Abstract

The coupling of mechanical and optical degrees of freedom via radiation pressure has been a subject of early research in the context of gravitational wave detection. Recent experimental advances have allowed studying for the first time the modifications of mechanical dynamics provided by radiation pressure. This paper reviews the consequences of back-action of light confined in whispering-gallery dielectric micro-cavities, and presents a unified treatment of its two manifestations: notably the parametric instability (mechanical amplification and oscillation) and radiation pressure back-action cooling. Parametric instability offers a novel “photonic clock” which is driven purely by the pressure of light. In contrast, radiation pressure cooling can surpass existing cryogenic technologies and offers cooling to phonon occupancies below unity and provides a route towards cavity Quantum Optomechanics

© 2007 Optical Society of America

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2007 (10)

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
[CrossRef]

T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
[CrossRef]

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, "Feedback cooling of a cantilever’s fundamental mode below 5 mK," Physical Review Letters 99(1) (2007).

M. Eichenfeld, C. Michael, R. Perahia, and O. Painter, "Actuation ofMicro-Optomechanical Systems Via Cavity-Enhanced Optical Dipole Forces," Nature Photonics 1(7), 416 (2007).
[CrossRef]

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion," Physical Review Letters 99, 093,902 (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," Physical Review Letters 99, 093,902 (2007).
[CrossRef]

M. Hossein-Zadeh and K. J. Vahala, "Observation of optical spring effect in a microtoroidal optomechanical resonator," Optics Letters 32(12), 1611-1613 (2007).
[CrossRef]

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Optics Letters 32(15), 2200-2202 (2007).
[CrossRef]

T. Carmon, M. C. Cross, and K. J. Vahala, "Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure," Physical Review Letters98(16) (2007). 0031-9007.

T. Carmon and K. J. Vahala, "Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency," Physical Review Letters 98(12) (2007).

2006 (11)

K. Karrai, "Photonics - A cooling light breeze," Nature 444(7115), 41-42 (2006).
[CrossRef]

O. Arcizet, T. Briant, A. Heidmann, and M. Pinard, "Beating quantum limits in an optomechanical sensor by cavity detuning," Physical Review A 73(3) (2006).

F. Marquardt, J. Harris, and S. Girvin, "Dynamical Multistability Induced by Radiation Pressure in High-Finesse Micromechanical Optical Cavities," Physical Review Letters 96(103901-1) (2006).

M. Hossein-Zadeh, H. Rokhsari, A. Hajimiri, and K. J. Vahala, "Characterization of a radiation-pressure-driven micromechanical oscillator," Physical Review A 74(2) (2006).

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

D. Kleckner and D. Bouwmeester, "Sub-kelvin optical cooling of a micromechanical resonator," Nature 444(7115), 75-78 (2006).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444(7115), 71-74 (2006).
[CrossRef]

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
[CrossRef]

A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, "Radiation pressure cooling of a micromechanical oscillator using dynamical backaction," Physical Review Letters 97(24), 243,905 (2006).

A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
[CrossRef]

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, "Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity," Physical Review A 74(2) (2006).

2005 (6)

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Physical Review Letters 95, 033,901 (2005).
[CrossRef]

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Optics Express 13(14), 5293-5301 (2005).
[CrossRef]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode," Physical Review Letters 94(22) (2005).

H. Rokhsari and K. J. Vahala, "Observation of Kerr nonlinearity in microcavities at room temperature," Optics Letters 30(4), 427-429 (2005).
[CrossRef]

K. C. Schwab and M. L. Roukes, "Putting mechanics into quantum mechanics," Physics Today 58(7), 36-42 (2005).

M. L. Povinelli, J.M. Johnson,M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Optics Express 13(20), 8286-8295 (2005).
[CrossRef]

2004 (8)

P. Maunz, T. Puppe, I. Schuster, N. Syassen, P. W. H. Pinkse, and G. Rempe, "Cavity cooling of a single atom," Nature 428(6978), 50-52 (2004).
[CrossRef]

C. H. Metzger and K. Karrai, "Cavity cooling of a microlever," Nature 432(7020), 1002-1005 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Optics Express 12(20), 4742-4750 (2004).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Physical Review Letters 93(8) (2004).

I. Wilson-Rae, P. Zoller, and A. Imamoglu, "Laser cooling of a nanomechanical resonator mode to its quantum ground state," Physical Review Letters 92(7), 075,507 (2004).

L. Tian and P. Zoller, "Coupled ion-nanomechanical systems," Physical Review Letters 93(26), 266,403 (2004).

M. D. LaHaye, O. Buu, B. Camarota, and K. C. Schwab, "Approaching the quantum limit of a nanomechanical resonator," Science 304(5667), 74-77 (2004).
[CrossRef]

B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, "Observation and characterization of an optical spring," Physical Review A 69(5) (2004).

2003 (8)

K. J. Vahala, "Optical microcavities," Nature 424(6950), 839-846 (2003).
[CrossRef]

J. M. Courty, A. Heidmann, and M. Pinard, "Quantum locking of mirrors in interferometers," Physical Review Letters 90(8) (2003).

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Fabrication and coupling to planar high-Q silica disk microcavities," Applied Physics Letters 83(4), 797-799 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421(6926), 925-928 (2003).
[CrossRef]

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Reviews of Modern Physics 75(1), 281-324 (2003).
[CrossRef]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Physical Review Letters91(4), art. no.-043,902 (2003).

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425(6961), 944-947 (2003).
[CrossRef]

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards quantum superpositions of a mirror," Physical Review Letters 91(13) (2003).

2002 (4)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415(6872), 621-623 (2002).
[CrossRef]

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, "Entangling macroscopic oscillators exploiting radiation pressure," Physical Review Letters 88(12), 120,401 (2002).

V. B. Braginsky and S. P. Vyatchanin, "Low quantum noise tranquilizer for Fabry-Perot interferometer," Physics Letters A 293(5-6), 228-234 (2002).
[CrossRef]

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Analysis of parametric oscillatory instability in power recycled LIGO interferometer," Physics Letters A 305(3-4), 111-124 (2002).
[CrossRef]

2001 (3)

V. Giovannetti, S. Mancini, and P. Tombesi, "Radiation pressure induced Einstein-Podolsky-Rosen paradox," Europhysics Letters 54(5), 559-565 (2001).
[CrossRef]

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Physics Letters A 287(5-6), 331-338 (2001).
[CrossRef]

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
[CrossRef]

2000 (2)

V. Vuletic and S. Chu, "Laser cooling of atoms, ions, or molecules by coherent scattering," Physical Review Letters 84(17), 3787-3790 (2000).
[CrossRef]

H. G. Craighead, "Nanoelectromechanical systems," Science 290(5496), 1532-1535 (2000).
[CrossRef]

1999 (4)

K. Jacobs, I. Tittonen, H. M. Wiseman, and S. Schiller, "Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion," Physical Review A 60(1), 538-548 (1999).
[CrossRef]

I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Muller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Physical Review A 59(2), 1038-1044 (1999).
[CrossRef]

P. F. Cohadon, A. Heidmann, and M. Pinard, "Cooling of a mirror by radiation pressure," Physical Review Letters 83(16), 3174-3177 (1999).
[CrossRef]

M. Pinard, Y. Hadjar, and A. Heidmann, "Effective mass in quantum effects of radiation pressure," European Physical Journal D 7(1), 107-116 (1999).

1998 (3)

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Haroche, "Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium," European Physical Journal D 1(3), 235-238 (1998).

S. Mancini, D. Vitali, and P. Tombesi, "Optomechanical cooling of a macroscopic oscillator by homodyne feedback," Physical Review Letters 80(4), 688-691 (1998).
[CrossRef]

H. J. Kimble, "Strong interactions of single atoms and photons in cavity QED," Physica Scripta T76, 127-137 (1998).
[CrossRef]

1997 (1)

S. Bose, K. Jacobs, and P. L. Knight, "Preparation of nonclassical states in cavities with a moving mirror," Physical Review A 56(5), 4175-4186 (1997).
[CrossRef]

1996 (2)

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Physical Review Letters 76(11), 1796-1799 (1996).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, "A "Schrodinger cat" superposition state of an atom," Science 272(5265), 1131-1136 (1996).
[CrossRef]

1995 (1)

C. K. Law, "Interaction between aMovingMirror and Radiation Pressure - a Hamiltonian-Formulation," Physical Review A 51(3), 2537-2541 (1995).
[CrossRef]

1994 (1)

S. Mancini and P. Tombesi, "Quantum-Noise Reduction by Radiation Pressure," Physical Review A 49(5), 4055-4065 (1994).
[CrossRef]

1989 (2)

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-Factor and Nonlinear Properties of Optical Whispering- Gallery Modes," Physics Letters A 137(7-8), 393-397 (1989).
[CrossRef]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser Cooling to the Zero-Point Energy of Motion," Physical Review Letters 62(4), 403-406 (1989).
[CrossRef]

1986 (1)

S. Stenholm, "The Semiclassical Theory of Laser Cooling," Reviews of Modern Physics 58(3), 699-739 (1986).
[CrossRef]

1985 (2)

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
[CrossRef]

S. Vandermeer, "Stochastic Cooling and the Accumulation of Antiprotons," Reviews of Modern Physics 57(3), 689-697 (1985).
[CrossRef]

1983 (2)

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Physical Review Letters 51(17), 1550-1553 (1983).
[CrossRef]

G. Bjorklund, M. Levenson, W. Lenth, and C. Ortiz, "Frequency modulation (FM) spectroscopy," Applied Physics B Lasers and Optics 32(3), 145-152 (1983).

1981 (1)

C. M. Caves, "Quantum-Mechanical Noise in an Interferometer," Physical Review D 23(8), 1693-1708 (1981).
[CrossRef]

1979 (1)

D. J. Wineland and W. M. Itano, "Laser Cooling of Atoms," Physical Review A 20(4), 1521-1540 (1979).
[CrossRef]

1978 (1)

D. J. Wineland, R. E. Drullinger, and F. L. Walls, "Radiation-Pressure Cooling of Bound Resonant Absorbers," Physical Review Letters 40(25), 1639-1642 (1978).
[CrossRef]

1975 (1)

T.W. Hansch and A. L. Schawlow, "Cooling of Gases by Laser Radiation," Optics Communications 13(1), 68-69 (1975).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425(6961), 944-947 (2003).
[CrossRef]

Anetsberger, G.

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Optics Letters 32(15), 2200-2202 (2007).
[CrossRef]

Arcizet, O.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444(7115), 71-74 (2006).
[CrossRef]

O. Arcizet, T. Briant, A. Heidmann, and M. Pinard, "Beating quantum limits in an optomechanical sensor by cavity detuning," Physical Review A 73(3) (2006).

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

Armani, D. K.

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Fabrication and coupling to planar high-Q silica disk microcavities," Applied Physics Letters 83(4), 797-799 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421(6926), 925-928 (2003).
[CrossRef]

Armour, A. D.

A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425(6961), 944-947 (2003).
[CrossRef]

Ashkin, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
[CrossRef]

Aspelmeyer, M.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
[CrossRef]

Bauerle, D.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
[CrossRef]

Bergquist, J. C.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser Cooling to the Zero-Point Energy of Motion," Physical Review Letters 62(4), 403-406 (1989).
[CrossRef]

Bjorkholm, J. E.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
[CrossRef]

Bjorklund, G.

G. Bjorklund, M. Levenson, W. Lenth, and C. Ortiz, "Frequency modulation (FM) spectroscopy," Applied Physics B Lasers and Optics 32(3), 145-152 (1983).

Blanc, N.

I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Muller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Physical Review A 59(2), 1038-1044 (1999).
[CrossRef]

Blaser, F.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
[CrossRef]

Blatt, R.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Reviews of Modern Physics 75(1), 281-324 (2003).
[CrossRef]

Blencowe, M. P.

A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
[CrossRef]

Bohm, H. R.

S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
[CrossRef]

Bose, S.

S. Bose, K. Jacobs, and P. L. Knight, "Preparation of nonclassical states in cavities with a moving mirror," Physical Review A 56(5), 4175-4186 (1997).
[CrossRef]

Bouwmeester, D.

D. Kleckner and D. Bouwmeester, "Sub-kelvin optical cooling of a micromechanical resonator," Nature 444(7115), 75-78 (2006).
[CrossRef]

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards quantum superpositions of a mirror," Physical Review Letters 91(13) (2003).

Braginsky, V. B.

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Analysis of parametric oscillatory instability in power recycled LIGO interferometer," Physics Letters A 305(3-4), 111-124 (2002).
[CrossRef]

V. B. Braginsky and S. P. Vyatchanin, "Low quantum noise tranquilizer for Fabry-Perot interferometer," Physics Letters A 293(5-6), 228-234 (2002).
[CrossRef]

V. B. Braginsky, S. E. Strigin, and S. P. Vyatchanin, "Parametric oscillatory instability in Fabry-Perot interferometer," Physics Letters A 287(5-6), 331-338 (2001).
[CrossRef]

V. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-Factor and Nonlinear Properties of Optical Whispering- Gallery Modes," Physics Letters A 137(7-8), 393-397 (1989).
[CrossRef]

Breitenbach, G.

I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Muller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Physical Review A 59(2), 1038-1044 (1999).
[CrossRef]

Briant, T.

O. Arcizet, T. Briant, A. Heidmann, and M. Pinard, "Beating quantum limits in an optomechanical sensor by cavity detuning," Physical Review A 73(3) (2006).

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444(7115), 71-74 (2006).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

Britton, J.

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
[CrossRef]

Brown, K.

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
[CrossRef]

Buu, O.

A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
[CrossRef]

M. D. LaHaye, O. Buu, B. Camarota, and K. C. Schwab, "Approaching the quantum limit of a nanomechanical resonator," Science 304(5667), 74-77 (2004).
[CrossRef]

Cable, A.

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
[CrossRef]

Camarota, B.

M. D. LaHaye, O. Buu, B. Camarota, and K. C. Schwab, "Approaching the quantum limit of a nanomechanical resonator," Science 304(5667), 74-77 (2004).
[CrossRef]

Capasso, F.

M. L. Povinelli, J.M. Johnson,M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Optics Express 13(20), 8286-8295 (2005).
[CrossRef]

Carmon, T.

T. Carmon, M. C. Cross, and K. J. Vahala, "Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure," Physical Review Letters98(16) (2007). 0031-9007.

T. Carmon and K. J. Vahala, "Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency," Physical Review Letters 98(12) (2007).

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode," Physical Review Letters 94(22) (2005).

H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Radiation-pressure-driven micro-mechanical oscillator," Optics Express 13(14), 5293-5301 (2005).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Physical Review Letters 95, 033,901 (2005).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Optics Express 12(20), 4742-4750 (2004).
[CrossRef]

Caves, C. M.

C. M. Caves, "Quantum-Mechanical Noise in an Interferometer," Physical Review D 23(8), 1693-1708 (1981).
[CrossRef]

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," Physical Review Letters 99, 093,902 (2007).
[CrossRef]

Chen, Y. B.

T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
[CrossRef]

Chiaverini, J.

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
[CrossRef]

Chu, S.

V. Vuletic and S. Chu, "Laser cooling of atoms, ions, or molecules by coherent scattering," Physical Review Letters 84(17), 3787-3790 (2000).
[CrossRef]

S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
[CrossRef]

Clerk, A. A.

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, "Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion," Physical Review Letters 99, 093,902 (2007).
[CrossRef]

A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
[CrossRef]

Cohadon, P. F.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444(7115), 71-74 (2006).
[CrossRef]

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

P. F. Cohadon, A. Heidmann, and M. Pinard, "Cooling of a mirror by radiation pressure," Physical Review Letters 83(16), 3174-3177 (1999).
[CrossRef]

Conradt, R.

I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Muller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Physical Review A 59(2), 1038-1044 (1999).
[CrossRef]

Corbitt, T.

T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
[CrossRef]

T. Corbitt, D. Ottaway, E. Innerhofer, J. Pelc, and N. Mavalvala, "Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity," Physical Review A 74(2) (2006).

Courty, J. M.

J. M. Courty, A. Heidmann, and M. Pinard, "Quantum locking of mirrors in interferometers," Physical Review Letters 90(8) (2003).

Craighead, H. G.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
[CrossRef]

H. G. Craighead, "Nanoelectromechanical systems," Science 290(5496), 1532-1535 (2000).
[CrossRef]

Cross, M. C.

T. Carmon, M. C. Cross, and K. J. Vahala, "Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure," Physical Review Letters98(16) (2007). 0031-9007.

Czaplewski, D.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
[CrossRef]

Dabirian, A.

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Optics Letters 32(15), 2200-2202 (2007).
[CrossRef]

de Rooij, N. F.

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F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Haroche, "Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium," European Physical Journal D 1(3), 235-238 (1998).

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M. Hossein-Zadeh and K. J. Vahala, "Photonic RF Down-Converter Based on Optomechanical Oscillation," (to be published).

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M. L. Povinelli, J.M. Johnson,M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Optics Express 13(20), 8286-8295 (2005).
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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode," Physical Review Letters 94(22) (2005).

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Physical Review Letters 95, 033,901 (2005).
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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Physical Review Letters91(4), art. no.-043,902 (2003).

T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Fabrication and coupling to planar high-Q silica disk microcavities," Applied Physics Letters 83(4), 797-799 (2003).
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K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
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M. L. Povinelli, J.M. Johnson,M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Optics Express 13(20), 8286-8295 (2005).
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M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, "Feedback cooling of a cantilever’s fundamental mode below 5 mK," Physical Review Letters 99(1) (2007).

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S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, "Entangling macroscopic oscillators exploiting radiation pressure," Physical Review Letters 88(12), 120,401 (2002).

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T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
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B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, "Observation and characterization of an optical spring," Physical Review A 69(5) (2004).

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A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Physical Review Letters 51(17), 1550-1553 (1983).
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C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, "A "Schrodinger cat" superposition state of an atom," Science 272(5265), 1131-1136 (1996).
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A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Physical Review Letters 51(17), 1550-1553 (1983).
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O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

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D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Reviews of Modern Physics 75(1), 281-324 (2003).
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I. Tittonen, G. Breitenbach, T. Kalkbrenner, T. Muller, R. Conradt, S. Schiller, E. Steinsland, N. Blanc, and N. F. de Rooij, "Interferometric measurements of the position of a macroscopic body: Towards observation of quantum limits," Physical Review A 59(2), 1038-1044 (1999).
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B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, "Observation and characterization of an optical spring," Physical Review A 69(5) (2004).

Wilson-Rae, I.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, "Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction," Physical Review Letters 99, 093,902 (2007).
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I. Wilson-Rae, P. Zoller, and A. Imamoglu, "Laser cooling of a nanomechanical resonator mode to its quantum ground state," Physical Review Letters 92(7), 075,507 (2004).

Wineland, D.

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
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D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Reviews of Modern Physics 75(1), 281-324 (2003).
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Wineland, D. J.

C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, "A "Schrodinger cat" superposition state of an atom," Science 272(5265), 1131-1136 (1996).
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D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Physical Review Letters 76(11), 1796-1799 (1996).
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F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser Cooling to the Zero-Point Energy of Motion," Physical Review Letters 62(4), 403-406 (1989).
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D. J. Wineland and W. M. Itano, "Laser Cooling of Atoms," Physical Review A 20(4), 1521-1540 (1979).
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Wipf, C.

T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
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Wiseman, H. M.

K. Jacobs, I. Tittonen, H. M. Wiseman, and S. Schiller, "Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion," Physical Review A 60(1), 538-548 (1999).
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Yang, L.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode," Physical Review Letters 94(22) (2005).

T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Optics Express 12(20), 4742-4750 (2004).
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Zalalutdinov, M.

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
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M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
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S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
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L. Tian and P. Zoller, "Coupled ion-nanomechanical systems," Physical Review Letters 93(26), 266,403 (2004).

I. Wilson-Rae, P. Zoller, and A. Imamoglu, "Laser cooling of a nanomechanical resonator mode to its quantum ground state," Physical Review Letters 92(7), 075,507 (2004).

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," Physical Review Letters 99, 093,902 (2007).
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Applied Physics Letters (2)

M. Zalalutdinov, A. Zehnder, A. Olkhovets, S. Turner, L. Sekaric, B. Ilic, D. Czaplewski, J. M. Parpia, and H. G. Craighead, "Autoparametric optical drive for micromechanical oscillators," Applied Physics Letters 79(5), 695-697 (2001).
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T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Fabrication and coupling to planar high-Q silica disk microcavities," Applied Physics Letters 83(4), 797-799 (2003).
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European Physical Journal D (2)

F. Treussart, V. S. Ilchenko, J. F. Roch, J. Hare, V. Lefevre-Seguin, J. M. Raimond, and S. Haroche, "Evidence for intrinsic Kerr bistability of high-Q microsphere resonators in superfluid helium," European Physical Journal D 1(3), 235-238 (1998).

M. Pinard, Y. Hadjar, and A. Heidmann, "Effective mass in quantum effects of radiation pressure," European Physical Journal D 7(1), 107-116 (1999).

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Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425(6961), 944-947 (2003).
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S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, "Ultralow-threshold Raman laser using a spherical dielectric microcavity," Nature 415(6872), 621-623 (2002).
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D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421(6926), 925-928 (2003).
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A. Naik, O. Buu, M. D. LaHaye, A. D. Armour, A. A. Clerk, M. P. Blencowe, and K. C. Schwab, "Cooling a nanomechanical resonator with quantum back-action," Nature 443(7108), 193-196 (2006).
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O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, and A. Heidmann, "Radiation-pressure cooling and optomechanical instability of a micromirror," Nature 444(7115), 71-74 (2006).
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S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, "Self-cooling of a micromirror by radiation pressure," Nature 444(7115), 67-70 (2006).
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D. Kleckner and D. Bouwmeester, "Sub-kelvin optical cooling of a micromechanical resonator," Nature 444(7115), 75-78 (2006).
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M. L. Povinelli, J.M. Johnson,M. Loncar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. D. Joannopoulos, "High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators," Optics Express 13(20), 8286-8295 (2005).
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T. Carmon, L. Yang, and K. J. Vahala, "Dynamical thermal behavior and thermal self-stability of microcavities," Optics Express 12(20), 4742-4750 (2004).
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Optics Letters (3)

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, "Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres," Optics Letters 32(15), 2200-2202 (2007).
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M. Hossein-Zadeh and K. J. Vahala, "Observation of optical spring effect in a microtoroidal optomechanical resonator," Optics Letters 32(12), 1611-1613 (2007).
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H. Rokhsari and K. J. Vahala, "Observation of Kerr nonlinearity in microcavities at room temperature," Optics Letters 30(4), 427-429 (2005).
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Photonic RF Down-Converter Based on Optomechanical Oscillation (1)

M. Hossein-Zadeh and K. J. Vahala, "Photonic RF Down-Converter Based on Optomechanical Oscillation," (to be published).

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B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, "Observation and characterization of an optical spring," Physical Review A 69(5) (2004).

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Physical Review Letters (27)

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T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, "Temporal behavior of radiation-pressureinduced vibrations of an optical microcavity phonon mode," Physical Review Letters 94(22) (2005).

M. Poggio, C. L. Degen, H. J. Mamin, and D. Rugar, "Feedback cooling of a cantilever’s fundamental mode below 5 mK," Physical Review Letters 99(1) (2007).

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Francais, and L. Rousseau, "High-sensitivity optical monitoring of a micromechanical resonator with a quantumlimited optomechanical sensor," Physical Review Letters 97(13), 133,601 (2006).

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A. Schliesser, P. Del’Haye, N. Nooshi, K. J. Vahala, and T. J. Kippenberg, "Radiation pressure cooling of a micromechanical oscillator using dynamical backaction," Physical Review Letters 97(24), 243,905 (2006).

T. Corbitt, Y. B. Chen, E. Innerhofer, H. Muller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, "An all-optical trap for a gram-scale mirror," Physical Review Letters 98, 150,802 (2007).
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L. Tian and P. Zoller, "Coupled ion-nanomechanical systems," Physical Review Letters 93(26), 266,403 (2004).

I. Wilson-Rae, P. Zoller, and A. Imamoglu, "Laser cooling of a nanomechanical resonator mode to its quantum ground state," Physical Review Letters 92(7), 075,507 (2004).

K. Brown, J. Britton, R. Epstein, J. Chiaverini, D. Leibfried, and D. Wineland, "Passive Cooling of a Micromechanical Oscillator with a Resonant Electric Circuit," Physical Review Letters 99, 137,205 (2007).
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A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, and H. Walther, "Optical Bistability and Mirror Confinement Induced by Radiation Pressure," Physical Review Letters 51(17), 1550-1553 (1983).
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S. Chu, L. Hollberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, "3-Dimensional Viscous Confinement and Cooling of Atoms by Resonance Radiation Pressure," Physical Review Letters 55(1), 48-51 (1985).
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T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity," Physical Review Letters 93(8) (2004).

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser Cooling to the Zero-Point Energy of Motion," Physical Review Letters 62(4), 403-406 (1989).
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D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Physical Review Letters 76(11), 1796-1799 (1996).
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T. Carmon, M. C. Cross, and K. J. Vahala, "Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure," Physical Review Letters98(16) (2007). 0031-9007.

T. Carmon and K. J. Vahala, "Modal spectroscopy of optoexcited vibrations of a micron-scale on-chip resonator at greater than 1 GHz frequency," Physical Review Letters 98(12) (2007).

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Physical Review Letters91(4), art. no.-043,902 (2003).

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I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, "Theory of Ground State Cooling of a Mechanical Oscillator Using Dynamical Backaction," Physical Review Letters 99, 093,902 (2007).
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J. M. Courty, A. Heidmann, and M. Pinard, "Quantum locking of mirrors in interferometers," Physical Review Letters 90(8) (2003).

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Figures (18)

Fig. 1.
Fig. 1.

(a)A cavity optomechanical system consisting of a Fabry Perot cavity with a harmonically bound end mirror. (b): Different physical realizations of cavity optomechanical experiments employing cantilevers [34], micro-mirrors [26, 27], micro-cavities [22, 28], nano-membranes [30] and macroscopic mirror modes [29]. Red and green arrows represent the optical trajectory and mechanical motion.

Fig. 2.
Fig. 2.

The two manifestations of dynamic back-action: blue-detuned and red-detuned pump wave (green) with respect to optical mode line-shape (blue) provide mechanical amplification and cooling, respectively. Also shown in the lower panels are motional sidebands (Stokes and anti-Stokes fields) generated by mirror vibration and subsequent Doppler-shifts of the circulating pump field. The amplitudes of these motional sidebands are asymmetric owing to cavity enhancement of the Doppler scattering process.

Fig. 3.
Fig. 3.

Work done during one cycle of mechanical oscillation can be understood using a PV diagram for the radiation pressure applied to a piston-mirror versus the mode volume displaced during the cycle. In this diagram the cycle follows a contour that circumscribes an area in PV space and hence work is performed during the cycle. The sense in which the contour is traversed (clockwise or counterclockwise) depends upon whether the pump is blue or red detuned with respect to the optical mode. Positive work (amplification) or negative work (cooling) are performed by the photon gas on the piston mirror in the corresponding cases.

Fig. 4.
Fig. 4.

Dynamics in the weak retardation regime. Experimental displacement spectral density functions for a mechanical mode with eigenfrequency 40.6 MHz measured using three, distinct pump powers for both blue and red pump detuning. The mode is thermally excited (green data) and its linewidth can be seen to narrow under blue pump detuning (red data) on account of the presence of mechanical gain (not sufficient in the present measurement to excite full, regenerative oscillations); and to broaden under red pump detuning on account of radiation pressure damping (blue data).

Fig. 5.
Fig. 5.

Upper panel shows mechanical linewidth (δm eff /2π) and shift in mechanical frequency (lower panel) measured versus pump wave detuning in the regime where κ≲Ω m . For negative (positive) detuning cooling (amplification) occurs. The region between the dashed lines denotes the onset of the parametric oscillation, where gain compensates mechanical loss. Figure stems from reference [28]. Solid curves are theoretical predictions based on the sideband model (see section 2.2).

Fig. 6.
Fig. 6.

The mechanical amplification and cooling rate as a function of detuning and normalized mechanical frequency. Also shown is the optimum amplification and cooling rate for fixed frequency (dotted lines). In the simulation, pump power and cavity dimension are fixed parameters.

Fig. 7.
Fig. 7.

Dynamics in the regime where Ω m >κ as reported in reference [28]. Upper panel shows the induced damping/amplification rate (δm eff /2π) as a function of normalized detuning of the laser at constant power. The points represent actual experiments on toroidal microcavities, and the solid line denotes a fit using the sideband theoretical model (Equations 16 and 20). Lower panel shows the mechanical frequency shift as a function of normalized detuning. Arrow denotes the point where the radiation pressure force is entirely viscous causing negligible in phase, but a maximum quadrature component. The region between the dotted lines denotes the onset of the parametric instability (as discussed in section 4). Graph stems from reference [28].

Fig. 8.
Fig. 8.

Upper panel: SEM images and mechanical modes of several types of whispering gallery mode microcavities: toroid microcavities [60] microdisks [59] and microspheres [58]. Also shown are the stress and strain field in cross section of the fundamental radial breathing modes, which include radial dilatation of the cavity boundary. Lower panel: the dispersion diagram for the lowest lying, rotationally symmetric mechanical modes for a toroid (as a function of its undercut) and for a microsphere (as a function of radius).

Fig. 9.
Fig. 9.

Scanning probe microscopy of the two lowest lying micro-mechanical resonances of a toroid microcavity. Lower graph: The normalized mechanical frequency shift for the first mode as a function of position. Upper graph: The normalized frequency shift for the second mechanical mode as a function of scanned distance across the toroid. Superimposed is the scaled amplitude (solid line) and the amplitude squared (dotted line) of the mechanical oscillator modes obtained by finite element simulation of the exact geometry parameters (as inferred by SEM).

Fig. 10.
Fig. 10.

Experimental setup for the observation of cavity cooling or amplification of a mechanical oscillator. All relevant data from the electronic spectrum analyzer and the oscilloscope are transferred to a computer controlling the experiment. More details in the text. IR: iris, FSFC: free-space to fibre coupler, PC: fibre polarization controller, FC: fibre coupler, AUX: auxiliary input, SC: sealed chamber, DET: fast photoreceiver.

Fig. 11.
Fig. 11.

Calibrated [47] displacement spectral density as measured by the setup shown in Figure 10. The peaks denote different mechanical eigenmodes of the toroidal microcavity. The probe power is sufficiently weak such that the mechanical modes amplitude is dominated by Brownian motion at room temperature and backaction effects are negligible. Cross-sectional representations of the n=1,2,3 modes and their corresponding spectral peaks are also given as inferred by finite element simulations.

Fig. 12.
Fig. 12.

Back-action tuning for mode selection with a fixed laser detuning corresponding to Δ=κ/2. The target mode that receives maximum gain (or optimal cooling for Δ=-κ/2) can be controlled by setting the cavity linewidth to produce maximum sideband asymmetry for that particular mechanical mode. In this schematic, three mechanical modes (having frequencies Ωm,i, i=1,2,3) interact with an optical pump, however, in the present scenario only the intermediate mode experiences maximum gain (or cooling) since its sideband asymmetry is maximal (since Ωm,2/κ=0.5). It is important to note however, that if the laser detuning is allowed to vary as well, the highest frequency mode would experience the the largest gain if Δ=Ωm,2 was chosen.

Fig. 13.
Fig. 13.

Regenerative oscillation amplitude plotted versus pump power. The threshold knee is clearly visible. In this case a threshold of 20 μW is observed. Figure from reference [23].

Fig. 14.
Fig. 14.

Main figure: The observed threshold for the parametric oscillation (of an n=1 mode) as a function of inverse mechanical quality factor. In the experiment, variation of Q factor was achieved by placing a fiber tip in mechanical contact with the silica membrane, which thereby allowed reduction of the mechanical Q (cf. inset). The mechanical mode was a 6 MHz flexural mode.

Fig. 15.
Fig. 15.

Main panel shows the measured mechanical oscillation threshold (in micro-Watts) from Ref. [22] plotted versus the optical Q factor for the fundamental flexural mode (n=1, Ω m /2π=4.4MHz, meff ≈3.3×10-8 kg, Qm ≈3500). The solid line is a one-parameter theoretical fit obtained from the minimum threshold equation by first performing a minimization with respect to coupling (C) and pump wavelength detuning (D), and then fitting by adjustment of the effective mass. Inset: The measured threshold for the 3 rd order mode (n=3, Ω m /2π=49MHz, meff ≈5×10-11 kg, Qm ≈2800) plotted versus optical Q. The solid line gives again the theoretical prediction. The n=1 data from the main panel is superimposed for comparison. Figure stems from reference [22].

Fig. 16.
Fig. 16.

Line-width measurements from Ref. [67] of the opto-mechanical oscillator for different amplitudes of oscillation plotted in picometers. The measurement is done at room temperature (dots) and at temperature 90 °C above room temperature (stars). The solid lines and the corresponding equations are the best fits to the log-log data. Solid line denotes theoretically expected behavior.

Fig. 17.
Fig. 17.

Main figure shows the normalized, measured noise spectra around the mechanical breathing mode frequency for Δ·τ≈-0.5 and varying power (0.25,0.75,1.25, and 1.75 mW). The effective temperatures were inferred using mechanical damping, with the lowest attained temperature being 11K. (b) Inset shows increase in the linewidth (effective damping δm eff /2π) of the 57.8-MHz mode as a function of launched power, exhibiting the expected linear behavior as theoretically predicted. From reference [28].

Fig. 18.
Fig. 18.

The frequency response from 0–200MHz of a toroidal opto-mechanical system, adopted from Reference [28]. The plateau occurring above 1MHz is ascribed to the (instantaneous) Kerr nonlinearity of silica (dotted line). The high-frequency cutoff is due to both detector and cavity bandwidth. The response poles at low frequency are thermal in nature. Inset: Data in the vicinity of mechanical oscillator response shows the interference of the Kerr nonlinearity and the radiation pressure-driven micromechanical resonator (which, on resonance, is π/2 out-of phase with the modulating pump and the instantaneous Kerr nonlinearity). From the fits (solid lines) it can be inferred that the radiation pressure response is a factor of 260 larger than the Kerr response and a factor of ×100 larger than the thermo-mechanical contribution.

Equations (29)

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da dt = i Δ ( x ) a ( 1 2 τ 0 + 1 2 τ ex ) a + i 1 τ ex s
d 2 x dt 2 + Ω m 2 Q m dx dt + Ω m 2 x = F RP ( t ) m eff + F L ( t ) m eff = ζ c m eff a 2 T rt + F L ( t ) m eff
Δ ( x ) = Δ + ω 0 R x
τ 2 τ ex s 2 = c m eff ζ Ω m 2 x ̅ ( 4 τ 2 ( Δ + ω 0 R x ̅ ) 2 + 1 )
P cav = P cav 0 + P cav 0 ( 8 Δ τ 2 4 τ 2 Δ 2 + 1 ) ω 0 R x τ P cav 0 ( 8 Δ τ 2 4 τ 2 Δ 2 + 1 ) ω 0 R dx dt
Δ Ω m = κ Ω m 2 8 n 2 ω 0 Ω m m eff c 2 C · [ 2 Δ τ ( 4 τ 2 Δ 2 + 1 ) ] P
Γ = κ Ω m 3 8 n 3 ω 0 R m eff c 3 C · [ 16 Δ τ ( 4 τ 2 Δ 2 + 1 ) 2 ] P
Γ eff = Γ + Γ m
a n = 0 ε n a n
a 0 ( t ) = i 1 τ ex i Δ 1 2 τ s e i ω t
a 1 ( t ) = a 0 ( t ) 2 τ ω 0 ( e i Ω m t 2 i ( Δ + Ω m ) τ 1 + e i Ω m t 2 i ( Δ Ω m ) τ 1 )
F RP ( t ) = cos ( Ω m t ) F I + sin ( Ω m t ) F Q
F I (t)=ε 4πn c T rt ω 0 τ 2 / τ ex 4 Δ 2 τ 2 +1 ( 2(Δ+ Ω m ) 4 (Δ+ Ω m ) 2 τ 2 +1 2(Δ Ω m ) 4 (Δ Ω m ) 2 τ 2 +1 )P
F Q ( t ) = ε 4 π n c T rt ω 0 τ 2 τ ex 4 Δ 2 τ 2 + 1 ( 2 τ 4 ( Δ + Ω m ) 2 τ 2 + 1 2 τ 4 ( Δ Ω m ) 2 τ 2 + 1 ) P
P m = x 2 2 π n c T rt ω 0 1 τ ex 4 τ 2 Δ ω 2 + 1 Ω m 2 R ( 2 τ 4 ( Δ + Ω m ) 2 τ 2 + 1 2 τ 4 ( Δ Ω m ) 2 τ 2 + 1 ) P
Γ = 2 8 n 2 ω 0 Ω m m eff c 2 C · ( 1 4 ( Δ Ω m ) 2 τ 2 + 1 1 4 ( Δ + Ω m ) 2 τ 2 + 1 ) P
lim Ω m 0 1 2 Ω m ( 1 4 ( Δ Ω m ) 2 τ 2 + 1 1 4 ( Δ + Ω m ) 2 τ 2 + 1 ) = 8 Δ τ 2 ( 4 Δ 2 τ 2 + 1 ) 2
d dt E m = ( Γ m + Γ ) E m + k B T R Γ m
T eff Γ m Γ m + Γ T R
Δ Ω m = 2 8 n 2 ω 0 Ω m m eff c 2 C τ . ( Δ Ω m 4 ( Δ Ω m ) 2 τ 2 + 1 + Δ + Ω m 4 ( Δ + Ω m ) 2 τ 2 + 1 ) P
δ x min λ 8 π η P ω
P thresh = Ω m 2 Q m m eff c 2 ω 0 2 8 n 2 C · ( 1 4 ( Δ Ω m ) 2 τ 2 + 1 1 4 ( Δ + Ω m ) 2 τ 2 + 1 ) 1
P thresh = κ Ω m Ω m Q m m eff c 3 3 8 n 3 RC ω 0 ( 16 Δ τ ( 4 τ 2 Δ 2 + 1 ) 2 ) 1
Δ Ω m k B T R P ( Ω m Q m ) 2
T eff Γ m Γ m + Γ T R
n f = A + A A +
n f κ 4 Ω m 1
n f κ 2 16 Ω m 2 1
n f = A + A A + + Γ m Γ m + Γ n R

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