Laser cooling of a nanomechanical oscillator into its quantum ground state

Journal name:
Nature
Volume:
478,
Pages:
89–92
Date published:
DOI:
doi:10.1038/nature10461
Received
Accepted
Published online

The simple mechanical oscillator, canonically consisting of a coupled mass–spring system, is used in a wide variety of sensitive measurements, including the detection of weak forces1 and small masses2. On the one hand, a classical oscillator has a well-defined amplitude of motion; a quantum oscillator, on the other hand, has a lowest-energy state, or ground state, with a finite-amplitude uncertainty corresponding to zero-point motion. On the macroscopic scale of our everyday experience, owing to interactions with its highly fluctuating thermal environment a mechanical oscillator is filled with many energy quanta and its quantum nature is all but hidden. Recently, in experiments performed at temperatures of a few hundredths of a kelvin, engineered nanomechanical resonators coupled to electrical circuits have been measured to be oscillating in their quantum ground state3, 4. These experiments, in addition to providing a glimpse into the underlying quantum behaviour of mesoscopic systems consisting of billions of atoms, represent the initial steps towards the use of mechanical devices as tools for quantum metrology5, 6 or as a means of coupling hybrid quantum systems7, 8, 9. Here we report the development of a coupled, nanoscale optical and mechanical resonator10 formed in a silicon microchip, in which radiation pressure from a laser is used to cool the mechanical motion down to its quantum ground state (reaching an average phonon occupancy number of ). This cooling is realized at an environmental temperature of 20K, roughly one thousand times larger than in previous experiments and paves the way for optical control of mesoscale mechanical oscillators in the quantum regime.

At a glance

Figures

  1. Optomechanical resonator with phononic shield.
    Figure 1: Optomechanical resonator with phononic shield.

    a, Scanning electron microscope (SEM) image of the patterned silicon nanobeam and the external phononic bandgap shield. b, Enlarged SEM image of the central cavity region of the nanobeam. c, Top: normalized electric field (colour scale) of the localized optical resonance of the nanobeam cavity, simulated using the finite-element method (FEM). Bottom: FEM simulation of the normalized displacement field of the acoustic resonance (breathing mode), which is coupled by radiation pressure to the co-localized optical resonance. The displacement field is indicated by the exaggerated deformation of the structure, with the relative magnitude of the local displacement (strain) indicated by the colour. d, SEM image of the interface between the nanobeam and the phononic bandgap shield. e, FEM simulation of the normalized squared displacement field amplitude of the localized acoustic resonance at the nanobeam–shield interface, indicating the strong suppression of acoustic radiation provided by the phononic bandgap shield. The colour scale represents log[x2/max(x2)], where x is the displacement field amplitude.

  2. Experimental set-up.
    Figure 2: Experimental set-up.

    A single, tunable, 1,550-nm diode laser is used as the cooling and mechanical transduction beam sent into the nanobeam optomechanical resonator cavity held in a continuous-flow helium cryostat. A wavemetre (WM) is used to track and lock the laser frequency, and a variable optical attenuator (VOA) is used to set the laser power. The transmitted signal is amplified by an erbium-doped fibre amplifier (EDFA) and detected on a high-speed photodetector (D2) connected to a real-time spectrum analyser (RSA), where the mechanical noise power spectrum is measured. A slowly modulated probe signal used for optical spectroscopy and calibration is generated from the cooling laser beam using an amplitude electro-optic modulator (EOM) driven by a microwave source (RFSG). The reflected component of this signal is separated from the input by an optical circulator (CIRC), sent to a photodetector (D1) and then demodulated using a lock-in amplifier (LIA). Paddle-wheel fibre polarization controllers (FPCs) are used to set the laser polarization at the input to the EOM and the input to the optomechanical cavity. For more detail, see Supplementary Information.

  3. Mechanical and optical response.
    Figure 3: Mechanical and optical response.

    a, Typical measured mechanical noise spectra around the resonance frequency of the breathing mode for low drive-laser power (nc = 1.4). The blue and red curves correspond to the spectra measured with the drive laser blue- and, respectively, red-detuned by a mechanical frequency from the optical cavity resonance. The black trace corresponds to the measured noise floor (dominated by EDFA noise) with the drive laser detuned far from the cavity resonance. b, Plot of the measured (squares) mechanical mode bath temperature (Tb) as a function of cryostat sample mount temperature (Tc). The dashed line indicates the curve corresponding to perfect following of the cryostat temperature by the mode temperature (Tb = Tc). c, Typical reflection spectrum (normalized power reflection) of the cavity while driven by the cooling laser (Δ = ωm, nc = 56, C = 11), as measured by a weaker probe beam at two-photon detuning Δsl. The signature reflection dip on resonance with the bare cavity mode, highlighted in the inset, is indicative of EIT caused by coupling of the optical and mechanical degrees of freedom by the cooling laser beam.

  4. Optical cooling results.
    Figure 4: Optical cooling results.

    a, Measured mechanical mode linewidth (squares), EIT transparency bandwidth (circles) and predicted optomechanical damping rate estimated using the zero-point optomechanical coupling rate, g/2π = 910kHz (red dashed line). Inset, measured EIT transparency window at the highest cooling-beam drive power. b, Measured (circles) average phonon number, , in the breathing mechanical mode at ωm/2π = 3.68GHz, versus cooling drive-laser power (in units of intracavity photons, nc), as deduced from the calibrated area under the Lorentzian line shape of the mechanical noise power spectrum. The inset spectra show the measured noise PSD (using xzpf = 2.7fm, corresponding to the numerically computed motional mass for the breathing mode with m = 311fg). The dashed blue line indicates the estimated mode phonon number calculated from the measured optical damping alone. Error bars indicate estimated uncertainties as outlined in Supplementary Information. c, Estimated bath temperature, Tb, versus cooling laser intracavity photon number, nc. d, Measured change in the intrinsic mechanical damping rate versus nc (circles). A polynomial fit to the mechanical damping dependence on nc is shown as a dashed line. For more details, see Supplementary Information. e, The measured (squares) background noise PSD versus drive-laser power (nc), in units of effective phonon quanta. The red dashed curve corresponds to the theoretical imprecision assuming shot-noise-limited detection but all other cavity properties and optical loss as in the experiment. The solid black curve is for an ideal, quantum-limited continuous position measurement of mechanical motion.

References

  1. Braginsky, V. & Manukin, A. Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977)
  2. Jensen, K., Kim, K. & Zettl, A. An atomic-resolution nanomechanical mass sensor. Nature Nanotechnol. 3, 533537 (2008)
  3. O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697703 (2010)
  4. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359363 (2011)
  5. Caves, C., Thorne, K., Drever, R., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. Rev. Mod. Phys. 52, 341392 (1980)
  6. Regal, C. A., Teufel, J. D. & Lehnert, K. W. Measuring nanomechanical motion with a microwave cavity interferometer. Nature Phys. 4, 555560 (2008)
  7. Wallquist, M., Hammerer, K., Rabl, P., Lukin, M. & Zoller, P. Hybrid quantum devices and quantum engineering. Phys. Scr. 2009, 014001 (2009)
  8. Stannigel, K., Rabl, P., Sørensen, A. S., Zoller, P. & Lukin, M. D. Optomechanical transducers for long-distance quantum communication. Phys. Rev. Lett. 105, 220501 (2010)
  9. Safavi-Naeini, A. H. & Painter, O. Proposal for an optomechanical traveling wave phonon-photon translator. N. J. Phys. 13, 013017 (2011)
  10. Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 7882 (2009)
  11. Cohen-Tannoudji, C. N. & Phillips, W. D. New mechanisms for laser cooling. Phys. Today 43, 3340 (1990)
  12. Diedrich, F., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62, 403406 (1989)
  13. Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: back-action at the mesoscale. Science 321, 11721176 (2008)
  14. Cohadon, P.-F., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83, 31743177 (1999)
  15. Metzger, C. H. & Karrai, K. Cavity cooling of a microlever. Nature 432, 10021005 (2004)
  16. Gigan, S. et al. Self-cooling of a micromirror by radiation pressure. Nature 444, 6770 (2006)
  17. Arcizet, O., Cohadon, P.-F., Briant, T., Pinard, M. & Heidmann, A. Radiation-pressure cooling and optomechanical instability of a micromirror. Nature 444, 7174 (2006)
  18. Gröblacher, S. et al. Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity. Nature Phys. 5, 485488 (2009)
  19. Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 7275 (2008)
  20. Rivière, R. et al. Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state. Phys. Rev. A 83, 063835 (2011)
  21. Rocheleau, T. et al. Preparation and detection of a mechanical resonator near the ground state of motion. Nature 463, 7275 (2010)
  22. Teufel, J. D. et al. Circuit cavity electromechanics in the strong-coupling regime. Nature 471, 204208 (2011)
  23. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2010)
  24. Alegre, T. P. M., Safavi-Naeini, A., Winger, M. & Painter, O. Quasi-two-dimensional optomechanical crystals with a complete phononic bandgap. Opt. Express 19, 56585669 (2011)
  25. 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)
  26. Safavi-Naeini, A. H. et al. Electromagnetically induced transparency and slow light with optomechanics. Nature 472, 6973 (2011)
  27. Vitali, D. et al. Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett. 98, 030405 (2007)
  28. Akram, U., Kiesel, N., Aspelmeyer, M. & Milburn, G. J. Single-photon optomechanics in the strong coupling regime. N. J. Phys. 12, 083030 (2010)
  29. Chang, D., Safavi-Naeini, A. H., Hafezi, M. & Painter, O. Slowing and stopping light using an optomechanical crystal array. N. J. Phys. 13, 023003 (2011)
  30. Rabl, P. Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011)

Download references

Author information

Affiliations

  1. Thomas J. Watson, Sr, Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA

    • Jasper Chan,
    • T. P. Mayer Alegre,
    • Amir H. Safavi-Naeini,
    • Jeff T. Hill,
    • Alex Krause,
    • Simon Gröblacher &
    • Oskar Painter
  2. Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria

    • Simon Gröblacher &
    • Markus Aspelmeyer
  3. Present address: Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, UNICAMP, 13083-859, Campinas, SP, Brazil.

    • T. P. Mayer Alegre

Contributions

J.C., T.P.M.A. and A.H.S.-N. designed the device, and J.C. fabricated it with support from J.T.H. J.C., T.P.M.A., A.H.S.-N., J.T.H., A.K. and S.G. performed the measurements and analysed the measured data. O.P. and M.A. supervised the measurements and the data analysis. All authors contributed to the writing of the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary Information (744K)

    The file contains Supplementary Text, Supplementary Figures 1-7 with legends and additional references.

Additional data