Abstract

The strength of optomechanical interactions in a cavity optomechanical system can be quantified by a vacuum coupling rate g0 analogous to cavity quantum electrodynamics. This single figure of merit removes the ambiguity in the frequently quoted coupling parameter defining the frequency shift for a given mechanical displacement, and the effective mass of the mechanical mode. Here we demonstrate and verify a straightforward experimental technique to derive the vacuum optomechanical coupling rate. It only requires applying a known frequency modulation of the employed electromagnetic probe field and knowledge of the mechanical oscillator’s occupation. The method is experimentally verified for a micromechanical mode in a toroidal whispering-gallery-resonator and a nanomechanical oscillator coupled to a toroidal cavity via its near field.

© 2010 Optical Society of America

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2010 (1)

J. Hofer, A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with ultra-high Q crystalline microresonators," Phys. Rev. A 82, 031804 (2010).
[CrossRef]

2009 (4)

F. Marquardt and S. M. Girvin, "Optomechanics," Physics 2, 40 (2009).
[CrossRef]

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
[CrossRef] [PubMed]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

2008 (8)

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, "Parametric normal-mode splitting in cavity optomechanics," Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

C. A. Regal, J. D. Teufel, and K. W. Lehnert, "Measuring nanomechanical motion with a microwave cavity interferometer," Nat. Phys. 4, 555-560 (2008).
[CrossRef]

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

K. J. Vahala, "Back-action limit of linewidth in an optomechanical oscillator," Phys. Rev. A 78, 023832 (2008).
[CrossRef]

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

2007 (3)

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

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

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Opt. Lett. 32, 2200-2202 (2007).
[CrossRef] [PubMed]

2006 (1)

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

2005 (3)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, 5293-5301 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (2)

V. B. Braginsky and S. P. Vyatchanin, "Low quantum noise tranquilizer for Fabry-Perot interferometer," Phys. Lett. A 293, 228-234 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

2001 (1)

V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287, 331-338 (2001).
[CrossRef]

1999 (2)

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

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

1995 (2)

C. K. Law, "Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation," Phys. Rev. A 51, 2537-2541 (1995).
[CrossRef] [PubMed]

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

1994 (1)

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, "Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter," Opt. Commun. 107, 41-48 (1994).
[CrossRef]

1993 (1)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
[CrossRef]

1990 (2)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

P. R. Saulson, "Thermal noise in mechanical experiments," Phys. Rev. D Part. Fields 42, 2437-2445 (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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

1981 (1)

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981).
[CrossRef]

1980 (1)

T. W. Hänsch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

1975 (1)

V. B. Braginsky and Y. I. Vorontsov, "Quantum-mechanical limitations in macroscopic experiments and modern experimental technique," Sov. Phys. Usp. 17, 644-650 (1975).
[CrossRef]

1951 (1)

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

Aminoff, C. G.

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

Anetsberger, G.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Opt. Lett. 32, 2200-2202 (2007).
[CrossRef] [PubMed]

anf Cohadon, T.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Arcizet, O.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
[CrossRef] [PubMed]

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Bäuerle, D.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Blaser, F.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Böhm, H. R.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Braginsky, V. B.

V. B. Braginsky and S. P. Vyatchanin, "Low quantum noise tranquilizer for Fabry-Perot interferometer," Phys. Lett. A 293, 228-234 (2002).
[CrossRef]

V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287, 331-338 (2001).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
[CrossRef]

V. B. Braginsky and Y. I. Vorontsov, "Quantum-mechanical limitations in macroscopic experiments and modern experimental technique," Sov. Phys. Usp. 17, 644-650 (1975).
[CrossRef]

Briant, P.-F.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Callen, H. B.

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

Camacho, R. M.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
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T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
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H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, 5293-5301 (2005).
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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
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M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
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Chen, J. P.

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

Clerk, A. A.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. Thomson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, "Dispersive optomechanics: a membrane inside a cavity," N. J. Phys. 10, 095008 (2008).
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F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

Cohadon, P. F.

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
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Couillaud, B.

T. W. Hänsch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
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Dabirian, A.

Del’Haye, P.

Dobrindt, J. M.

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, "Parametric normal-mode splitting in cavity optomechanics," Phys. Rev. Lett. 101, 263602 (2008).
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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 Resonators," Appl. Phys. B 31, 97-105 (1983).
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M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
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Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
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Ford, G. M.

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
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Francais, O.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
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S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
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Gillespie, A.

A. Gillespie and F. Raab, "Thermally excited vibrations of the mirrors of laser interferometer gravitational wave detectors," Phys. Rev. D Part. Fields 52, 577-585 (1995).
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Girvin, S. M.

F. Marquardt and S. M. Girvin, "Optomechanics," Physics 2, 40 (2009).
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A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. Thomson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, "Dispersive optomechanics: a membrane inside a cavity," N. J. Phys. 10, 095008 (2008).
[CrossRef]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

Gorodetsky, M. L.

M. L. Gorodetsky, and I. S. Grudinin, "Fundamental thermal fluctuations in microspheres," J. Opt. Soc. Am. B 21, 697-705 (2004).
[CrossRef]

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, "Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter," Opt. Commun. 107, 41-48 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
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Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
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Grudinin, I. S.

Hadjar, Y.

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

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

Hall, J. L.

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Hammerer, K.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
[CrossRef] [PubMed]

Hänsch, T. W.

T. W. Hänsch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

Harris, J. G. E.

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

Heidmann, A.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

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

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

Hertzberg, J. B.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Hill, S. C.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Hofer, J.

J. Hofer, A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with ultra-high Q crystalline microresonators," Phys. Rev. A 82, 031804 (2010).
[CrossRef]

Hough, J.

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Ilchenko, V. S.

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, "Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter," Opt. Commun. 107, 41-48 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
[CrossRef]

Jayich, A. M.

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

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Kippenberg, T.

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Opt. Lett. 32, 2200-2202 (2007).
[CrossRef] [PubMed]

Kippenberg, T. J.

J. Hofer, A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with ultra-high Q crystalline microresonators," Phys. Rev. A 82, 031804 (2010).
[CrossRef]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, "Parametric normal-mode splitting in cavity optomechanics," Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

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

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, 5293-5301 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Kotthaus, J. P.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

Kowalski, F. V.

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Langer, G.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Law, C. K.

C. K. Law, "Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation," Phys. Rev. A 51, 2537-2541 (1995).
[CrossRef] [PubMed]

Lehnert, K. W.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, "Measuring nanomechanical motion with a microwave cavity interferometer," Nat. Phys. 4, 555-560 (2008).
[CrossRef]

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Ma, R.

Mackowksi, J.-M.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Marquardt, F.

F. Marquardt and S. M. Girvin, "Optomechanics," Physics 2, 40 (2009).
[CrossRef]

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

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

Michel, C.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Molinelli, C.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Munley, A. J.

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Nooshi, N.

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

Painter, O.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
[CrossRef] [PubMed]

Paternosto, M.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Pinard, L.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Pinard, M.

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

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

Raab, F.

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

Regal, C. A.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, "Measuring nanomechanical motion with a microwave cavity interferometer," Nat. Phys. 4, 555-560 (2008).
[CrossRef]

Rivière, R.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, 5293-5301 (2005).
[CrossRef] [PubMed]

Rousseau, L.

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Sankey, J. C.

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

Saulson, P. R.

P. R. Saulson, "Thermal noise in mechanical experiments," Phys. Rev. D Part. Fields 42, 2437-2445 (1990).
[CrossRef]

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Schliesser, A.

J. Hofer, A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with ultra-high Q crystalline microresonators," Phys. Rev. A 82, 031804 (2010).
[CrossRef]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Opt. Lett. 32, 2200-2202 (2007).
[CrossRef] [PubMed]

Schwab, K. C.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Strigin, S. E.

V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287, 331-338 (2001).
[CrossRef]

Teufel, J. D.

C. A. Regal, J. D. Teufel, and K. W. Lehnert, "Measuring nanomechanical motion with a microwave cavity interferometer," Nat. Phys. 4, 555-560 (2008).
[CrossRef]

Thomson, J.

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

Unterreithmeier, Q. P.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

Vahala, K. J.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
[CrossRef] [PubMed]

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

K. J. Vahala, "Back-action limit of linewidth in an optomechanical oscillator," Phys. Rev. A 78, 023832 (2008).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Opt. Express 13, 5293-5301 (2005).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
[CrossRef] [PubMed]

Vorontsov, Y. I.

V. B. Braginsky and Y. I. Vorontsov, "Quantum-mechanical limitations in macroscopic experiments and modern experimental technique," Sov. Phys. Usp. 17, 644-650 (1975).
[CrossRef]

Vyatchanin, S. P.

V. B. Braginsky and S. P. Vyatchanin, "Low quantum noise tranquilizer for Fabry-Perot interferometer," Phys. Lett. A 293, 228-234 (2002).
[CrossRef]

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, "Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter," Opt. Commun. 107, 41-48 (1994).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
[CrossRef]

Vyatchanin, V. P.

V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287, 331-338 (2001).
[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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Weig, E. M.

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Welton, T. A.

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

Wilson-Rae, I.

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, "Parametric normal-mode splitting in cavity optomechanics," Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

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

Yang, C.

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

Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

Young, K.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

Zeilinger, A.

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Zwerger, W.

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

Zwickl, B. M.

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

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 Resonators," Appl. Phys. B 31, 97-105 (1983).
[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).

Europhys. Lett. (1)

Y. Hadjar, P. F. Cohadon, C. G. Aminoff, M. Pinard, and A. Heidmann, "High-sensitivity optical measurement of mechanical Brownian motion," Europhys. Lett. 47, 545-551 (1999).
[CrossRef]

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

N. J. Phys. (3)

A. Schliesser, G. Anetsberger, R. Rivière, O. Arcizet, and T. J. Kippenberg, "High-sensitivity monitoring of micromechanical vibration using optical whispering gallery mode resonators," N. J. Phys. 10, 095015 (2008).
[CrossRef]

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

O. Arcizet, C. Molinelli, P.-F. Briant, T. anf Cohadon, A. Heidmann, J.-M. Mackowksi, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "Experimental optomechanics with silicon micromirrors," N. J. Phys. 10, 125021 (2008).
[CrossRef]

Nat. Phys. (3)

C. A. Regal, J. D. Teufel, and K. W. Lehnert, "Measuring nanomechanical motion with a microwave cavity interferometer," Nat. Phys. 4, 555-560 (2008).
[CrossRef]

G. Anetsberger, O. Arcizet, Q. P. Unterreithmeier, R. Rivière, A. Schliesser, E. M. Weig, J. P. Kotthaus, and T. J. Kippenberg, "Near-field cavity optomechanics with nanomechanical oscillators," Nat. Phys. 5, 909-914 (2009).
[CrossRef]

A. Schliesser, R. Rivière, G. Anetsberger, O. Arcizet, and T. Kippenberg, "Resolved-sideband cooling of a micromechanical oscillator," Nat. Phys. 4, 415-419 (2008).
[CrossRef]

Nature (3)

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, "Optomechanical crystals," Nature 462, 78-82 (2009).
[CrossRef] [PubMed]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009).
[CrossRef] [PubMed]

S. Gigan, H. R. Böhm, M. Paternosto, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bäuerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444, 67-70 (2006).
[CrossRef] [PubMed]

Opt. Commun. (2)

T. W. Hänsch and B. Couillaud, "Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity," Opt. Commun. 35, 441-444 (1980).
[CrossRef]

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, "Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter," Opt. Commun. 107, 41-48 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (3)

V. B. Braginsky, M. L. Gorodetsky, V. S. Ilchenko, and S. P. Vyatchanin, "On the ultimate sensitivity in coordinate measurements," Phys. Lett. A 179, 244-248 (1993).
[CrossRef]

V. B. Braginsky, S. E. Strigin, and V. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Phys. Lett. A 287, 331-338 (2001).
[CrossRef]

V. B. Braginsky and S. P. 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 (4)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, "Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets," Phys. Rev. A 41, 5187-5198 (1990).
[CrossRef] [PubMed]

K. J. Vahala, "Back-action limit of linewidth in an optomechanical oscillator," Phys. Rev. A 78, 023832 (2008).
[CrossRef]

J. Hofer, A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with ultra-high Q crystalline microresonators," Phys. Rev. A 82, 031804 (2010).
[CrossRef]

C. K. Law, "Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation," Phys. Rev. A 51, 2537-2541 (1995).
[CrossRef] [PubMed]

Phys. Rev. D (1)

C. M. Caves, "Quantum-mechanical noise in an interferometer," Phys. Rev. D 23, 1693 (1981).
[CrossRef]

Phys. Rev. D Part. Fields (2)

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

P. R. Saulson, "Thermal noise in mechanical experiments," Phys. Rev. D Part. Fields 42, 2437-2445 (1990).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, "Perturbation theory for Maxwell’s equations with shifting material boundaries," Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007).
[CrossRef] [PubMed]

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

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Phys. Rev. Lett. 95, 033901 (2005).
[CrossRef] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode," Phys. Rev. Lett. 94, 223902 (2005).
[CrossRef] [PubMed]

J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, "Parametric normal-mode splitting in cavity optomechanics," Phys. Rev. Lett. 101, 263602 (2008).
[CrossRef] [PubMed]

Physics (1)

F. Marquardt and S. M. Girvin, "Optomechanics," Physics 2, 40 (2009).
[CrossRef]

Science (1)

T. J. Kippenberg and K. J. Vahala, "Cavity Optomechanics: Back-Action at the Mesoscale," Science 321, 1172-1176 (2008).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. B. Braginsky and Y. I. Vorontsov, "Quantum-mechanical limitations in macroscopic experiments and modern experimental technique," Sov. Phys. Usp. 17, 644-650 (1975).
[CrossRef]

Other (7)

A. Schliesser, and T. J. Kippenberg, "Cavity optomechanics with silica microresonators," in "Advances in atomic, molecular and optical physics," vol. 58, E. Arimondo, P. Berman, and C. C. Lin, eds. (Elsevier Academic Press, 2010), chap. 5, pp. 207-323.

For open systems, the integration boundaries should be chosen close to the surface of the resonator, to avoid divergence of the integral in the denominator. Alternatively, radiating fields escaping from the volume of interest have to be taken into account by a surface integral.

H. J. Kimble, "Structure and dynamics in cavity quantum electrodynamics," in "Cavity Quantum Electrodynamics," P. R. Berman, ed. (Academic Press, 1994), Advances in Atomic, Molecular and Optical Physics.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. P. Unterreithmeier, E. M. Weig, M. L. Gorodetsky, J. P. Kotthaus, and T. J. Kippenberg, "Measuring nanomechanical motion with an imprecision far below the standard quantum limit," arXiv:1003.3752 (2010).

G. Heinzel, A. Rüdiger, and R. Schilling, "Spectrum and spectral density estimation by the discrete Fourier transform (DFT), including a comprehensive list of window functions and some new at-top windows," Tech. rep., Max Planck Society (2002). http://pubman.mpdl.mpg.de/pubman/item/escidoc:152164:1.

Agilent Technologies, Agilent Application Note 1303: Spectrum and Signal Analyzer Measurements and Noise.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, "Optomechanically induced transparency," arXiv:1007.0565 (2010).

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Figures (2)

Fig. 1
Fig. 1

Generic scheme for the determination of the vacuum optomechanical coupling rate. The cavity optomechanical system is probed with a monochromatic source of electromagnetic waves which is frequency-modulated by a known amount at a Fourier frequency close to the mechanical resonance frequency. A phase-sensitive detector generates a signal I, which is analyzed with a spectrum analyzer. As two possible examples, a homodyne detector measures the phase difference between the arms in an interferometer, one of which accommodates the optomechanical system (shutter S open). If the shutter S is closed, the transmission signal I of an optomechanical system is amplitude-dependent when the driving wave is detuned with respect to the optical resonance.

Fig. 2
Fig. 2

Measured (single-sided) frequency noise spectra S ν ν meas (Ω) (blue lines, ν = ωc/2π) induced by a nanomechanical string oscillator (8.3 MHz) coupled to a silica microtoroid [42] (left) and a radial breathing mode of a silica microtoroid (right), calibrated using laser frequency modulation at frequencies of 8 and 71.38MHz, respectively. Orange lines are Lorentzian fits, the gray area underneath them yield the optomechanical coupling rates multiplied with the occupation number of the oscillator.

Equations (37)

Equations on this page are rendered with MathJax. Learn more.

G d ω c d x .
H ^ int = h ¯ G x ^ n ^ o = h ¯ G x zpf ( a ^ m + a ^ m ) a ^ o a ^ o ,
x zpf = h ¯ 2 m eff Ω m
Δ ω c ω c 1 2 | E ( r ) | 2 ( ɛ ( r + u ( r ) ) ɛ ( r ) ) d r 3 | E ( r ) | 2 ɛ ( r ) d r 3
U = 1 2 m eff Ω m 2 x 2 .
g 0 G x zpf
S xx ( Ω ) = Γ m h ¯ Ω m eff coth ( h ¯ Ω 2 k B T ) ( Ω 2 Ω m 2 ) 2 + Γ m 2 Ω 2 1 m eff 2 Γ m k B T ( Ω 2 Ω m 2 ) 2 + Γ m 2 Ω 2 ,
S ω ω ( Ω ) = G 2 S x x ( Ω ) g 0 2 2 Ω m h ¯ 2 Γ m k B T ( Ω 2 Ω m 2 ) 2 + Γ m 2 Ω 2 .
δ ω c 2 = + S ω ω ( Ω ) d Ω 2 π = S ω ω ( Ω m ) Γ m 2 = 2 n m g 0 2 ,
S II ( Ω ) = K ( Ω ) S ψ ψ ( Ω ) = K ( Ω ) Ω 2 S ω ω ( Ω ) ,
S I I ( Ω ) = K ( Ω ) S ϕ ϕ ( Ω ) ,
S II meas ( Ω ) = 2 F ( Ω ) * ( K ( Ω ) ( S ψ ψ ( Ω ) + S ϕ ϕ ( Ω ) ) ) ,
F ( 0 ) ENBW = + F ( Ω ) d Ω 2 π = 1 ,
S II meas ( Ω ) 2 K ( Ω ) S ψ ψ ( Ω ) + ϕ 0 2 2 K ( Ω mod ) ( F ( Ω Ω mod ) + F ( Ω + Ω mod ) ) .
S II meas ( ± Ω mod ) ϕ 0 2 2 K ( Ω mod ) F ( 0 ) = ϕ 0 2 2 K ( Ω mod ) ENBW
K D ( Ω ) = S PP P in 2 S ψ ψ = S PP P in 2 S ϕ ϕ = 4 η c 2 κ 2 Δ 2 Ω 2 ( Ω 2 + κ 2 ( 1 η c ) 2 ) ( ( Ω + Δ ) 2 + κ 2 / 4 ) ( ( Ω Δ ) 2 + κ 2 / 4 ) ( Δ 2 + κ 2 / 4 ) 2 .
K H ( Ω ) = S HH P in P LO S ψ ψ = S HH P in P LO S ϕ ϕ = = 4 κ 2 η c 2 Ω 2 ( Ω 2 ( 1 2 η c ) 2 κ 2 / 4 + ( Δ 2 ( 1 2 η c ) κ 2 / 4 ) 2 ) ( ( Δ Ω ) 2 + κ 2 / 4 ) ( ( Δ + Ω ) 2 + κ 2 / 4 ) ( Δ 2 + ( 1 2 η c ) 2 κ 2 / 4 ) ( Δ 2 + κ 2 / 4 ) .
K H ( Ω ) = 16 η c 2 Ω 2 Ω 2 + κ 2 / 4 .
K H ( Ω m ) 4 η c 2 ( 1 + κ 2 ( 16 η c 13 ) 16 Ω m 2 ) .
g 0 2 1 2 n m ϕ 0 2 Ω mod 2 2 S II meas ( Ω m ) Γ m / 4 S II meas ( Ω mod ) ENBW .
a ˙ = ( i Δ i G x ( t ) κ / 2 ) a ( t ) + η c κ s in ( t ) , x ¨ ( t ) + Γ m x ˙ ( t ) + Ω m 2 x ( t ) = h ¯ G | a ¯ | 2 ,
x ( t ) = x 0 cos ( Ω m t ) .
a x = s in η c κ ( 0 ) ( 1 i ψ 0 Ω m ( + Ω m ) 2 e i Ω m t i ψ 0 Ω m ( Ω m ) 2 e + i Ω m t ) , s x , out = s in η c κ a x , ( Ω ) = 1 i ( Δ + Ω ) + κ / 2 .
S ϕ , in = s in ( 1 i ϕ 0 2 e i Ω mod t i ϕ 0 2 e + i Ω mod t ) , a ϕ = s in η c κ ( ( 0 ) i ϕ 0 ( + Ω mod ) 2 e i Ω mod t i ϕ 0 ( + Ω mod ) 2 e + i Ω mod t ) .
S ϕ , out = S ϕ , in η c κ a ϕ .
K D ( Ω ) = S PP ( Ω ) P in 2 S ψ ψ ( Ω ) = S P P ( Ω ) P in 2 S ϕ ϕ ( Ω ) = = 4 η c 2 κ 2 Δ 2 Ω 2 ( Ω 2 + κ 2 ( 1 η c ) 2 ) ( ( Ω + Δ ) 2 + κ 2 / 4 ) ( ( Ω Δ ) 2 + κ 2 / 4 ) ( Δ 2 + κ 2 / 4 ) 2 .
Δ = ± 1 2 2 Ω 2 κ 2 2 Ω 4 2 κ 2 Ω 2 ± κ 2 ( 1 + κ 2 4 Ω 2 ) , Δ = ± 1 2 2 Ω 2 κ 2 + 2 Ω 4 2 κ 2 Ω 2 ± Ω ( 1 + 3 κ 2 8 Ω 2 ) ,
K D ( Ω ) = 4 η c 2 ( 1 + κ 2 ( 1 η c ) 2 ) Ω 2 ) .
Δ = ± 1 6 12 Ω 2 + 3 κ 2 , K D ( Ω ) = 27 Ω 2 η c 2 κ 2 ( Ω 2 + κ 2 ( 1 η c ) 2 ) ( Ω 2 + κ 2 ) 3 .
H h ¯ ω 0 = | i 2 s out 1 2 s LO | 2 | i 2 s LO 1 2 s out | 2 = i ( s LO s out * s LO * s out ) = i ( s LO s in * s LO * s in ) + i η c κ ( a s LO * a * s LO ) = 2 | s LO | | S in | sin ( ϕ LO ϕ in ) + i η c κ ( a s LO * a * s LO )
s x , LO = s LO s in s x , in e i ϕ LO = s LO e i ϕ LO ,
s ϕ , LO = s LO s in s ϕ , in e i ϕ LO = s LO e i ϕ LO ( 1 i ϕ 0 2 e i Ω mod t i ϕ 0 2 e + i Ω mod t ) ,
ϕ LO = arctan ( η c κ Δ Δ 2 + ( 1 2 η c ) κ 2 / 4 ) .
S HH P in P LO S ψ ψ = S H H P in P LO S ϕ ϕ
K H ( Ω ) = 4 κ 2 η c 2 Ω ( Ω 2 ( 1 2 η c ) 2 κ 2 / 4 + ( Δ 2 ( 1 2 η c ) κ 2 / 4 ) 2 ) ( ( Δ Ω ) 2 + κ 2 / 4 ) ( ( Δ + Ω ) 2 + κ 2 / 4 ) ( Δ 2 + ( 1 2 η c ) 2 κ 2 / 4 ) ( Δ 2 + κ 2 / 4 ) .
K H ( Ω ) = 16 η c 2 Ω 2 Ω 2 + κ 2 / 4 .
K H ( ± Ω m ) 4 η c 2 ( 1 + κ 2 ( 16 η c 13 ) 16 Ω m 2 ) .

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