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Nanomechanical motion measured with an imprecision below that at the standard quantum limit

Abstract

Nanomechanical oscillators are at the heart of ultrasensitive detectors of force1, mass2 and motion3,4,5,6,7. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. If the imprecision of a measurement of the displacement of an oscillator8 is pushed below a scale set by the standard quantum limit, the measurement must perturb the motion of the oscillator by an amount larger than that scale. Here we show a displacement measurement with an imprecision below the standard quantum limit scale. We achieve this imprecision by measuring the motion of a nanomechanical oscillator with a nearly shot-noise limited microwave interferometer9. As the interferometer is naturally operated at cryogenic temperatures, the thermal motion of the oscillator is minimized, yielding an excellent force detector with a sensitivity of 0.51 aN Hz−1/2. This measurement is a critical step towards observing quantum behaviour in a mechanical object.

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Figure 1: Ideal displacement measurement.
Figure 2: Interferometric measurement schematic.
Figure 3: Total displacement noise demonstrating imprecision below the SQL.
Figure 4: Force sensitivity.

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References

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

    Article  CAS  Google Scholar 

  2. Jensen, K., Kim, K. & Zettl, A. An atomic-resolution nanomechanical mass sensor. Nature Nanotech. 3, 533–537 (2008).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  4. Anetsberger, G. et al. Near-field cavity optomechanics with nanomechanical oscillators. Nature Phys. 10.1038/nphys1425 (2009).

  5. Knobel, R. G. & Cleland, A. N. Nanometre-scale displacement sensing using a single electron transistor. Nature 424, 291–293 (2003).

    Article  CAS  Google Scholar 

  6. Poggio, M. et al. An off-board quantum point contact as a sensitive detector of cantilever motion. Nature Phys. 4, 635–638 (2008).

    Article  CAS  Google Scholar 

  7. Etaki, S. et al. Motion detection of a micromechanical resonator embedded in a d.c. SQUID. Nature Phys. 4, 785–788 (2008).

    Article  CAS  Google Scholar 

  8. 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. 1. Issues of principle. Rev. Mod. Phys. 52, 341–392 (1980).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  11. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).

    Article  Google Scholar 

  12. Abbott, B. et al. Analysis of LIGO data for gravitational waves from binary neutron stars. Phys. Rev. D 69, 122001 (2004).

    Article  Google Scholar 

  13. Arcizet, O. et al. High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor. Phys. Rev. Lett. 97, 133601 (2006).

    Article  CAS  Google Scholar 

  14. Corbitt, T. et al. Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK. Phys. Rev. Lett. 99, 160801 (2007).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. 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 

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

    Article  CAS  Google Scholar 

  18. Eichenfield, M., Camacho, R., Chan, J., Vahala, K. J. & Painter, O. A picogram- and nanometre-scale photonic-crystal optomechanical cavity. Nature 459, 550–555 (2009).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. Vitali, D., Tombesi, P., Woolley, M. J., Doherty, A. C. & Milburn, G. J. Entangling a nanomechanical resonator and a superconducting microwave cavity. Phys. Rev. A 76, 042336 (2007).

    Article  Google Scholar 

  21. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    Article  CAS  Google Scholar 

  22. Castellanos-Beltran, M. A., Irwin, K. D., Hilton, G. C., Vale, L. R. & Lehnert, K. W. Amplification and squeezing of quantum noise with a tunable Josephson metamaterial. Nature Phys. 4, 929–931 (2008).

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. 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  CAS  Google Scholar 

  25. 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  Google Scholar 

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

  27. Degen, C. L., Poggio, M., Mamin, H. J., Rettner, C. T. & Rugar, D. Nanoscale magnetic resonance imaging. Proc. Natl Acad. Sci. USA 106, 1313–1317 (2009).

    Article  CAS  Google Scholar 

  28. 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  Google Scholar 

  29. Mancini, S. & Tombesi, P. Quantum noise reduction by radiation pressure. Phys. Rev. A 49, 4055–4065 (1994).

    Article  CAS  Google Scholar 

  30. Mancini, S., Giovannetti, V., Vitali, D. & Tombesi, P. Entangling macroscopic oscillators exploiting radiation pressure. Phys. Rev. Lett. 88, 120401 (2002).

    Article  Google Scholar 

  31. Marshall, W., Simon, C., Penrose, R. & Bouwmeester, D. Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 130401 (2003).

    Article  Google Scholar 

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Acknowledgements

We acknowledge support from the National Science Foundation's Physics Frontier Center for Atomic, Molecular and Optical Physics and from the National Institute of Standards and Technology. T. D. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG). We thank N. E. Flowers-Jacobs for valuable conversations and technical assistance, and K. D. Irwin, G. C. Hilton, and L. R. Vale for fabrication, and help with the design, of the JPA.

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All authors contributed to project planning and data analysis. Experimental work was carried out by J.D.T., T.D., M.A.C. and J.W.H. Samples were fabricated by J.W.H. The manuscript was written by J.D.T., T.D., J.W.H. and K.W.L.

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Correspondence to K. W. Lehnert.

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Teufel, J., Donner, T., Castellanos-Beltran, M. et al. Nanomechanical motion measured with an imprecision below that at the standard quantum limit. Nature Nanotech 4, 820–823 (2009). https://doi.org/10.1038/nnano.2009.343

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