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:

Tunable phonon-cavity coupling in graphene membranes

Abstract

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators1,2,3. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling—energy exchange between the modes of a single system mediated by intrinsic material nonlinearity4,5. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 105) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena6, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

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: The nonlinear system under test.
Figure 2: Multimode membrane characterization.
Figure 3: Phonon pumping in Device 1.
Figure 4: Parametric self-oscillation and cooling in Device 2.

Similar content being viewed by others

References

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nature Phys. 10, 321–326 (2014).

    Article  CAS  Google Scholar 

  4. Mahboob, I., Nishiguchi, K., Okamoto, H. & Yamaguchi, H. Phonon-cavity electromechanics. Nature Phys. 8, 387–392 (2012).

    Article  CAS  Google Scholar 

  5. Mahboob, I., Nishiguchi, K., Fujiwara, A. & Yamaguchi, H. Phonon lasing in an electromechanical resonator. Phys. Rev. Lett. 110, 127202 (2013).

    Article  CAS  Google Scholar 

  6. Khan, R., Massel, F. & Heikkilä, T. T. Tension-induced nonlinearities of flexural modes in nanomechanical resonators. Phys. Rev. B 87, 235406 (2013).

    Article  Google Scholar 

  7. Bunch, J. S. et al. Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).

    Article  CAS  Google Scholar 

  8. Chen, C. et al. Performance of monolayer graphene nanomechanical resonators with electrical readout. Nature Nanotech. 4, 861–867 (2009).

    Article  CAS  Google Scholar 

  9. Singh, V. et al. Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators. Nanotechnology 21, 165204 (2010).

    Article  Google Scholar 

  10. Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nature Nanotech. 7, 301–304 (2012).

    Article  CAS  Google Scholar 

  11. Barton, R. A. et al. Photothermal self-oscillation and laser cooling of graphene optomechanical systems. Nano Lett. 12, 4681–4686 (2012).

    Article  CAS  Google Scholar 

  12. Song, X. et al. Stamp transferred suspended graphene mechanical resonators for radio frequency electrical readout. Nano Lett. 12, 198–202 (2012).

    Article  CAS  Google Scholar 

  13. Eichler, A. et al. Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. Nature Nanotech. 6, 339–342 (2011).

    Article  CAS  Google Scholar 

  14. Eichler, A., del Álamo Ruiz, M., Plaza, J. A. & Bachtold, A. Strong coupling between mechanical modes in a nanotube resonator. Phys. Rev. Lett. 109, 025503 (2012).

    Article  CAS  Google Scholar 

  15. Lee, J., Wang, Z., He, K., Shan, J. & Feng, P. X.-L. High frequency MoS2 nanomechanical resonators. ACS Nano 7, 6086–6091 (2013).

    Article  CAS  Google Scholar 

  16. Liu, C. H., Kim, I. S. & Lauhon, L. J. Optical control of mechanical mode-coupling within a MoS2 resonator in the strong-coupling regime. Nano Lett. 15, 6727–6731 (2015).

    Article  CAS  Google Scholar 

  17. Cole, R. M. et al. Evanescent-field optical readout of graphene mechanical motion at room temperature. Phys. Rev. Appl. 3, 1–7 (2015).

    Article  Google Scholar 

  18. Weber, P., Güttinger, J., Tsioutsios, I., Chang, D. E. & Bachtold, A. Coupling graphene mechanical resonators to superconducting microwave cavities. Nano Lett. 14, 2854–2860 (2014).

    Article  CAS  Google Scholar 

  19. Song, X., Oksanen, M., Li, J., Hakonen, P. J. & Sillanpää, M. A. Graphene optomechanics realized at microwave frequencies. Phys. Rev. Lett. 113, 1–5 (2014).

    Google Scholar 

  20. Singh, V. et al. Optomechanical coupling between a graphene mechanical resonator and a superconducting microwave cavity. Nature Nanotech. 9, 1–5 (2014).

    Article  Google Scholar 

  21. Atalaya, J., Kinaret, J. M. & Isacsson, A. Narrowband nanomechanical mass measurement using nonlinear response of a graphene membrane. Europhys. Lett. 91, 48001 (2009).

    Article  Google Scholar 

  22. Westra, H. J. R., Poot, M., van der Zant, H. S. J. & Venstra, W. J. Nonlinear modal interactions in clamped-clamped mechanical resonators. Phys. Rev. Lett. 105, 117205 (2010).

    Article  CAS  Google Scholar 

  23. Patil, Y. S., Chakram, S., Chang, L. & Vengalattore, M. Thermomechanical two-mode squeezing in an ultrahigh Q membrane resonator. Phys. Rev. Lett. 115, 017202 (2015).

    Article  CAS  Google Scholar 

  24. Ruiz-Vargas, C. S. et al. Softened elastic response and unzipping in chemical vapor deposition graphene membranes. Nano Lett. 11, 2259–2263 (2011).

    Article  CAS  Google Scholar 

  25. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and Intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    Article  CAS  Google Scholar 

  26. Bunch, J. S. et al. Impermeable atomic membranes from graphene sheets. Nano Lett. 8, 2458–2462 (2008).

    Article  CAS  Google Scholar 

  27. Lee, S. et al. Electrically integrated SU-8 clamped graphene drum resonators for strain engineering. Appl. Phys. Lett. 102, 153101 (2013).

    Article  Google Scholar 

  28. Wang, Z., Lee, J., He, K., Shan, J. & Feng, P. X.-L. Embracing structural nonidealities and asymmetries in two-dimensional nanomechanical resonators. Sci. Rep. 4, 3919 (2014).

    Article  Google Scholar 

  29. Van Der Zande, A. M. et al. Large-scale arrays of single-layer graphene resonators. Nano Lett. 10, 4869–4873 (2010).

    Article  CAS  Google Scholar 

  30. Mahboob, I. & Yamaguchi, H. Bit storage and bit flip operations in an electromechanical oscillator. Nature Nanotech. 3, 275–279 (2008).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors are grateful to P. Rose for assistance in growing the CVD graphene and to D. MacNeill for insightful discussions and comments. This work was supported by the Cornell Center for Materials Research with funding from the NSF MRSEC program (grant no. DMR-1120296) and by Nanoelectronics Research Initiative (NRI) through the Institute for Nanoelectronics Discovery and Exploration (INDEX). Support was also provided by the Academy of Finland (through the project ‘Quantum properties of optomechanical systems’). Fabrication was performed in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Coordinated Infrastructure, which is supported by the NSF (grant no. ECCS-15420819).

Author information

Authors and Affiliations

Authors

Contributions

J.M.P., H.G.C., P.L.M. and R.D.A. designed the experiment; F.M. developed the supporting theory. R.D.A. and T.S.A. fabricated the samples; I.R.S. contributed to the design of the samples and the experimental set-up. R.D.A. and A.H. carried out the measurements. F.M. and R.D.A. analysed the data. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to R. De Alba.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2449 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De Alba, R., Massel, F., Storch, I. et al. Tunable phonon-cavity coupling in graphene membranes. Nature Nanotech 11, 741–746 (2016). https://doi.org/10.1038/nnano.2016.86

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2016.86

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