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Cooling a nanomechanical resonator with quantum back-action


Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action1,2,3. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK—an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

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  1. 1

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

  2. 2

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

  3. 3

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

  4. 4

    Abbott, B. et al. Upper limits on gravitational wave bursts in LIGO's second science run. Phys. Rev. D 72, 062001 (2005)

  5. 5

    Rugar, D., Budakian, R., Mamin, H. J. & Chui, B. W. Single spin detection by magnetic resonance force microscopy. Nature 430, 329–332 (2004)

  6. 6

    Tittonen, I. et al. Interferometric measurements of the position of a macroscopic body: Towards observations of quantum limits. Phys. Rev. A 59, 1038–1044 (1999)

  7. 7

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

  8. 8

    Schoelkopf, R. J., Wahlgren, P., Kozhevnikov, A. A., Delsing, P. & Prober, D. The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer. Science 280, 1238–1242 (1998)

  9. 9

    Fulton, T. A., Gammel, P. L., Bishop, D. J., Dunkleberger, L. N. & Dolan, G. J. Observation of combined Josephson and charging effects in small tunnel junction circuits. Phys. Rev. Lett. 63, 1307–1310 (1989)

  10. 10

    Clerk, A. A. & Bennett, S. Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects. N. J. Phys. 7, 238 (2005)

  11. 11

    Blencowe, M. P., Imbers, J. & Armour, A. D. Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor. N. J. Phys. 7, 236 (2005)

  12. 12

    Mozyrsky, D., Martin, I. & Hastings, M. B. Quantum-limited sensitivity of single-electron-transistor-based displacement detectors. Phys. Rev. Lett. 92, 018303 (2004)

  13. 13

    Armour, A. D., Blencowe, M. P. & Zhang, Y. Classical dynamics of a nanomechanical resonator coupled to a single-electron transistor. Phys. Rev. B 69, 125313 (2004)

  14. 14

    Mozyrsky, D. & Martin, I. Quantum-classical transition induced by electrical measurement. Phys. Rev. Lett. 89, 018301 (2002)

  15. 15

    Ojha, R. P., Lemieux, P.-A., Dixon, P. K., Liu, A. J. & Durian, D. J. Statistical mechanics of a gas-fluidized particle. Nature 427, 521–523 (2004)

  16. 16

    Clerk, A. A., Girvin, S. M., Nguyen, A. K. & Stone, A. D. Resonant Cooper-pair tunneling: quantum noise and measurement characteristics. Phys. Rev. Lett. 89, 176804 (2002)

  17. 17

    Gavish, U., Levinson, Y. & Imry, Y. Detection of quantum noise. Phys. Rev. B 62, R10637 (2000)

  18. 18

    Schoelkopf, R. J., Clerk, A. A., Girvin, S. M., Lehnert, K. W. & Devoret, M. H. in Quantum Noise is Mesoscopic Physics (Kluwer Academic, Norwell, Massachusetts, 2003)

  19. 19

    Deblock, R., Onac, E., Gurevich, L. & Kouwenhoven, L. P. Detection of quantum noise from an electrically driven two-level system. Science 301, 203–206 (2003)

  20. 20

    Braginsky, V. B. & Vyatchanin, S. P. Low quantum noise tranquilizer for Fabry-Perot interferometer. Phys. Lett. A 293, 228–234 (2002)

  21. 21

    Lett, P. D. et al. Optical molasses. J. Opt. Soc. Am. B 6, 2084–2107 (1989)

  22. 22

    Pohlen, S. L., Fitzgerald, R. J. & Tinkham, M. The Josephson-quasiparticle (JQP) current cycle in the superconducting single-electron transistor. Physica B 284–288, 1812–1813 (2000)

  23. 23

    Choi, M.-S., Plastina, F. & Fazio, R. Charge and current fluctuations in a superconducting single-electron transistor near a Cooper pair resonance. Phys. Rev. B 67, 045105 (2003)

  24. 24

    Ruskov, R., Schwab, K. & Korotkov, A. N. Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback. Phys. Rev. B 71, 235407 (2005)

  25. 25

    Armour, A. D., Blencowe, M. P. & Schwab, K. C. Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. Phys. Rev. Lett. 88, 148301 (2002)

  26. 26

    Irish, E. K. & Schwab, K. Quantum measurement of a coupled nanomechanical resonator-Cooper-pair box system. Phys. Rev. B 68, 155311 (2003)

  27. 27

    Martin, I., Shnirman, A., Tian, L. & Zoller, P. Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)

  28. 28

    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)

  29. 29

    Lundin, U. Localized heating or cooling in mesocopic devices by electron transport. Phys. Lett. A 332, 127–130 (2004)

  30. 30

    Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999)

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We thank A. Rimberg and A. Vandaley for discussions, and B. Camarota for assistance with the fabrication of the samples. M.P.B. is supported by the NSF through an NIRT grant, A.D.A. is supported by the EPSRC, and A.A.C. is supported by NSERC. Author Contributions A.N. and O.B. contributed equally to this work.

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Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Correspondence to K. C. Schwab.

Supplementary information

  1. Supplementary Notes

    This file contains details of the nanoelectromechanical device, both electronic and mechanical properties and describes the calibration procedure, noise thermometry, data analysis, and the analysis of the backaction and comparison to the quantum limit. This file also contains figures that show the SSET bias points used and typical noise spectra. (DOC 689 kb)

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Figure 1: Nanodevice and measurement diagram.
Figure 2: Resonator temperature versus bath temperature and coupling voltage.
Figure 3: Resonator damping rate and frequency shift versus coupling voltage.
Figure 4: Back-action effects versus SSET bias point.


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