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.

  • Article
  • Published:

Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field

Nature Nanotechnology volume 9, pages 920–926 (2014)Cite this article

Subjects

Abstract

Optomechanics, which explores the fundamental coupling between light and mechanical motion, has made important advances in manipulating macroscopic mechanical oscillators down to the quantum level. However, dynamical effects related to the vectorial nature of the optomechanical interaction remain to be investigated. Here we study a nanowire with subwavelength dimensions coupled strongly to a tightly focused beam of light, enabling an ultrasensitive readout of the nanoresonator dynamics. We determine experimentally the vectorial structure of the optomechanical interaction and demonstrate that a bidimensional dynamical backaction governs the nanowire dynamics. Moreover, the spatial topology of the optomechanical interaction is responsible for novel canonical signatures of strong coupling between mechanical modes, which leads to a topological instability that underlies the non-conservative nature of the optomechanical interaction. These results have a universal character and illustrate the increased sensitivity of nanomechanical devices towards spatially varying interactions, opening fundamental perspectives in nanomechanics, optomechanics, ultrasensitive scanning force microscopy and nano-optics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: An ultrasensitive optical readout of motion at the nanoscale.
Figure 2: Measurement of the bidimensional topology of the optomechanical interaction force field.
Figure 3: Optomechanical backaction in 2D.
Figure 4: Dynamical bifurcation and topological instability in a non-conservative vectorial force field.

Similar content being viewed by others

References

  1. Bohr, N. Discussion with Einstein on Epistemological Problems in Atomic Physics (University of Copenhagen, 1949).

    Google Scholar 

  2. Caves, C. M. Quantum limits on noise in linear amplifiers. Phys. Rev. D 26, 1817–1839 (1982).

    Article  Google Scholar 

  3. Braginsky, V. B. & Khalili, F. Y. Quantum Measurement (Cambridge Univ. Press, 1995).

    Google Scholar 

  4. Jaekel, M. T. & Reynaud, S. Quantum limits in interferometric measurements. Europhys. Lett. 13, 301–306 (1990).

    Article  Google Scholar 

  5. 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 

  6. Cohadon, P. F., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83, 3174–3177 (1999).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. 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 

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

    Article  CAS  Google Scholar 

  10. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  13. Verhagen, E., Deléglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012).

    Article  CAS  Google Scholar 

  14. Verlot, P., Tavernarakis, A., Briant, T., Cohadon, P.-F. & Heidmann, A. Scheme to probe optomechanical correlations between two optical beams down to the quantum level. Phys. Rev. Lett. 102, 103601 (2009).

    Article  CAS  Google Scholar 

  15. Marino, F., Cataliotti, F. S., Farsi, A., de Cumis, M. S. & Marin, F. Classical signature of ponderomotive squeezing in a suspended mirror resonator. Phys. Rev. Lett. 104, 73601 (2010).

    Article  Google Scholar 

  16. Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).

    Article  CAS  Google Scholar 

  17. Verlot, P., Tavernarakis, A., Briant, T., Cohadon, P-F. & Heidmann, A. Backaction amplification and quantum limits in optomechanical measurements. Phys. Rev. Lett. 104, 133602 (2010).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. Pinard, M., Hadjar, Y. & Heidmann, A. Effective mass in quantum effects of radiation pressure. Eur. Phys. J. D 7, 107–116 (1999).

    CAS  Google Scholar 

  21. Bowman, R. W. & Padgett, M. J. Optical trapping and binding. Rep. Prog. Phys. 76, 026401 (2013).

    Article  Google Scholar 

  22. Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, 2004).

    Google Scholar 

  23. Novotny, L. & Hecht, B. Principles of Nano-Optics (Cambridge Univ. Press, 2006).

    Book  Google Scholar 

  24. Roichman, Y., Sun, B., Stolarski, A. & Grier, D. G. Influence of nonconservative optical forces on the dynamics of optically trapped colloidal spheres: the fountain of probability. Phys. Rev. Lett. 101, 128301 (2008).

    Article  Google Scholar 

  25. Sun, B., Lin, J., Darby, E., Grosberg, A. Y. & Grier, D. G. Brownian vortexes. Phys. Rev. E 80, 010401 (2009).

    Article  Google Scholar 

  26. Krechetnikov, R. & Marsden, J. E. Dissipation-induced instabilities in finite dimensions. Rev. Mod. Phys. 79, 519–553 (2007).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. Favero, I. & Karrai, K. Optomechanics of deformable optical cavities. Nature Photon. 3, 201–205 (2009).

    Article  CAS  Google Scholar 

  30. Gavartin, E. et al. Optomechanical coupling in a two-dimensional photonic crystal defect cavity. Phys. Rev. Lett. 106, 203902 (2011).

    Article  CAS  Google Scholar 

  31. Ramos, D. et al. Optomechanics with silicon nanowires by harnessing confined electromagnetic modes. Nano Lett. 12, 932–937 (2012).

    Article  CAS  Google Scholar 

  32. Perisanu, S. et al. High Q factor for mechanical resonances of batch-fabricated SiC nanowires. Appl. Phys. Lett. 90, 043113 (2007).

    Article  Google Scholar 

  33. Ren, K. F., Gréhan, G. & Gouesbet, G. Prediction of reverse radiation pressure by generalized Lorenz–Mie theory. Appl. Opt. 35, 2702–2710 (1996).

    Article  CAS  Google Scholar 

  34. Dogariu, A., Sukhov, S. & Sáenz, J. Optically induced ‘negative forces’. Nature Photon. 7, 24–27 (2012).

    Article  Google Scholar 

  35. Wilson-Rae, I., Zoller, P. & Imamoglu, A. Laser cooling of a nanomechanical resonator mode to its quantum ground state. Phys. Rev. Lett. 92, 075507 (2004).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  37. Arcizet, O. et al. A single nitrogen-vacancy defect coupled to a nanomechanical oscillator. Nature Phys. 7, 879–883 (2011).

    Article  CAS  Google Scholar 

  38. Yeo, I. et al. Strain-mediated coupling in a quantum dot–mechanical oscillator hybrid system. Nature Nanotech. 9, 106–110 (2014).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nature Nanotech. 7, 300–303 (2012).

    Article  Google Scholar 

  41. Hanay, M. S. et al. Single-protein nanomechanical mass spectrometry in real time. Nature Nanotech. 7, 602–608 (2012).

    Article  CAS  Google Scholar 

  42. Nichol, J. M., Hemesath, E. R., Lauhon, L. J. & Budakian, R. Viewpoint: silicon nanowires feel the force of magnetic resonance. Phys. Rev. B 85, 054414 (2012).

    Article  Google Scholar 

  43. Li, T., Kheifets, S. & Raizen, M. G. Millikelvin cooling of an optically trapped microsphere in vacuum. Nature Phys. 7, 527–530 (2011).

    Article  CAS  Google Scholar 

  44. Gieseler, J., Deutsch, B., Quidant, R. & Novotny, L. Subkelvin parametric feedback cooling of a laser-trapped nanoparticle. Phys. Rev. Lett. 109, 103603 (2012).

    Article  Google Scholar 

  45. Treps, N. et al. A quantum laser pointer. Science 301, 940–943 (2003).

    Article  CAS  Google Scholar 

  46. Nichol, J. M., Hemesath, E. R., Lauhon, L. J. & Budakian, R. Displacement detection of silicon nanowires by polarization-enhanced fiber-optic interferometry. Appl. Phys. Lett. 93, 193110–193110 (2008).

    Article  Google Scholar 

  47. Kubo, R. The fluctuation–dissipation theorem. Rep. Prog. Phys. 29, 255–284 (1966).

    Article  CAS  Google Scholar 

  48. Caniard, T., Verlot, P., Briant, T., Cohadon, P-F. & Heidmann, A. Observation of back-action noise cancellation in interferometric and weak force measurements. Phys. Rev. Lett. 99, 110801 (2007).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  50. Rugar, D. et al. Single spin detection by magnetic resonance force microscopy. Nature 430, 329–332 (2004).

    Article  CAS  Google Scholar 

  51. Novotny, L. Strong coupling, energy splitting, and level crossings: a classical perspective. Am. J. Phys. 78, 1199 (2010).

    Article  Google Scholar 

  52. Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles (Wiley, 1983).

    Google Scholar 

  53. Heinrich, G., Ludwig, M., Qian, J., Kubala, B. & Marquardt, F. Collective dynamics in optomechanical arrays. Phys. Rev. Lett. 107, 043603 (2011).

    Article  Google Scholar 

  54. Zhang, M. et al. Synchronization of micromechanical oscillators using light. Phys. Rev. Lett. 109, 233906 (2012).

    Article  Google Scholar 

  55. Seok, H., Buchmann, L. F., Wright, E. M. & Meystre, P. Multimode strong-coupling quantum optomechanics. Phys. Rev. A 88, 063850 (2013).

    Article  Google Scholar 

  56. Bauer, T., Orlov, S., Peschel, U., Banzer, P. & Leuchs, G. Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams. Nature Photon. 8, 23–27 (2014).

    Article  CAS  Google Scholar 

  57. Chen, J., Ng, J., Lin, Z. & Chan, C. T. Optical pulling force. Nature Photon. 5, 531–534 (2011).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank B. Pigeau, J.P. Poizat, A. Kuhn, N. Roch, G. Nogues, J. Jarreau, L. Del Rey, D. Maillard, E. Eyraud, C. Hoarau and D. Lepoittevin for fruitful interactions and technical developments. This work was supported by the Agence Nationale de la Recherche (RPDoc-2010, FOCUS 2013), Lanef (CryOptics) and the European Research Council (ERC-StG-2012, HQ-NOM).

Author information

Authors and Affiliations

  1. Institut Néel, Université Grenoble Alpes – CNRS:UPR2940, Grenoble, 38042, France

    A. Gloppe, P. Verlot, E. Dupont-Ferrier, G. Bachelier & O. Arcizet

  2. Institut Lumière Matière, UMR5306, CNRS – Université Claude Bernard Lyon 1, Villeurbanne, 69622, France

    A. Siria, P. Poncharal & P. Vincent

Authors
  1. A. Gloppe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Verlot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Dupont-Ferrier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Siria
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Poncharal
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. Bachelier
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. Vincent
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. O. Arcizet
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to all aspects of this work.

Corresponding author

Correspondence to O. Arcizet.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 11838 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gloppe, A., Verlot, P., Dupont-Ferrier, E. et al. Bidimensional nano-optomechanics and topological backaction in a non-conservative radiation force field. Nature Nanotech 9, 920–926 (2014). https://doi.org/10.1038/nnano.2014.189

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2014.189

This article is cited by

Search

Advanced 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