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:

Back-action-evading measurements of nanomechanical motion

Nature Physics volume 6, pages 213–217 (2010)Cite this article

Abstract

When carrying out ultrasensitive continuous measurements of position, one must ultimately confront the fundamental effects of detection back-action. Back-action forces set a lower bound on the uncertainty in the measured position, the ‘standard quantum limit’ (SQL). Recent measurements of nano- and micromechanical resonators are rapidly approaching this limit. Making measurements with sensitivities surpassing the SQL will require a new kind of approach: back-action-evading (BAE), quantum non-demolition measurement techniques. Here we realize a BAE measurement based on the parametric coupling between a nanomechanical and a microwave resonator. We demonstrate for the first time BAE detection of a single quadrature of motion with sensitivity four times the quantum zero-point motion of the mechanical resonator. We identify a limiting parametric instability inherent in BAE measurement, and describe how to improve the technique to surpass the SQL and permit the formation of squeezed states of motion.

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: Device and measurement scheme.
Figure 2: Mechanical linewidth and occupation factor versus pump occupation.
Figure 3: Measured position sensitivity Δx or ΔX1 versus superconducting resonator pump occupation.
Figure 4: Single-quadrature detection and BAE.

Similar content being viewed by others

References

  1. Caves, C. M., Thorne, K. S., Drever, R. W. P., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).

    Article  ADS  Google Scholar 

  2. Clerk, A. A. Quantum-limited position detection and amplification: A linear response perspective. Phys. Rev. B 70, 245306 (2004).

    Article  ADS  Google Scholar 

  3. Braginskii, V. B. & Vorontsov, Yu. I. Quantum-mechanical limitations in macroscopic experiments and modern experimental design. Sov. Phys. Usp. 17, 644–650 (1975).

    Article  ADS  Google Scholar 

  4. Thorne, K. S., Drever, R. W. P., Caves, C. M., Zimmermann, M. & Sandberg, V. D. Quantum nondemolition measurements of harmonic oscillators. Phys. Rev. Lett. 40, 667–671 (1978).

    Article  ADS  Google Scholar 

  5. Braginsky, V. B., Vorontsov, Y. I. & Thorne, K. S. Quantum nondemolition measurements. Science 209, 547–557 (1980).

    Article  ADS  Google Scholar 

  6. Clerk, A. A., Marquardt, F. & Jacobs, K. Back-action evasion and squeezing of a mechanical resonator using a cavity detector. New J. Phys. 10, 095010 (2008).

    Article  ADS  Google Scholar 

  7. Bocko, M. F. & Onofrio, R. On the measurement of a weak classical force coupled to a harmonic oscillator: Experimental progress. Rev. Mod. Phys. 68, 755–799 (1996).

    Article  ADS  Google Scholar 

  8. Johnson, W. W. & Bocko, M. Approaching the quantum ‘limit’ for force detection. Phys. Rev. Lett. 47, 1184–1187 (1981).

    Article  ADS  Google Scholar 

  9. Naik, A. et al. Cooling a nanomechanical resonator with quantum back-action. Nature 443, 193–196 (2006).

    Article  ADS  Google Scholar 

  10. Teufel, J. D., Donner, T., Castellanos-Beltran, M. A., Harlow, J. W. & Lehnert, K. W. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nature Nanotech.doi:10.1038/nnano.2009.343 (2009).

  11. 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  ADS  Google Scholar 

  12. Abbott, B. et al. (LIGO Scientific Collaboration). Observation of a kilogram-scale oscillator near its quantum ground state. New J. Phys. 11, 073032 (2009).

    Article  ADS  Google Scholar 

  13. Briant, T. et al. Thermal and back-action noises in dual-sphere gravitational-wave detectors. Phys. Rev. D 67, 102005 (2003).

    Article  ADS  Google Scholar 

  14. 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  ADS  Google Scholar 

  15. Day, P. K., LeDuc, H. G., Mazin, B. A., Vayonakis, A. & Zmuidzinas, J. A broadband superconducting detector suitable for use in large arrays. Nature 425, 817–821 (2003).

    Article  ADS  Google Scholar 

  16. McNeilage, C. et al. IEEE International Ultrasonics, Ferroelectrics, and Frequency Control Joint 50th Anniversary Conference 210–218 (2004).

    Google Scholar 

  17. Verbridge, S. S., Craighead, H. G. & Parpia, J. M. A megahertz nanomechanical resonator with room temperature quality factor over a million. Appl. Phys. Lett. 92, 013112 (2008).

    Article  ADS  Google Scholar 

  18. Teufel, J. D., Regal, C. A. & Lehnert, K. W. Prospects for cooling nanomechanical motion by coupling to a superconducting microwave resonator. New J. Phys. 10, 095002 (2008).

    Article  ADS  Google Scholar 

  19. Teufel, J. D., Harlow, J. W., Regal, C. A. & Lehnert, K. W. Dynamical backaction of microwave fields on a nanomechanical oscillator. Phys. Rev. Lett. 101, 197203 (2008).

    Article  ADS  Google Scholar 

  20. Rocheleau, T. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Preprint at <http://arxiv.org/abs/0907.3313v1> (2009).

  21. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555–560 (2008).

    Article  Google Scholar 

  22. 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).

    Article  ADS  Google Scholar 

  23. Genes, C., Vitali, D., Tombesi, P., Gigan, S. & Aspelmeyer, M. Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes. Phys. Rev. A 77, 033804 (2008).

    Article  ADS  Google Scholar 

  24. Blencowe, M. P. & Buks, E. Quantum analysis of a linear dc squid mechanical displacement detector. Phys. Rev. B 76, 014511 (2007).

    Article  ADS  Google Scholar 

  25. Woolley, M. J., Doherty, A. C., Milburn, G. J. & Schwab, K. C. Nanomechanical squeezing with detection via a microwave cavity. Phys. Rev. A 78, 062303 (2008).

    Article  ADS  Google Scholar 

  26. Cleland, A. N. & Roukes, M. L. A nanometre-scale mechanical electrometer. Nature 392, 160–162 (1998).

    Article  ADS  Google Scholar 

  27. 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).

    Article  ADS  Google Scholar 

  28. LaHaye, M. D., Buu, O., Camarota, B. & Schwab, K. C. Approaching the quantum limit of a nanomechanical resonator. Science 304, 74–77 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. 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 

  31. Schliesser, A., Revière, R., Anetsberger, G., Arcizet, O. & Kippenberg, T. J. Resolved-sideband cooling of a micromechanical oscillator. Nature Phys. 4, 415–419 (2008).

    Article  ADS  Google Scholar 

  32. 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  ADS  Google Scholar 

  33. Xue, F., Wang, Y. D., Liu, Y.-X. & Nori, F. Cooling a micromechanical beam by coupling it to a transmission line. Phys. Rev. B 76, 205302 (2007).

    Article  ADS  Google Scholar 

  34. Braginsky, V. B. & Khalili, F. Ya. Quantum Measurement (Cambridge Univ. Press, 1992).

    Book  Google Scholar 

  35. Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement and amplification. Preprint at <http://arxiv.org/abs/0810.4729v1> (2008).

  36. Castellanos-Beltran, M. A. & Lehnert, K. W. Widely tunable parametric amplifier based on a superconducting quantum interference device array resonator. Appl. Phys. Lett. 91, 083509 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Marchese, L. E., Bocko, M. F. & Onofrio, R. Multipump and quasistroboscopic back-action evasion measurements for resonant-bar gravitational-wave antennas. Phys. Rev. D 45, 1869–1877 (1992).

    Article  ADS  Google Scholar 

  39. Poggio, M., Degen, C. L., Mamin, H. J. & Rugar, D. Feedback cooling of a cantilever’s fundamental mode below 5 mK. Phys. Rev. Lett. 99, 017201 (2007).

    Article  ADS  Google Scholar 

  40. Briant, T., Cohadon, P. F., Pinard, M. & Heidmann, A. Optical phase-space reconstruction of mirror motion at the attometer level. Eur. Phys. J. D 22, 131–140 (2003).

    Article  ADS  Google Scholar 

  41. Kleckner, D. & Bouwmeester, D. Sub-kelvin optical cooling of a micromechanical resonator. Nature 444, 75–78 (2006).

    Article  ADS  Google Scholar 

  42. Rugar, D. & Grütter, P. Mechanical parametric amplification and thermomechanical noise squeezing. Phys. Rev. Lett. 67, 699–702 (1991).

    Article  ADS  Google Scholar 

  43. Hu, B. L. & Zhang, Y. Squeezed states and the uncertainty relation at finite temperature. Mod. Phys. Lett. A 8, 3575–3584 (1993).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge helpful conversations with G. Milburn, M. Aspelmeyer, B. Plourde, M. Blencowe and R. Onofrio, and the assistance of P. Hauck, M. Corbett, S. Rosenthal and C. Macklin. The work has been supported by Cornell University and grants from FQXi and the National Science Foundation. A.A.C. wishes to thank the Canadian Institute for Advanced Research. Device fabrication was carried out at the NSF-sponsored Cornell Nanoscale Facility.

Author information

Authors and Affiliations

  1. Department of Physics, Laboratory for Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

    J. B. Hertzberg, T. Rocheleau, T. Ndukum & M. Savva

  2. Department of Physics, University of Maryland, College Park, Maryland 20742, USA

    J. B. Hertzberg

  3. Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada

    A. A. Clerk

  4. Applied Physics, Caltech, Pasadena, California 91125, USA

    K. C. Schwab

Authors
  1. J. B. Hertzberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Rocheleau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Ndukum
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Savva
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. A. Clerk
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. K. C. Schwab
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.B.H., T.R. and T.N. contributed equally to the execution and analysis of this work. M.S. built key apparatus. A.A.C. provided analysis and theoretical support. K.C.S. designed and oversaw all aspects of the work.

Corresponding author

Correspondence to K. C. Schwab.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 1086 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hertzberg, J., Rocheleau, T., Ndukum, T. et al. Back-action-evading measurements of nanomechanical motion. Nature Phys 6, 213–217 (2010). https://doi.org/10.1038/nphys1479

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1479

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