Abstract
Mechanical resonators are ubiquitous in modern information technology. With the possibility of coupling them to electromagnetic and plasmonic modes, they hold promise as the key building blocks in future quantum information technology. Graphene-based resonators are of interest for technological applications due to their high resonant frequencies, multiple mechanical modes and low mass1,2,3,4,5,6,7. The tension-mediated nonlinear coupling between various modes of the resonator can be excited in a controllable manner8,9,10,11. Here we engineer a graphene resonator with large frequency tunability at low temperatures, resulting in a large intermodal coupling strength. We observe the emergence of new eigenmodes and amplification of the coupled modes using red and blue parametric excitation, respectively. We demonstrate that the dynamical intermodal coupling is tunable. A cooperativity of 60 between two resonant modes of ∼100 MHz is achieved in the strong coupling regime. The ability to dynamically control the coupling between the high-frequency eigenmodes of a mechanical system opens up the possibility of quantum mechanical experiments at low temperatures12,13.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Bunch, J. S. et al. Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007).
Chen, C. et al. Performance of monolayer graphene nanomechanical resonators with electrical readout. Nature Nanotech. 4, 861–867 (2009).
Singh, V. et al. Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nanoelectromechanical systems resonators. Nanotechnology 21, 165204 (2010).
Barton, R. A. et al. Photothermal self-oscillation and laser cooling of graphene optomechanical systems. Nano Lett. 12, 4681–4686 (2012).
Singh, V. et al. Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity. Nature Nanotech. 9, 820–824 (2014).
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).
Song, X., Oksanen, M., Li, J., Hakonen, P. & Sillanpää, M. Graphene optomechanics realized at microwave frequencies. Phys. Rev. Lett. 113, 027404 (2014).
Eriksson, A., Midtvedt, D., Croy, A. & Isacsson, A. Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators. Nanotechnology 24, 395702 (2013).
Westra, H., Poot, M., Van der Zant, H. & Venstra, W. Nonlinear modal interactions in clamped-clamped mechanical resonators. Phys. Rev. Lett. 105, 117205 (2010).
Eichler, A., del Álamo Ruiz, M., Plaza, J. & Bachtold, A. Strong coupling between mechanical modes in a nanotube resonator. Phys. Rev. Lett. 109, 025503 (2012).
Castellanos-Gomez, A., Meerwaldt, H. B., Venstra, W. J., van der Zant, H. S. & Steele, G. A. Strong and tunable mode coupling in carbon nanotube resonators. Phys. Rev. B 86, 041402 (2012).
Santamore, D. H., Doherty, A. C. & Cross, M. C. Quantum nondemolition measurement of Fock states of mesoscopic mechanical oscillators. Phys. Rev. B 70, 144301 (2004).
Mahboob, I., Okamoto, H., Onomitsu, K. & Yamaguchi, H. Two-mode thermal-noise squeezing in an electromechanical resonator. Phys. Rev. Lett. 113, 167203 (2014).
Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204–208 (2011).
Massel, F. et al. Microwave amplification with nanomechanical resonators. Nature 480, 351–354 (2011).
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).
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).
Teufel, J. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).
Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).
Palomaki, T., Teufel, J., Simmonds, R. & Lehnert, K. Entangling mechanical motion with microwave fields. Science 342, 710–713 (2013).
Mahboob, I., Nishiguchi, K., Okamoto, H. & Yamaguchi, H. Phonon-cavity electromechanics. Nature Phys. 8, 387–392 (2012).
Okamoto, H. et al. Coherent phonon manipulation in coupled mechanical resonators. Nature Phys. 9, 480–484 (2013).
Faust, T. et al. Nonadiabatic dynamics of two strongly coupled nanomechanical resonator modes. Phys. Rev. Lett. 109, 037205 (2012).
Faust, T., Rieger, J., Seitner, M. J., Kotthaus, J. P. & Weig, E. M. Coherent control of a classical nanomechanical two-level system. Nature Phys. 9, 485–488 (2013).
Kippenberg, T. J. & Vahala, K. J. Cavity opto-mechanics. Opt. Express 15, 17172–17205 (2007).
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.
Weis, S. et al. Optomechanically induced transparency. Science 330, 1520–1523 (2010).
Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).
Rugar, D. & Grütter, P. Mechanical parametric amplification and thermomechanical noise squeezing. Phys. Rev. Lett. 67, 699–702 (1991).
Eichler, A., Chaste, J., Moser, J. & Bachtold, A. Parametric amplification and self-oscillation in a nanotube mechanical resonator. Nano Lett. 11, 2699–2703 (2011).
Turner, K. L. et al. Five parametric resonances in a microelectromechanical system. Nature 396, 149–152 (1998).
Eichler, A. et al. Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. Nature Nanotech. 6, 339–342 (2011).
Acknowledgements
We thank V. Singh, A. A. Clerk, A. Bhushan and A. Naik for discussions and comments on the manuscript. We acknowledge funding from the Department of Atomic Energy, the Department of Science and Technology (Swarnajayanti Fellowship for M.M.D) of the Government of India and ITC-PAC Grant No. FA5209-15-P-0092.
Author information
Authors and Affiliations
Contributions
J.P.M performed the experiments, simulations and analysed the data. R.N.P fabricated the devices and contributed to experiments. A.B. contributed to the fabrication and experiments. R.V. provided input for the measurements. J.P.M. and M.M.D co-wrote the manuscript. All authors provided input on the manuscript. M.M.D supervised the project.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary information
Supplementary information (PDF 994 kb)
Rights and permissions
About this article
Cite this article
Mathew, J., Patel, R., Borah, A. et al. Dynamical strong coupling and parametric amplification of mechanical modes of graphene drums. Nature Nanotech 11, 747–751 (2016). https://doi.org/10.1038/nnano.2016.94
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nnano.2016.94
This article is cited by
-
Nonlinear optical response in multiple-mode coupling nanomechanical system
Nonlinear Dynamics (2024)
-
Extreme mechanical tunability in suspended MoS2 resonator controlled by Joule heating
npj 2D Materials and Applications (2023)
-
Nonlinearity-mediated digitization and amplification in electromechanical phonon-cavity systems
Nature Communications (2022)
-
Quality factor control of mechanical resonators using variable phononic bandgap on periodic microstructures
Scientific Reports (2022)
-
Sliding nanomechanical resonators
Nature Communications (2022)
