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Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation

Nature Nanotechnology volume 6, pages 726–732 (2011)Cite this article

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Abstract

The ability to control mechanical motion with optical forces has made it possible to cool mechanical resonators to their quantum ground states. The same techniques can also be used to amplify rather than reduce the mechanical motion of such systems. Here, we study nanomechanical resonators that are slightly buckled and therefore have two stable configurations, denoted ‘buckled up’ and ‘buckled down’, when they are at rest. The motion of these resonators can be described by a double-well potential with a large central energy barrier between the two stable configurations. We demonstrate the high-amplitude operation of a buckled resonator coupled to an optical cavity by using a highly efficient process to generate enough phonons in the resonator to overcome the energy barrier in the double-well potential. This allows us to observe the first evidence for nanomechanical slow-down and a zero-frequency singularity predicted by theorists. We also demonstrate a non-volatile mechanical memory element in which bits are written and reset by using optomechanical backaction to direct the relaxation of a resonator in the high-amplitude regime to a specific stable configuration.

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Figure 1: The two states of a coupled mechanical resonator–optical cavity system.
Figure 2: Resolved and unresolved sideband regimes.
Figure 3: Optomechanical amplification and relaxation of a nanomechanical resonator in a double-well potential.
Figure 4: Ring-down and zero-frequency singularity.
Figure 5: All-optical, non-volatile nanomechanical memory.

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References

  1. Marquardt, F. & Girvin, S. M. Optomechanics. Physics 2, 40 (2009).

    Article  Google Scholar 

  2. Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: back-action at the mesoscale. Science 321, 1172–1176 (2008).

    Article  CAS  Google Scholar 

  3. Schliesser, A., Arcizet, O., Riviere, R., Anetsberger, G. & Kippenberg, T. J. Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit. Nature Phys. 5, 509–514 (2009).

    Article  CAS  Google Scholar 

  4. Riviere, R. et al. Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state. Phys. Rev. A 83, 063835 (2011).

    Article  Google Scholar 

  5. Gröblacher, S. et al. Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity. Nature Phys. 5, 485–488 (2009).

    Article  Google Scholar 

  6. Naik, A. et al. Quantum measurement backaction and cooling observed with a nanomechanical resonator. Nature 443, 193–196 (2006).

    Article  CAS  Google Scholar 

  7. Poot, M. & van der Zant, H. S. J. Mechanical systems in the quantum regime. Preprint at http://arxiv.org/abs/1106.2060v1 (2011).

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. 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 

  11. Braginsky, V. B., Strigin, S. E. & Vyatchanin, S. P. Parametric oscillatory instability instability in Fabry–Perot interferometer. Phys. Lett. A. 287, 331–338 (2001).

    Article  CAS  Google Scholar 

  12. 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).

    Article  CAS  Google Scholar 

  13. Mamin, H. J. & Rugar, D. Sub-attonewton force detection at millikelvin temperatures. Appl. Phys. Lett. 79, 3358–3360 (2001).

    Article  CAS  Google Scholar 

  14. Liftshitz, R. & Cross, M. C. in Nonlinear Dynamics (eds Radons, G., Rumpf, B. & Schuster, H. G.) (Wiley-VCH, 2010).

    Google Scholar 

  15. Savel'ev, S., Hu, X. D. & Nori, F. Quantum electrodynamics: qubits from buckling nanobars. New J. Phys. 8, 105 (2006).

    Article  Google Scholar 

  16. Rabl, P. et al. A quantum spin transducer based on nanoelectromechanical resonator arrays. Nature Phys. 6, 602–608 (2010).

    Article  CAS  Google Scholar 

  17. Nguyen, C. T. C. Frequency-selective MEMs for miniaturized low-power communication devices. IEEE Trans. Microw. Theory Tech. 47, 1486–1503 (1999).

    Article  Google Scholar 

  18. Yang, Y. T., Callegari, C., Feng, X. L., Ekinci, K. L. & Roukes, M. L. Zeptogram-scale nanomechanical mass sensing. Nano Lett. 6, 583–586 (2006).

    Article  CAS  Google Scholar 

  19. Liu, N. et al. Time-domain control of ultrahigh-frequency nanomechanical systems. Nature Nanotech. 3, 715–719 (2008).

    Article  CAS  Google Scholar 

  20. Hossein-Zadeh, M. & Vahala, K. J. Observation of injection locking in an optomechanical RF oscillator. Appl. Phys. Lett. 93, 191115 (2008).

    Article  Google Scholar 

  21. Henrich, G., Ludwig, M., Qiang, J., Kubala, B. & Marquardt, F. Collective dynamics in optomechanical arrays. Preprint at http://arxiv.org/abs/1007.4819 (2010).

  22. Wiederhecker, G. S., Chen, L., Gondarenko, A. & Lipson, M. Controlling photonic structures using optical forces. Nature 462, 633–636 (2009).

    Article  CAS  Google Scholar 

  23. Rosenberg, J., Lin, Q. & Painter, O. Static and dynamic wavelength routing via the gradient optical force. Nature Photon. 3, 478–483 (2009).

    Article  CAS  Google Scholar 

  24. Postma, H. W. C., Kozinsky, I., Husain, A. & Roukes, M. L. Dynamic range of nanotube- and nanowire-based electromechanical systems. Appl. Phys. Lett. 86, 223105 (2005).

    Article  Google Scholar 

  25. Dorsel, A., McCullen, J. D., Meystre, P., Vignes, E. & Walther, H. Optical bistability and mirror confinement induced by radiation pressure. Phys. Rev. Lett. 51, 1550–1553 (1983).

    Article  Google Scholar 

  26. Sheard, B. S., Gray, M. B., Mow-Lowry, C. M. & McClelland, D. E. Observation and characterization of an optical spring. Phys. Rev A 69, 051801 (2004).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  30. Dykman, A. et al. Spectral density of fluctuations of a double-well Duffing oscillator driven by white noise. Phys. Rev. A 37, 1303–1313 (1988).

    Article  CAS  Google Scholar 

  31. Halg, B. On a micro-electro-mechanical nonvolatile memory Cell. IEEE Trans. Electron. Device 37, 2230–2236 (1990).

    Article  Google Scholar 

  32. Rueckes, T. et al. Carbon nanotube-based nonvolatile random access memory for molecular computing. Science 289, 94–97 (2000).

    Article  CAS  Google Scholar 

  33. Roodenburg, D., Spronck, J. W., Van der Zant, H. S. J. & Venstra, W. J. Buckling beam micromechanical memory with on-chip readout. Appl. Phys. Lett. 94, 123108 (2009).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  35. Venstra, W. J., Westra, H. J. R., & Van der Zant, H. S. J. Mechanical stiffening, bistability, and bit operations in a microcantilever. Appl. Phys. Lett. 97, 193107 (2010).

    Article  Google Scholar 

  36. Freeman, M. & Heibert, W. Taking another swing at computing. Nature Nanotech. 3, 251–252 (2008).

    Article  CAS  Google Scholar 

  37. Jang, J. E. et al. Nanoscale memory cell based on nanoelectromechanical switched capacitor. Nature Nanotech. 3, 26–30 (2008).

    Article  CAS  Google Scholar 

  38. Li, M. et al. Harnessing optical forces in integrated photonic circuits. Nature 456, 480–484 (2008).

    Article  CAS  Google Scholar 

  39. Krylov, S., Ilic, B. R., Schreiber, D., Seretensky, S. & Craighead, H. The pull-in behavior of electrostatically actuated bistable microstructures. J. Micromech. Microeng. 18, 055026 (2008).

    Article  Google Scholar 

  40. Feng, X. L., White, C. J., Hajimiri, A. & Roukes, M. L. A self-sustaining ultrahigh-frequency nanoelectromechanical oscillator. Nature Nanotech. 3, 342–346 (2008).

    Article  CAS  Google Scholar 

  41. 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).

    Article  CAS  Google Scholar 

  42. Marquardt, F., Harris, J. G. E. & Girvin, S. M. Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. Phys Rev. Lett. 96, 103901 (2006).

    Article  Google Scholar 

  43. Metzger, C. et al. Self-induced oscillations in an optomechanical system driven by bolometric backaction. Phys Rev. Lett. 101, 133903 (2008).

    Article  Google Scholar 

  44. Anetsberger, G. et al. Near-field cavity optomechanics with nanomechanical oscillators. Nature Phys. 5, 909–914 (2009).

    Article  CAS  Google Scholar 

  45. Voigtlaender, K. & Risken H. Solutions of the Fokker–Planck equation for a double-well potential in terms of matrix continued fractions. J. Stat. Phys. 40, 397–429 (1985).

    Article  Google Scholar 

  46. Soskin, S. M., Mannella, R. & McClintock, P. V. E. Zero-dispersion phenomena in oscillatory systems. Phys. Rep. 73, 247–408 (2003).

    Article  Google Scholar 

  47. Cross, M. C., Zumdieck, A., Lifshitz, R. & Rogers, J. L. Synchronization by nonlinear frequency pulling. Phys. Rev. Lett. 93, 224101 (2004).

    Article  CAS  Google Scholar 

  48. Badzey, R. L., Zolfagharkhani, G., Gaidarzhy, A. & Mohanty, P. A controllable nanomechanical memory element. Appl. Phys. Lett. 85, 3587–3589 (2004).

    Article  CAS  Google Scholar 

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Acknowledgements

The authors thank M. Rooks (Yale Institute for Nanoscience and Quantum Engineering) for help with electron-beam lithography, and M. Power for help with device fabrication. The authors also acknowledge funding support from the DARPA/MTO ORCHID programme through a grant from the Air Force Office of Scientific Research (AFOSR). H.X.T. acknowledges support from a Packard Fellowship in Science and Engineering and a career award from the National Science Foundation. M.P. acknowledges a Rubicon fellowship from the Netherlands Organization for Scientific Research (NWO)/Marie Curie Cofund Action.

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  1. Mo Li

    Present address: Present address: Department of Electrical and Computer Engineering, University of Minnesota, Minnesota 55455, USA,

Authors and Affiliations

  1. Department of Electrical Engineering, Yale University, New Haven, Connecticut, 06511, USA

    Mahmood Bagheri, Menno Poot, Mo Li, Wolfram P. H. Pernice & Hong X. Tang

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Contributions

M.B. performed the device fabrication and carried out measurements and data analysis under the supervision of H.X.T. M.B. and M.P. contributed to numerical analysis of the coupled optomechanical system. M.B., M.P., M.L., W.P.H.P. and H.X.T. discussed the results and all authors contributed to the writing of the manuscript.

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Correspondence to Hong X. Tang.

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Bagheri, M., Poot, M., Li, M. et al. Dynamic manipulation of nanomechanical resonators in the high-amplitude regime and non-volatile mechanical memory operation. Nature Nanotech 6, 726–732 (2011). https://doi.org/10.1038/nnano.2011.180

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