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Optomechanically induced stochastic resonance and chaos transfer between optical fields

Nature Photonics volume 10, pages 399–405 (2016)Cite this article

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Abstract

Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.

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Figure 1: Whispering-gallery-mode microtoroid optomechanical resonator.
Figure 2: Optomechanically mediated chaos generation and transfer between optical fields.
Figure 3: Maximal Lyapunov exponents and probe bandwidth.
Figure 4: Optomechanically induced chaos-mediated stochastic resonance in an optomechanical resonator.

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References

  1. Arcizet, O., Cohadon, P.-F., Briant, T., Pinard, M. & Heidman, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 71–74 (2006).

    Article  ADS  Google Scholar 

  2. Gigan, S. et al. Self-cooling of a micromirror by radiation pressure. Nature 444, 67–70 (2006).

    Article  ADS  Google Scholar 

  3. 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  ADS  Google Scholar 

  4. Carmon, T., Rokhsari, H., Yang, L., Kippenberg, T. J. & Vahala, K. J. Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode. Phys. Rev. Lett. 94, 223902 (2005).

    Article  ADS  Google Scholar 

  5. Park, Y.-S. & Wang, H. Resolved-sideband and cryogenic cooling of an optomechanical resonator. Nature Phys. 5, 489–493 (2009).

    Article  ADS  Google Scholar 

  6. Dong, C., Fiore, V., Kuzyk, M. C. & Wang, H. Optomechanical dark mode. Science 338, 1609–1613 (2012).

    Article  ADS  Google Scholar 

  7. Tomes, M. & Carmon, T. Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates. Phys. Rev. Lett. 102, 113601 (2009).

    Article  ADS  Google Scholar 

  8. Hofer, J., Schliesser, A. & Kippenberg, T. J. Cavity optomechanics with ultrahigh-Q crystalline microresonators. Phys. Rev. A 82, 031804(R) (2010).

    Article  ADS  Google Scholar 

  9. Ding, L. et al. Wavelength-sized GaAs optomechanical resonators with gigahertz frequency. Appl. Phys. Lett. 98, 113108 (2011).

    Article  ADS  Google Scholar 

  10. Zhang, M., Luiz, G., Shah, S., Wiederhecker, G. & Lipson, M. Eliminating anchor loss in optomechanical resonators using elastic wave interference. Appl. Phys. Lett. 105, 051904 (2014).

    Article  ADS  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  ADS  Google Scholar 

  12. Chan, J., Eichenfield, M., Camacho, R. & Painter, O. Optical and mechanical design of a ‘zipper’ photonic crystal optomechanical cavity. Opt. Express 17, 3802–3817 (2009).

    Article  ADS  Google Scholar 

  13. Brooks, D. W. C. et al. Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012).

    Article  ADS  Google Scholar 

  14. Rabl, P. Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011).

    Article  ADS  Google Scholar 

  15. Braginsky, V. B. & Manukin, A. B. Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).

    Google Scholar 

  16. Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nature Nanotech. 7, 509–514 (2012).

    Article  ADS  Google Scholar 

  17. Grudinin, I. S., Lee, H., Painter, O. & Vahala, K. J. Phonon laser action in a tunable two-level system. Phys. Rev. Lett. 104, 083901 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Jing, H. et al. PT-symmetric phonon laser. Phys. Rev. Lett. 113, 053604 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Sciamanna, M. & Shore, K. A. Physics and applications of laser diode chaos. Nature Photon. 9, 151–162 (2015).

    Article  ADS  Google Scholar 

  24. Uchida, A. et al. Fast physical random bit generation with chaotic semiconductor lasers. Nature Photon. 2, 728–732 (2008).

    Article  ADS  Google Scholar 

  25. Redding, B. et al. Low spatial coherence electrically pumped semiconductor laser for speckle-free full-field imaging. Proc. Natl Acad. Sci. USA 112, 1304–1309 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. McDonnell, M. D. & Abbott, D. What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput. Biol. 5, e1000348 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  28. Gang, H., Ditzinger, T., Ning, C. Z. & Haken, H. Stochastic resonance without external periodic force. Phys. Rev. Lett. 71, 807 (1993).

    Article  ADS  Google Scholar 

  29. McDonnell, M. D. & Ward, L. M. The benefits of noise in neural systems: bridging theory and experiment. Nature Rev. Neurosci. 12, 415–426 (2011).

    Article  Google Scholar 

  30. Anishchenko, V. S., Neiman, A. B. & Safanova, M. A. Stochastic resonance in chaotic systems. J. Stat. Phys. 70, 183–196 (1993).

    Article  ADS  Google Scholar 

  31. Mantegna, R. N. & Spagnolo, B. Stochastic resonance in a tunnel diode. Phys. Rev. E 49, R1792–R1795 (1994).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. Hänggi, P. Stochastic resonance in biology how noise can enhance detection of weak signals and help improve biological information processing. ChemPhysChem. 3, 285–290 (2002).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Gammaitoni, L., Marchesoni, F., Menichella-Saetta, E. & Santucci, S. Stochastic resonance in bistable systems. Phy. Rev. Lett. 62, 349–352 (1989).

    Article  ADS  Google Scholar 

  37. Abbaspour, H., Trebaol, S., Portella-Oberli, M. & Deveaud, B. Stochastic resonance in collective exciton–polariton excitations inside a GaAs microcavity. Phys. Rev. Lett. 113, 057401 (2014).

    Article  ADS  Google Scholar 

  38. Liu, Z. & Lai, Y.-C. Coherence resonance in coupled chaotic oscillators. Phys. Rev. Lett. 86, 4737–4740 (2001).

    Article  ADS  Google Scholar 

  39. Karsaklian Dal Bosco, A., Wolfersberger, D. & Sciamanna, M. Delay-induced deterministic resonance of chaotic dynamics. Euro. Phys. Lett. 101, 24001 (2013).

    Article  ADS  Google Scholar 

  40. Masoller, C. Noise-induced resonance in delayed feedback systems. Phys. Rev. Lett. 88, 034102 (2002).

    Article  ADS  Google Scholar 

  41. Arteaga, M. A. et al. Experimental evidence of coherence resonance in a time-delayed bistable system. Phys. Rev. Lett. 99, 023903 (2007).

    Article  ADS  Google Scholar 

  42. Pikovsky, A. S. & Kurths, J. Coherence resonance in a noise-driven excitable system. Phys. Rev. Lett. 78, 775–778 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  43. Neiman, A., Saparin, P. I. & Stone, L. Coherence resonance at noisy precursors of bifurcations in nonlinear dynamical systems. Phys. Rev. E 56, 270–273 (1997).

    Article  ADS  Google Scholar 

  44. Lindner, B. & Schimansky-Geier, L. Analytical approach to the stochastic FitzHugh–Nagumo system and coherence resonance. Phys. Rev. E 60, 7270–7276 (1999).

    Article  ADS  Google Scholar 

  45. Postnov, D. E., Han, S. K., Yim, T. G. & Sosnovtseva, O. V. Experimental observation of coherence resonance in cascaded excitable systems. Phys. Rev. E 59, R3791–R3794 (1999).

    Article  ADS  Google Scholar 

  46. Ilchenko, V. S. & Gorodetskii, M. L. Thermal nonlinear effects in optical whispering gallery microresonators. Laser Phys. 2, 1004–1009 (1992).

    Google Scholar 

  47. Carmon, T., Yang, L. & Vahala, K. J. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express 12, 4742–4750 (2004).

    Article  ADS  Google Scholar 

  48. Carmon, T., Cross, M. C. & Vahala, K. J. Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure. Phys. Rev. Lett. 98, 167203 (2007).

    Article  ADS  Google Scholar 

  49. Bakemeier, L., Alvermann, A. & Fehske, H. Route to chaos in optomechanics. Phys. Rev. Lett. 114, 013601 (2015).

    Article  ADS  Google Scholar 

  50. Marquardt, F. & Girvin, S. M. Trend: optomechanics. Physics 2, 40 (2009).

    Article  Google Scholar 

  51. Lemarchand, A., Gorecki, J., Gorecki, A. & Nowakows, B. Temperature-driven coherence resonance and stochastic resonance in a thermochemical system. Phys. Rev. E 89, 022916 (2014).

    Article  ADS  Google Scholar 

  52. Dunn, T., Wenzler, J. & Mohanty, P. Anharmonic modal coupling in a bulk micromechanical resonator. Appl. Phys. Lett. 97, 123109 (2010).

    Article  ADS  Google Scholar 

  53. Gaidarzhy, A., Dorignac, J., Zolfagharkhani, G., Imboden, M. & Mohanty, P. Energy measurement in nonlinearly coupled nanomechanical modes. Appl. Phys. Lett. 98, 264106 (2011).

    Article  ADS  Google Scholar 

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Acknowledgements

The authors thank F. Marchesoni for discussions and for interpreting the results on stochastic resonance. Ş.K.Ö. thanks J. Mateo for support. L.Y. and Ş.K.Ö. are supported by ARO grant no. W911NF-12-1-0026. J.Z. is supported by the NSFC under grants nos. 61174084 and 61134008. Y.X.L. is supported by the NSFC under grant no. 61025022. Y.X.L. and J.Z. are supported by the National Basic Research Program of China (973 Program) under grant no. 2014CB921401, the NSFC under grant no. 61328502, the Tsinghua University Initiative Scientific Research Program and the Tsinghua National Laboratory for Information Science and Technology (TNList) Cross-discipline Foundation. F.N. is partially supported by the RIKEN iTHES Project, MURI Center for Dynamic Magneto-Optics, via AFOSR award no. FA9550-14-1-0040 and a Grant-in-Aid for Scientific Research (A). F.B. is supported by the NSFC under grant no. 11374165 and the 973 Program under grant no. 2013CB328702. The authors thank Z. Shen for helping with the numerical simulations used in the Supplementary Information.

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Author notes

  1. Faraz Monifi & Bo Peng

    Present address: Present addresses: Department of Electrical and Computer Engineering, University of California, San Diego La Jolla, California 92093-0407, USA (F.M.); IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA (B.P.),

Authors and Affiliations

  1. Department of Electrical and Systems Engineering, Washington University, St Louis, 63130, Missouri, USA

    Faraz Monifi, Jing Zhang, Şahin Kaya Özdemir, Bo Peng, Fang Bo & Lan Yang

  2. Department of Automation, Tsinghua University, Beijing, 100084, China

    Jing Zhang

  3. Center for Quantum Information Science and Technology, TNList, Beijing, 100084, China

    Jing Zhang & Yu-xi Liu

  4. Institute of Microelectronics, Tsinghua University, Beijing, 100084, China

    Yu-xi Liu

  5. The MOE Key Laboratory of Weak Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin, 300457, China

    Fang Bo

  6. CEMS, RIKEN, Saitama, 351-0198, Japan

    Franco Nori

  7. Physics Department, The University of Michigan, Ann Arbor, 48109-1040, Michigan, USA

    Franco Nori

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Contributions

F.M., J.Z. and Ş.K.Ö. contributed equally to this work. J.Z. and Ş.K.Ö. conceived the idea, J.Z. provided theoretical analysis under the guidance of Ş.K.Ö., Y.-x.L. and F.N. Ş.K.Ö. and L.Y. designed the experiments. F.M., J.Z. and B.P. performed the experiments and processed the data with help from Ş.K.Ö. and F.B. J.Z. and Ş.K.Ö. wrote the manuscript with contributions from all authors.

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Correspondence to Jing Zhang, Şahin Kaya Özdemir or Lan Yang.

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Monifi, F., Zhang, J., Özdemir, Ş. et al. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nature Photon 10, 399–405 (2016). https://doi.org/10.1038/nphoton.2016.73

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