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Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance


Stochastic resonance1,2 is a counterintuitive concept: the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers3, superconducting quantum interference devices4,5 (SQUIDs), magnetoelastic ribbons6 and neurophysiological systems such as the receptors in crickets7 and crayfish8. Although fundamentally important as a mechanism of coherent signal amplification, stochastic resonance has yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators. Our nanomechanical systems consist of beams that are clamped at each end and driven into transverse oscillation with the use of a radiofrequency source. Modulation of the source induces controllable switching of the beams between two stable, distinct states. We observe that the addition of white noise causes a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems could have a function in the realization of controllable high-speed nanomechanical memory cells, and paves the way for exploring macroscopic quantum coherence and tunnelling.

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Figure 1: Diagram of measurement circuit.
Figure 2: Re-emergence of switching behaviour as a function of added white noise on beam 1 ( f drive = 23.4973 MHz).
Figure 3: Switching behaviour as a function of temperature on beam 2 ( f drive = 20.8348 MHz).
Figure 4: Behaviour of higher harmonics.


  1. Benzi, R., Sutera, A., Parisi, G. & Vulpiani, A. A theory of stochastic resonance in climatic change. J. Appl. Math. 43, 565–578 (1983)

    MathSciNet  MATH  Google Scholar 

  2. Gammaitoni, L., Hänggi, P., Jung, P. & Marchesoni, F. Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998)

    ADS  CAS  Article  Google Scholar 

  3. McNamara, B., Wiesenfeld, K. & Roy, R. Observation of stochastic resonance in a ring laser. Phys. Rev. Lett. 60, 2626–2629 (1988)

    ADS  CAS  Article  Google Scholar 

  4. Hibbs, A. D. et al. Stochastic resonance in a superconducting loop with a Josephson junction. J. Appl. Phys. 77, 2582–2590 (1995)

    ADS  CAS  Article  Google Scholar 

  5. Rouse, R., Han, S. & Lukens, J. E. Flux amplification using stochastic superconducting quantum interference devices. Appl. Phys. Lett. 66, 108–110 (1995)

    ADS  CAS  Article  Google Scholar 

  6. Spano, M. L., Wun-Fogle, M. & Ditto, W. L. Experimental observation of stochastic resonance in a magnetoelastic ribbon. Phys. Rev. A 46, R5253–R5256 (1992)

    ADS  Article  Google Scholar 

  7. Levin, J. E. & Miller, J. P. Broadband neural encoding in the cricket cercal sensory system enhanced by stochastic resonance. Nature 380, 165–168 (1996)

    ADS  CAS  Article  Google Scholar 

  8. Douglass, J. K., Wilkens, L., Pantazelou, E. & Moss, F. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature 365, 337–340 (1993)

    ADS  CAS  Article  Google Scholar 

  9. Carr, S. M., Lawrence, W. E. & Wybourne, M. N. Accessibility of quantum effects in mesomechanical systems. Phys. Rev. B 64, 220101 (2001)

    ADS  Article  Google Scholar 

  10. Nayfeh, A. H. & Mook, D. T. Nonlinear Oscillations (Wiley, New York, 1979)

    MATH  Google Scholar 

  11. Weaver, W., Timoshenko, S. P. & Young, D. H. Vibration Problems in Engineering (Wiley, New York, 1990)

    Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  13. Benzi, R., Sutera, A. & Vulpiani, A. Stochastic resonance in the Landau–Ginzburg equation. J. Phys. A 18, 2239–2245 (1985)

    ADS  MathSciNet  Article  Google Scholar 

  14. Greywall, D. S., Yurke, B., Busch, P. A., Pargellis, A. N. & Willett, R. L. Evading amplifier noise in nonlinear oscillators. Phys. Rev. Lett. 72, 2992–2995 (1994)

    ADS  CAS  Article  Google Scholar 

  15. Badzey, R. L., Zolfagharkhani, G., Gaidarzhy, A. & Mohanty, P. Temperature dependence of a nanomechanical switch. Appl. Phys. Lett. 86, 023106 (2005)

    ADS  Article  Google Scholar 

  16. Inchiosa, M. E., Bulsara, A. R. & Gammaitoni, L. Higher-order resonant behaviour in asymmetric nonlinear stochastic systems. Phys. Rev. E 55, 4049–4056 (1997)

    ADS  CAS  Article  Google Scholar 

  17. Inchiosa, M. E. & Bulsara, A. R. dc signal detection via dynamical asymmetry in a nonlinear device. Phys. Rev. E 58, 115–127 (1998)

    ADS  CAS  Article  Google Scholar 

  18. Bulsara, A., Jacobs, E. W., Zhou, T., Moss, F. & Kiss, L. Stochastic resonance in a single neuron model—theory and analog simulation. J. Theor. Biol. 152, 531–555 (1991)

    CAS  Article  Google Scholar 

  19. Gammaitoni, L., Marchesoni, F., Menichellasaetta, E. & Santucci, S. Multiplicative stochastic resonance. Phys. Rev. E 49, 4878–4881 (1994)

    ADS  CAS  Article  Google Scholar 

  20. McNamara, B. & Weisenfeld, K. Theory of stochastic resonance. Phys. Rev. A 39, 4854–4869 (1989)

    ADS  CAS  Article  Google Scholar 

  21. Morillo, M. & Gomez-Ordoñez, J. Amplification and distortion of a periodic rectangular driving signal by a noisy bistable system. Phys. Rev. E 51, 999–1003 (1995)

    ADS  CAS  Article  Google Scholar 

  22. Casado-Pascual, J., Gomez-Ordoñez, J. & Morillo, M. Nonlinear stochastic resonance with subthreshold rectangular pulses. Phys. Rev. E 69, 067101 (2004)

    ADS  Article  Google Scholar 

  23. Gaidarzhy, A., Zolfagharkhani, G., Badzey, R. & Mohanty, P. Evidence for quantized displacement in macroscopic nanomechanical oscillators. Phys. Rev. Lett. 94, 030402 (2005)

    ADS  Article  Google Scholar 

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We acknowledge the Nanoscale Exploratory Research (NER) program of the National Science Foundation and the DOD/ARL for the financial support of this research.

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Correspondence to Pritiraj Mohanty.

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Badzey, R., Mohanty, P. Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance. Nature 437, 995–998 (2005).

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