Abstract

Extraneous thermal motion can limit displacement sensitivity and radiation pressure effects, such as optical cooling, in a cavity-optomechanical system. Here we present an active noise suppression scheme and its experimental implementation. The main challenge is to selectively sense and suppress extraneous thermal noise without affecting motion of the oscillator. Our solution is to monitor two modes of the optical cavity, each with different sensitivity to the oscillator’s motion but similar sensitivity to the extraneous thermal motion. This information is used to imprint “anti-noise” onto the frequency of the incident laser field. In our system, based on a nano-mechanical membrane coupled to a Fabry-Pérot cavity, simulation and experiment demonstrate that extraneous thermal noise can be selectively suppressed and that the associated limit on optical cooling can be reduced.

© 2012 OSA

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    [CrossRef] [PubMed]
  3. F. Marquardt, “Optomechanics,” Physics 2, 40 (2009).
    [CrossRef]
  4. A. Cleland, “Optomechanics: Photons refrigerating phonons,” Nat. Phys. 5, 458–460 (2009).
    [CrossRef]
  5. M. Aspelmeyer, S. Gröblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics – throwing a glance,” J. Opt. Soc. Am. B 27, A189–A197 (2010).
    [CrossRef]
  6. S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
    [CrossRef]
  7. O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
    [CrossRef]
  8. A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
    [CrossRef]
  9. M. Eichenfield, J. Chan, A. Safavi-Naeini, K. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 020078 (2009).
    [CrossRef]
  10. G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
    [CrossRef] [PubMed]
  11. B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
    [CrossRef]
  12. G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
    [CrossRef]
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    [CrossRef]
  14. D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
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  16. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
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    [CrossRef]
  20. F. Marquardt, J. Chen, A. Clerk, and S. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 93902 (2007).
    [CrossRef]
  21. T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-q microcavities: application to micro-raman lasers and microparametric oscillators,” Opt. Express 13, 3558–3566 (2005).
    [CrossRef] [PubMed]
  22. P. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
    [CrossRef]
  23. L. Diósi, “Laser linewidth hazard in optomechanical cooling,” Phys. Rev. A 78, 021801 (2008).
    [CrossRef]
  24. G. Phelps and P. Meystre, “Laser phase noise effects on the dynamics of optomechanical resonators,” Phys. Rev. A 83, 063838 (2011).
    [CrossRef]
  25. P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009).
    [CrossRef]
  26. A. Gillespie and F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
    [CrossRef]
  27. G. Harry, H. Armandula, E. Black, D. Crooks, G. Cagnoli, J. Hough, P. Murray, S. Reid, S. Rowan, P. Sneddon, M. M. Fejer, R. Route, and S. D. Penn, “Thermal noise from optical coatings in gravitational wave detectors,” Appl. Opt. 45, 1569–1574 (2006).
    [CrossRef] [PubMed]
  28. H. J. Butt and M. Jaschke, “Calculation of thermal noise in atomic force microscopy,” Nanotechnology 6, 1 (1995).
    [CrossRef]
  29. K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
    [CrossRef]
  30. A. Cleland and M. Roukes, “Noise processes in nanomechanical resonators,” J. Appl. Phys. 92, 2758–2769 (2002).
    [CrossRef]
  31. T. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. Electron Dev. 40, 903–909 (1993).
    [CrossRef]
  32. V. Braginsky, V. Mitrofanov, V. Panov, K. Thorne, and C. Eller, Systems with Small Dissipation (Univ. of Chicago Press, 1986).
  33. S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
    [CrossRef]
  34. D. Santamore and Y. Levin, “Eliminating thermal violin spikes from ligo noise,” Phys. Rev. D 64, 042002 (2001).
    [CrossRef]
  35. P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett. 83, 3174–3177 (1999).
    [CrossRef]
  36. M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilevere’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
    [CrossRef] [PubMed]
  37. B. Sheard, M. Gray, B. Slagmolen, J. Chow, and D. McClelland, “Experimental demonstration of in-loop intra-cavity intensity-noise suppression,” IEEE J. Quantum Electron. 41, 434–440 (2005).
    [CrossRef]
  38. C. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
    [CrossRef] [PubMed]
  39. V. Braginsky and S. Vyatchanin, “Low quantum noise tranquilizer for fabry-perot interferometer,” Phys. Lett. A 293, 228–234 (2002).
    [CrossRef]
  40. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
    [CrossRef] [PubMed]
  41. A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
    [CrossRef]
  42. Prof. Jun Ye and Prof. Peter Zoller, private discussions.
  43. J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
    [CrossRef]
  44. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  45. E. Black, “An introduction to pounddreverhall laser frequency stabilization,” Am. J. Phys 69, 79 (2001).
    [CrossRef]
  46. For a generic time-dependent variable ζ(t), the Fourier transform is defined as ζ(f)≡∫−∞∞ζ(t)e−2πiftdt, and the one-sided power spectral density at Fourier frequency f is Sζ(f)≡2∫−∞∞〈ζ(t)ζ(t+τ)〉e2iπftdτ with unit [ζ]2/Hz. The normalization convention is that 〈ζ2(t)〉=∫0∞Sζ(f)df.
  47. Provided by Prof. Jun Ye’s group.
  48. M. Pinard, Y. Hadjar, and A. Heidmann, “Effective mass in quantum effects of radiation pressure,” Eur. Phys. J. D 7, 107–116 (1999).
  49. H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951).
    [CrossRef]
  50. www.comsol.com .
  51. D. F. Wall and G. J. Milburn, Quantum Optics (Springer, 1995), chap. 7.

2011 (5)

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

G. Phelps and P. Meystre, “Laser phase noise effects on the dynamics of optomechanical resonators,” Phys. Rev. A 83, 063838 (2011).
[CrossRef]

2010 (3)

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
[CrossRef]

M. Aspelmeyer, S. Gröblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics – throwing a glance,” J. Opt. Soc. Am. B 27, A189–A197 (2010).
[CrossRef]

2009 (7)

F. Marquardt, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

A. Cleland, “Optomechanics: Photons refrigerating phonons,” Nat. Phys. 5, 458–460 (2009).
[CrossRef]

M. Eichenfield, J. Chan, A. Safavi-Naeini, K. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 020078 (2009).
[CrossRef]

S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[CrossRef]

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009).
[CrossRef]

2008 (6)

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

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[CrossRef] [PubMed]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

L. Diósi, “Laser linewidth hazard in optomechanical cooling,” Phys. Rev. A 78, 021801 (2008).
[CrossRef]

2007 (4)

T. J. Kippenberg and K. J. Vahala, “Cavity Opto-Mechanics,” Opt. Express 15, 17172–17205 (2007).
[CrossRef] [PubMed]

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilevere’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[CrossRef] [PubMed]

F. Marquardt, J. Chen, A. Clerk, and S. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 93902 (2007).
[CrossRef]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

2006 (2)

S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
[CrossRef]

G. Harry, H. Armandula, E. Black, D. Crooks, G. Cagnoli, J. Hough, P. Murray, S. Reid, S. Rowan, P. Sneddon, M. M. Fejer, R. Route, and S. D. Penn, “Thermal noise from optical coatings in gravitational wave detectors,” Appl. Opt. 45, 1569–1574 (2006).
[CrossRef] [PubMed]

2005 (2)

T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-q microcavities: application to micro-raman lasers and microparametric oscillators,” Opt. Express 13, 3558–3566 (2005).
[CrossRef] [PubMed]

B. Sheard, M. Gray, B. Slagmolen, J. Chow, and D. McClelland, “Experimental demonstration of in-loop intra-cavity intensity-noise suppression,” IEEE J. Quantum Electron. 41, 434–440 (2005).
[CrossRef]

2004 (2)

C. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
[CrossRef] [PubMed]

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

2002 (2)

A. Cleland and M. Roukes, “Noise processes in nanomechanical resonators,” J. Appl. Phys. 92, 2758–2769 (2002).
[CrossRef]

V. Braginsky and S. Vyatchanin, “Low quantum noise tranquilizer for fabry-perot interferometer,” Phys. Lett. A 293, 228–234 (2002).
[CrossRef]

2001 (2)

D. Santamore and Y. Levin, “Eliminating thermal violin spikes from ligo noise,” Phys. Rev. D 64, 042002 (2001).
[CrossRef]

E. Black, “An introduction to pounddreverhall laser frequency stabilization,” Am. J. Phys 69, 79 (2001).
[CrossRef]

1999 (2)

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

P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett. 83, 3174–3177 (1999).
[CrossRef]

1995 (2)

A. Gillespie and F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

H. J. Butt and M. Jaschke, “Calculation of thermal noise in atomic force microscopy,” Nanotechnology 6, 1 (1995).
[CrossRef]

1993 (1)

T. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. Electron Dev. 40, 903–909 (1993).
[CrossRef]

1990 (1)

P. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1970 (1)

V. B. Braginsky, A. B. Manukin, and M. Y. Tikhonov, “Investigation of dissipative ponderomotive effects of electromagnetic radiation,” Sov. Phys. JETP 31, 829 (1970).

1951 (1)

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

Ageev, A.

S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
[CrossRef]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

Allman, M.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

Anetsberger, G.

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

Ansmann, M.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Arcizet, O.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

Armandula, H.

Aspelmeyer, M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

M. Aspelmeyer, S. Gröblacher, K. Hammerer, and N. Kiesel, “Quantum optomechanics – throwing a glance,” J. Opt. Soc. Am. B 27, A189–A197 (2010).
[CrossRef]

P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009).
[CrossRef]

S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[CrossRef]

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

Bialczak, R.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Black, E.

Braginsky, V.

V. Braginsky and S. Vyatchanin, “Low quantum noise tranquilizer for fabry-perot interferometer,” Phys. Lett. A 293, 228–234 (2002).
[CrossRef]

V. Braginsky, V. Mitrofanov, V. Panov, K. Thorne, and C. Eller, Systems with Small Dissipation (Univ. of Chicago Press, 1986).

Braginsky, V. B.

V. B. Braginsky, A. B. Manukin, and M. Y. Tikhonov, “Investigation of dissipative ponderomotive effects of electromagnetic radiation,” Sov. Phys. JETP 31, 829 (1970).

Busby, D.

S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
[CrossRef]

Butt, H. J.

H. J. Butt and M. Jaschke, “Calculation of thermal noise in atomic force microscopy,” Nanotechnology 6, 1 (1995).
[CrossRef]

Cagnoli, G.

Callen, H. B.

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

Camp, J.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

Carmon, T.

Chan, J.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

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[CrossRef]

Regal, C. A.

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Reid, S.

Riviere, R.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

Rivière, R.

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

Rokhsari, H.

Roukes, M.

A. Cleland and M. Roukes, “Noise processes in nanomechanical resonators,” J. Appl. Phys. 92, 2758–2769 (2002).
[CrossRef]

Route, R.

Rowan, S.

Rugar, D.

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilevere’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[CrossRef] [PubMed]

Safavi-Naeini, A.

M. Eichenfield, J. Chan, A. Safavi-Naeini, K. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 020078 (2009).
[CrossRef]

Safavi-Naeini, A. H.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

Sank, D.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Sankey, J.

J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
[CrossRef]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

Santamore, D.

D. Santamore and Y. Levin, “Eliminating thermal violin spikes from ligo noise,” Phys. Rev. D 64, 042002 (2001).
[CrossRef]

Saulson, P.

P. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
[CrossRef]

Schliesser, A.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

Schwab, K.

S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[CrossRef]

Shanks, W.

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

Sheard, B.

B. Sheard, M. Gray, B. Slagmolen, J. Chow, and D. McClelland, “Experimental demonstration of in-loop intra-cavity intensity-noise suppression,” IEEE J. Quantum Electron. 41, 434–440 (2005).
[CrossRef]

Simmonds, R.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

Sirois, A.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

Slagmolen, B.

B. Sheard, M. Gray, B. Slagmolen, J. Chow, and D. McClelland, “Experimental demonstration of in-loop intra-cavity intensity-noise suppression,” IEEE J. Quantum Electron. 41, 434–440 (2005).
[CrossRef]

Sneddon, P.

Spillane, S.

Teufel, J.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

Thompson, J.

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

Thompson, J. D.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[CrossRef] [PubMed]

Thorne, K.

V. Braginsky, V. Mitrofanov, V. Panov, K. Thorne, and C. Eller, Systems with Small Dissipation (Univ. of Chicago Press, 1986).

Tikhonov, M. Y.

V. B. Braginsky, A. B. Manukin, and M. Y. Tikhonov, “Investigation of dissipative ponderomotive effects of electromagnetic radiation,” Sov. Phys. JETP 31, 829 (1970).

Tombesi, P.

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

Vahala, K.

M. Eichenfield, J. Chan, A. Safavi-Naeini, K. Vahala, and O. Painter, “Modeling dispersive coupling and losses of localized optical and mechanical modes in optomechanical crystals,” Opt. Express 17, 020078 (2009).
[CrossRef]

T. Carmon, T. Kippenberg, L. Yang, H. Rokhsari, S. Spillane, and K. Vahala, “Feedback control of ultra-high-q microcavities: application to micro-raman lasers and microparametric oscillators,” Opt. Express 13, 3558–3566 (2005).
[CrossRef] [PubMed]

Vahala, K. J.

Vanner, M.

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[CrossRef]

Vitali, D.

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

Vyatchanin, S.

V. Braginsky and S. Vyatchanin, “Low quantum noise tranquilizer for fabry-perot interferometer,” Phys. Lett. A 293, 228–234 (2002).
[CrossRef]

Wall, D. F.

D. F. Wall and G. J. Milburn, Quantum Optics (Springer, 1995), chap. 7.

Wang, H.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Weides, M.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Weis, S.

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

Welton, T. A.

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

Wenner, J.

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

Werbach, K.

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

Whittaker, J.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

Willems, P.

S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
[CrossRef]

Wilson, D. J.

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

Wilson-Rae, I.

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

Yang, C.

J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
[CrossRef]

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

Yang, L.

Zwerger, W.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

Zwickl, B.

J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
[CrossRef]

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

Zwickl, B. M.

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[CrossRef] [PubMed]

Am. J. Phys (1)

E. Black, “An introduction to pounddreverhall laser frequency stabilization,” Am. J. Phys 69, 79 (2001).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

B. Zwickl, W. Shanks, A. Jayich, C. Yang, B. Jayich, J. Thompson, and J. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. 92, 103125–103125 (2008).
[CrossRef]

Eur. Phys. J. D (1)

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

IEEE J. Quantum Electron. (1)

B. Sheard, M. Gray, B. Slagmolen, J. Chow, and D. McClelland, “Experimental demonstration of in-loop intra-cavity intensity-noise suppression,” IEEE J. Quantum Electron. 41, 434–440 (2005).
[CrossRef]

IEEE Trans. Electron Dev. (1)

T. Gabrielson, “Mechanical-thermal noise in micromachined acoustic and vibration sensors,” IEEE Trans. Electron Dev. 40, 903–909 (1993).
[CrossRef]

J. Appl. Phys. (1)

A. Cleland and M. Roukes, “Noise processes in nanomechanical resonators,” J. Appl. Phys. 92, 2758–2769 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

N. J. Phys. (1)

A. Jayich, J. Sankey, B. Zwickl, C. Yang, J. Thompson, S. Girvin, A. Clerk, F. Marquardt, and J. Harris, “Dispersive optomechanics: a membrane inside a cavity,” N. J. Phys. 10, 095008 (2008).
[CrossRef]

Nanotechnology (1)

H. J. Butt and M. Jaschke, “Calculation of thermal noise in atomic force microscopy,” Nanotechnology 6, 1 (1995).
[CrossRef]

Nat. Commun. (1)

G. Cole, I. Wilson-Rae, K. Werbach, M. Vanner, and M. Aspelmeyer, “Phonon-tunneling dissipation in mechanical resonators,” Nat. Commun. 2, 231 (2011).
[CrossRef] [PubMed]

Nat. Photonics (1)

G. Anetsberger, R. Rivière, A. Schliesser, O. Arcizet, and T. Kippenberg, “Ultralow-dissipation optomechanical resonators on a chip,” Nat. Photonics 2, 627–633 (2008).
[CrossRef]

Nat. Phys. (3)

S. Gröblacher, J. Hertzberg, M. Vanner, G. Cole, S. Gigan, K. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nat. Phys. 5, 485–488 (2009).
[CrossRef]

A. Cleland, “Optomechanics: Photons refrigerating phonons,” Nat. Phys. 5, 458–460 (2009).
[CrossRef]

J. Sankey, C. Yang, B. Zwickl, A. Jayich, and J. Harris, “Strong and tunable nonlinear optomechanical coupling in a low-loss system,” Nat. Phys. 6, 707 (2010).
[CrossRef]

Nature (5)

J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
[CrossRef] [PubMed]

C. Metzger and K. Karrai, “Cavity cooling of a microlever,” Nature 432, 1002–1005 (2004).
[CrossRef] [PubMed]

A. O’Connell, M. Hofheinz, M. Ansmann, R. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[CrossRef]

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Sirois, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359 (2011).
[CrossRef] [PubMed]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Lett. A (2)

S. Penn, A. Ageev, D. Busby, G. Harry, A. Gretarsson, K. Numata, and P. Willems, “Frequency and surface dependence of the mechanical loss in fused silica,” Phys. Lett. A 352, 3–6 (2006).
[CrossRef]

V. Braginsky and S. Vyatchanin, “Low quantum noise tranquilizer for fabry-perot interferometer,” Phys. Lett. A 293, 228–234 (2002).
[CrossRef]

Phys. Rev. (1)

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83, 34–40 (1951).
[CrossRef]

Phys. Rev. A (6)

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

L. Diósi, “Laser linewidth hazard in optomechanical cooling,” Phys. Rev. A 78, 021801 (2008).
[CrossRef]

G. Phelps and P. Meystre, “Laser phase noise effects on the dynamics of optomechanical resonators,” Phys. Rev. A 83, 063838 (2011).
[CrossRef]

P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009).
[CrossRef]

O. Arcizet, R. Rivière, A. Schliesser, G. Anetsberger, and T. Kippenberg, “Cryogenic properties of optomechanical silica microcavities,” Phys. Rev. A 80, 021803 (2009).
[CrossRef]

R. Riviere, S. Deleglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011).
[CrossRef]

Phys. Rev. D (3)

A. Gillespie and F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

P. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
[CrossRef]

D. Santamore and Y. Levin, “Eliminating thermal violin spikes from ligo noise,” Phys. Rev. D 64, 042002 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

P. F. Cohadon, A. Heidmann, and M. Pinard, “Cooling of a mirror by radiation pressure,” Phys. Rev. Lett. 83, 3174–3177 (1999).
[CrossRef]

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, “Feedback cooling of a cantilevere’s fundamental mode below 5 mK,” Phys. Rev. Lett. 99, 017201 (2007).
[CrossRef] [PubMed]

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93, 250602 (2004).
[CrossRef]

F. Marquardt, J. Chen, A. Clerk, and S. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 93902 (2007).
[CrossRef]

D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, “Cavity optomechanics with stoichiometric SiN films,” Phys. Rev. Lett. 103, 207204 (2009).
[CrossRef]

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
[CrossRef] [PubMed]

Physics (1)

F. Marquardt, “Optomechanics,” Physics 2, 40 (2009).
[CrossRef]

Sov. Phys. JETP (1)

V. B. Braginsky, A. B. Manukin, and M. Y. Tikhonov, “Investigation of dissipative ponderomotive effects of electromagnetic radiation,” Sov. Phys. JETP 31, 829 (1970).

Other (7)

Prof. Jack Harris, private discussions.

V. Braginsky, V. Mitrofanov, V. Panov, K. Thorne, and C. Eller, Systems with Small Dissipation (Univ. of Chicago Press, 1986).

www.comsol.com .

D. F. Wall and G. J. Milburn, Quantum Optics (Springer, 1995), chap. 7.

For a generic time-dependent variable ζ(t), the Fourier transform is defined as ζ(f)≡∫−∞∞ζ(t)e−2πiftdt, and the one-sided power spectral density at Fourier frequency f is Sζ(f)≡2∫−∞∞〈ζ(t)ζ(t+τ)〉e2iπftdτ with unit [ζ]2/Hz. The normalization convention is that 〈ζ2(t)〉=∫0∞Sζ(f)df.

Provided by Prof. Jun Ye’s group.

Prof. Jun Ye and Prof. Peter Zoller, private discussions.

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