsaturyan, Y. et al. Demonstration of suppressed phonon tunneling losses in phononic bandgap shielded membrane resonators for high-Q optomechanics. Opt. Express 6, 6810–6821 (2013).

    Google Scholar 

  31. Yu, P.-L. et al. A phononic bandgap shield for high-Q membrane microresonators. Appl. Phys. Lett. 104, 023510 (2014).

    Article  Google Scholar 

  32. Mohammadi, S. et al. Complete phononic bandgaps and bandgap maps in two-dimensional silicon phononic crystal plates. Electron. Lett. 43, 898–899 (2007).

    Article  CAS  Google Scholar 

  33. Barasheed, A. Z., Müller, T. & Sankey, J. C. Optically defined mechanical geometry. Phys. Rev. A 93, 053811 (2016).

    Article  Google Scholar 

  34. Ghadimi, A. H., Wilson, D. J. & Kippenberg, T. J. Dissipation engineering of high-stress silicon nitride nanobeams. Preprint at https://arxiv.org/abs/1603.01605 (2016).

  35. Capelle, T., Tsaturyan, Y., Barg, A. & Schliesser, A. Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators. Appl. Phys. Lett. 110, 181106 (2017).

    Article  Google Scholar 

  36. Barg, A. et al. Measuring and imaging nanomechanical motion with laser light. Appl. Phys. B 123, 8 (2017).

    Article  Google Scholar 

  37. Lifshitz, R. & Roukes, M. L. Thermoelastic damping in micro- and nanomechanical systems. Phys. Rev. B 61, 5600–5609 (2000).

    Article  CAS  Google Scholar 

  38. Faust, T., Rieger, J., Seitner, M. J., Kotthaus, J. P. & Weig, E. M. Signatures of two-level defects in the temperature-dependent damping of nanomechanical silicon nitride resonators. Phys. Rev. B 89, 100102 (2014).

    Article  Google Scholar 

  39. Yuan, M., Cohen, M. A. & Steele, G. A. Silicon nitride membrane resonators at millikelvin temperatures with quality factors exceeding 108. Appl. Phys. Lett. 107, 263501 (2015).

    Article  Google Scholar 

  40. Laude, V., Achaoui, Y., Benchabane, S. & Khelif, A. Evanescent Bloch waves and the complex band structure of phononic crystals. Phys. Rev. B 80, 092301 (2009).

    Article  Google Scholar 

  41. 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  Google Scholar 

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

    Article  Google Scholar 

  43. Jain, V. et al. Direct measurement of photon recoil from a levitated nanoparticle. Phys. Rev. Lett. 116, 243601 (2016).

    Article  Google Scholar 

  44. Turchette, Q. A. et al. Heating of trapped ions from the quantum ground state. Phys. Rev. A 61, 063418 (2000).

    Article  Google Scholar 

  45. Poggio, M. & Degen, C. L. Force-detected nuclear magnetic resonance: recent advances and future challenges. Nanotechnology 21, 342001 (2010).

    Article  CAS  Google Scholar 

  46. Bagci, T. et al. Optical detection of radio waves through a nanomechanical transducer. Nature 507, 81–85 (2014).

    Article  CAS  Google Scholar 

  47. Hanay, M. S. et al. Inertial imaging with nanomechanical systems. Nat. Nanotechnol. 10, 339–344 (2015).

    Article  CAS  Google Scholar 

  48. Kolkowitz, S. et al. Coherent sensing of a mechanical resonator with a single-spin qubit. Science 335, 1603–1606 (2012).

    Article  CAS  Google Scholar 

  49. Møller, C. B. et al. Quantum back action evading quantum measurement of motion in a negative mass reference frame. Preprint at https://arxiv.org/abs/1608.03613 (2016).

  50. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. Sci. USA. 112, 3866–3873 (2015).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge discussions with S. Schmid from TU Wien and H. Tang from Yale University. A. Simonsen and M. B. Kristensen provided support with the imaging and noise measurements, respectively, of some of the devices. This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (ERC project Q-CEOM, grant agreement no. 638765), the European Union Seventh Framework programme (ERC project INTERFACE), a starting grant from the Danish Council for Independent Research and the Carlsberg Foundation.

Author information

Authors and Affiliations

Authors

Contributions

A.S. conceived the idea and directed the research. A.S. and E.S.P. provided general research supervision. Y.T. designed, simulated and fabricated the samples. Y.T. and A.B. characterized and imaged the samples. A.S. and Y.T. analysed the data, developed the model and wrote the paper. All authors commented on the manuscript.

Corresponding author

Correspondence to A. Schliesser.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 3454 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsaturyan, Y., Barg, A., Polzik, E. et al. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nature Nanotech 12, 776–783 (2017). https://doi.org/10.1038/nnano.2017.101

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2017.101

This article is cited by

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