Abstract

We propose a new method to optically levitate a macroscopic mirror with two vertical Fabry-Pérot cavities linearly aligned. This configuration gives the simplest possible optical levitation in which the number of laser beams used is the minimum of two. We demonstrate that reaching the standard quantum limit (SQL) of a displacement measurement with our system is feasible with current technology. The cavity geometry and the levitated mirror parameters are designed to ensure that the Brownian vibration of the mirror surface is smaller than the SQL. Our scheme provides a promising tool for testing macroscopic quantum mechanics.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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  3. A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
    [Crossref]
  4. Y. Chen, “Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics,” J. Phys. B 46, 104001 (2013).
    [Crossref]
  5. M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
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  7. U. B. Hoff, J. Kollath-Bönig, J. S. Neergaard-Nielsen, and U. L. Andersen, “Measurement-Induced Macroscopic Superposition States in Cavity Optomechanics,” Phys. Rev. Lett. 117, 143601 (2016).
    [Crossref] [PubMed]
  8. H. Müller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry,” Phys. Rev. Lett. 100, 013601 (2008).
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  9. V. B. Braginsky, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, Cambridge, UK, 1995).
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  12. R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
    [Crossref] [PubMed]
  13. T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
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    [Crossref] [PubMed]
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  22. T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
    [Crossref] [PubMed]
  23. S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry-Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  26. A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
    [Crossref]
  27. G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
    [Crossref]
  28. R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
    [Crossref]
  29. L. Pinard, C. Michel, B. Sassolas, L. Balzarini, J. Degallaix, V. Dolique, R. Flaminio, D. Forest, M. Granata, B. Lagrange, N. Straniero, J. Teillon, and G. Cagnoli, “Mirrors used in the LIGO interferometers for first detection of gravitational waves,” Appl. Opt. 56, C11 (2017).
    [Crossref] [PubMed]
  30. D. V. Martynov and others, “Sensitivity of the Advanced LIGO detectors at the beginning of gravitational wave astronomy,” Phys. Rev. D 93, 112004 (2016).
    [Crossref]
  31. P. R. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
    [Crossref]
  32. D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
    [Crossref]

2017 (1)

2016 (4)

D. V. Martynov and others, “Sensitivity of the Advanced LIGO detectors at the beginning of gravitational wave astronomy,” Phys. Rev. D 93, 112004 (2016).
[Crossref]

U. B. Hoff, J. Kollath-Bönig, J. S. Neergaard-Nielsen, and U. L. Andersen, “Measurement-Induced Macroscopic Superposition States in Cavity Optomechanics,” Phys. Rev. Lett. 117, 143601 (2016).
[Crossref] [PubMed]

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
[Crossref] [PubMed]

LIGO Scientific Collaboration and Virgo Collaboration, “GW150914: The Advanced LIGO Detectors in the Era of First Discoveries,” Phys. Rev. Lett. 116, 131103 (2016).
[Crossref] [PubMed]

2015 (2)

M. Bawaj and et al., “Probing deformed commutators with macroscopic harmonic oscillators,” Nat. Commun. 6, 7503 (2015).
[Crossref] [PubMed]

N. Matsumoto, K. Komori, Y. Michimura, G. Hayase, Y. Aso, and K. Tsubono, “5-mg suspended mirror driven by measurement-induced backaction,” Phys. Rev. A 92, 033825 (2015).
[Crossref]

2014 (2)

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

2013 (3)

G. Guccione, M. Hosseini, S. Adlong, M. T. Johnsson, J. Hope, B. C. Buchler, and P. K. Lam, “Scattering-Free Optical Levitation of a Cavity Mirror,” Phys. Rev. Lett. 111, 183001 (2013).
[Crossref] [PubMed]

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Y. Chen, “Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics,” J. Phys. B 46, 104001 (2013).
[Crossref]

2011 (2)

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

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

2010 (3)

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

S. Singh, G. A. Phelps, D. S. Goldbaum, E. M. Wright, and P. Meystre, “All-Optical Optomechanics: An Optical Spring Mirror,” Phys. Rev. Lett. 105, 213602 (2010).
[Crossref]

R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
[Crossref]

2008 (1)

H. Müller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry,” Phys. Rev. Lett. 100, 013601 (2008).
[Crossref] [PubMed]

2007 (3)

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

2003 (1)

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
[Crossref] [PubMed]

2002 (1)

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
[Crossref]

1998 (1)

Y. Levin, “Internal thermal noise in the LIGO test masses: A direct approach,” Phys. Rev. D 57, 659 (1998).
[Crossref]

1996 (1)

R. Penrose, “On Gravity’s role in Quantum State Reduction,” Gen. Relativ. Gravit. 28, 581–600 (1996).
[Crossref]

1991 (1)

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry-Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[Crossref] [PubMed]

1990 (1)

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

1989 (1)

L. Diósi, “Models for universal reduction of macroscopic quantum fluctuations,” Phys. Rev. A 40, 1165 (1989).
[Crossref]

1988 (1)

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
[Crossref]

1971 (1)

A. Ashkin and J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 119, 283 (1971).
[Crossref]

1970 (1)

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Abernathy, M. R.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Adlong, S.

G. Guccione, M. Hosseini, S. Adlong, M. T. Johnsson, J. Hope, B. C. Buchler, and P. K. Lam, “Scattering-Free Optical Levitation of a Cavity Mirror,” Phys. Rev. Lett. 111, 183001 (2013).
[Crossref] [PubMed]

Alegre, T.

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

Allman, M. S.

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Andersen, U. L.

U. B. Hoff, J. Kollath-Bönig, J. S. Neergaard-Nielsen, and U. L. Andersen, “Measurement-Induced Macroscopic Superposition States in Cavity Optomechanics,” Phys. Rev. Lett. 117, 143601 (2016).
[Crossref] [PubMed]

Andrews, R. W.

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
[Crossref] [PubMed]

Armandula, H.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Arndt, M.

M. Arndt and K. Hornberger, “Testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical Levitation by Radiation Pressure,” Appl. Phys. Lett. 119, 283 (1971).
[Crossref]

A. Ashkin, “Acceleration and Trapping of Particles by Radiation Pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Aso, Y.

N. Matsumoto, K. Komori, Y. Michimura, G. Hayase, Y. Aso, and K. Tsubono, “5-mg suspended mirror driven by measurement-induced backaction,” Phys. Rev. A 92, 033825 (2015).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

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

Balzarini, L.

Barone, F.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry-Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[Crossref] [PubMed]

Bassi, A.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Bawaj, M.

M. Bawaj and et al., “Probing deformed commutators with macroscopic harmonic oscillators,” Nat. Commun. 6, 7503 (2015).
[Crossref] [PubMed]

Becerra-Toledo, A. E.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Black, E.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Black, E. D.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

Bodiya, T.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

Bouwmeester, D.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
[Crossref] [PubMed]

Braginsky, V. B.

V. B. Braginsky, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, Cambridge, UK, 1995).

Buchler, B. C.

G. Guccione, M. Hosseini, S. Adlong, M. T. Johnsson, J. Hope, B. C. Buchler, and P. K. Lam, “Scattering-Free Optical Levitation of a Cavity Mirror,” Phys. Rev. Lett. 111, 183001 (2013).
[Crossref] [PubMed]

Cagnoli, G.

L. Pinard, C. Michel, B. Sassolas, L. Balzarini, J. Degallaix, V. Dolique, R. Flaminio, D. Forest, M. Granata, B. Lagrange, N. Straniero, J. Teillon, and G. Cagnoli, “Mirrors used in the LIGO interferometers for first detection of gravitational waves,” Appl. Opt. 56, C11 (2017).
[Crossref] [PubMed]

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
[Crossref]

Chan, J.

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

Chen, Y.

Y. Chen, “Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics,” J. Phys. B 46, 104001 (2013).
[Crossref]

H. Müller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry,” Phys. Rev. Lett. 100, 013601 (2008).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

Cicak, K.

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N. Matsumoto, K. Komori, Y. Michimura, G. Hayase, Y. Aso, and K. Tsubono, “5-mg suspended mirror driven by measurement-induced backaction,” Phys. Rev. A 92, 033825 (2015).
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T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
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R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
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R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
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T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
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G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
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[Crossref]

Ottaway, D.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

Painter, O.

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

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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
[Crossref]

Penrose, R.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
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R. Penrose, “On Gravity’s role in Quantum State Reduction,” Gen. Relativ. Gravit. 28, 581–600 (1996).
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R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
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Phelps, G. A.

S. Singh, G. A. Phelps, D. S. Goldbaum, E. M. Wright, and P. Meystre, “All-Optical Optomechanics: An Optical Spring Mirror,” Phys. Rev. Lett. 105, 213602 (2010).
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Pierro, V.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

Pinard, L.

L. Pinard, C. Michel, B. Sassolas, L. Balzarini, J. Degallaix, V. Dolique, R. Flaminio, D. Forest, M. Granata, B. Lagrange, N. Straniero, J. Teillon, and G. Cagnoli, “Mirrors used in the LIGO interferometers for first detection of gravitational waves,” Appl. Opt. 56, C11 (2017).
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A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
[Crossref]

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Pinto, I. M.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

Principe, M.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
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Purdy, T. P.

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
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Regal, C. A.

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
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Rehbein, H.

H. Müller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry,” Phys. Rev. Lett. 100, 013601 (2008).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

Reid, S.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Remillieux, A.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Route, R.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Rowan, S.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
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Rüdiger, A.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
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Russo, G.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry-Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
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Safavi-Naeini, A.

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

Sassolas, B.

L. Pinard, C. Michel, B. Sassolas, L. Balzarini, J. Degallaix, V. Dolique, R. Flaminio, D. Forest, M. Granata, B. Lagrange, N. Straniero, J. Teillon, and G. Cagnoli, “Mirrors used in the LIGO interferometers for first detection of gravitational waves,” Appl. Opt. 56, C11 (2017).
[Crossref] [PubMed]

R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
[Crossref]

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A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
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G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
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P. R. Saulson, “Thermal noise in mechanical experiments,” Phys. Rev. D 42, 2437 (1990).
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D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
[Crossref]

Schnabel, R.

H. Müller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry,” Phys. Rev. Lett. 100, 013601 (2008).
[Crossref] [PubMed]

Schnupp, L.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
[Crossref]

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D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
[Crossref]

Sigg, D.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

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J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Simon, C.

W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, “Towards Quantum Superpositions of a Mirror,” Phys. Rev. Lett. 91, 130401 (2003).
[Crossref] [PubMed]

Singh, S.

S. Singh, G. A. Phelps, D. S. Goldbaum, E. M. Wright, and P. Meystre, “All-Optical Optomechanics: An Optical Spring Mirror,” Phys. Rev. Lett. 105, 213602 (2010).
[Crossref]

Singh, T. P.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Sirois, A. J.

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Smith, N.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

Sneddon, P. H.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Solimeno, S.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry-Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[Crossref] [PubMed]

Startin, W. J.

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
[Crossref]

Straniero, N.

Taurasi, I.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

Teillon, J.

Teufel, J. D.

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
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V. B. Braginsky, F. Y. Khalili, and K. S. Thorne, Quantum Measurement (Cambridge University, Cambridge, UK, 1995).

Tsubono, K.

N. Matsumoto, K. Komori, Y. Michimura, G. Hayase, Y. Aso, and K. Tsubono, “5-mg suspended mirror driven by measurement-induced backaction,” Phys. Rev. A 92, 033825 (2015).
[Crossref]

Ulbricht, H.

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, “Models of wave-function collapse, underlying theories, and experimental tests,” Rev. Mod. Phys. 85, 471–527 (2013).
[Crossref]

Villar, A.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

Villar, A. E.

A. E. Villar, E. D. Black, R. DeSalvo, K. G. Libbrecht, C. Michel, N. Morgado, L. Pinard, I. M. Pinto, V. Pierro, V. Galdi, M. Principe, and I. Taurasi, “Measurement of thermal noise in multilayer coatings with optimized layer thickness,” Phys. Rev. D 81, 122001 (2010).
[Crossref]

Whitcomb, S.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

Whittaker, J. D.

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Winkler, W.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdiger, “Noise behavior of the Garching 30-meter prototype gravitational-wave detector,” Phys. Rev. D 38, 423 (1988).
[Crossref]

Wipf, C.

T. Corbitt, C. Wipf, T. Bodiya, D. Ottaway, D. Sigg, N. Smith, S. Whitcomb, and N. Mavalvala, “Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK,” Phys. Rev. Lett. 99, 160801 (2007).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An All-Optical Trap for a Gram-Scale Mirror,” Phys. Rev. Lett. 98, 150802 (2007).
[Crossref] [PubMed]

Wright, E. M.

S. Singh, G. A. Phelps, D. S. Goldbaum, E. M. Wright, and P. Meystre, “All-Optical Optomechanics: An Optical Spring Mirror,” Phys. Rev. Lett. 105, 213602 (2010).
[Crossref]

Yu, P.-L.

R. W. Peterson, T. P. Purdy, N. S. Kampel, R. W. Andrews, P.-L. Yu, K. W. Lehnert, and C. A. Regal, “Laser Cooling of a Micromechanical Membrane to the Quantum Backaction Limit,” Phys. Rev. Lett. 116, 063601 (2016).
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Class. Quantum Grav. (3)

G. M. Harry, A. M. Gretarsson, P. R. Saulson, S. E. Kittelberger, S. D. Penn, W. J. Startin, S. Rowan, M. M. Fejer, D. R. M. Crooks, G. Cagnoli, J. Hough, and N. Nakagawa, “Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings,” Class. Quantum Grav. 19, 897 (2002).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M Fejer, R. Route, S. D. Penn, P. Ganau, J. M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405 (2007).
[Crossref]

R. Flaminio, J. Franc, C. Michel, N. Morgado, L. Pinard, and B. Sassolas, “A study of coating mechanical and optical losses in view of reducing mirror thermal noise in gravitational wave detectors,” Class. Quantum Grav. 27, 084030 (2010).
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Y. Chen, “Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics,” J. Phys. B 46, 104001 (2013).
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J. Chan, T. Alegre, A. Safavi-Naeini, J. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89 (2011).
[Crossref] [PubMed]

J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref] [PubMed]

Phys. Rev. A (3)

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Figures (2)

Fig. 1
Fig. 1

Schematic of the sandwich configuration. The arcs and the centers of the sectors are the mirrors and their COCs, respectively. The blue and red lines are the circulating beams in the lower and upper cavities, respectively. (a) Balanced state. The vertical motion is constrained by the double optical spring. (b) Restoring torque due to the gravity. (c) Horizontal restoring force due to the upper cavity.

Fig. 2
Fig. 2

Noise spectra of the 0.2 mg mirror, using parameters in Table 1. The mirror reaches the SQL at 23 kHz, corresponding to the vertical displacement of 2.2 × 10−19 m/Hz1/2. The resonance at 340 Hz is due to the double optical spring.

Tables (1)

Tables Icon

Table 1 Parameters for reaching the SQL. The suffix indicates s for the substrate, Ta for the TiO2:Ta2O5 coating layer, Si for the SiO2 coating layer, L for the lower cavity and U for the upper cavity.

Equations (4)

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K I hor = k I hor + i ω γ I hor = ± F I a I [ 1 i ω π l I I c ( 1 G I ) ] ,
K = ( K L hor + K U hor 0 0 0 K L opt + K U opt 0 0 0 m g R ) .
f SQL 1 2 π 16 g λ L ,
4 k B T ω [ ϕ s π w L 1 ν s 2 Y s + c d c ϕ c π w L   2 Y c 2 ( 1 + ν s ) 2 ( 1 2 ν s ) 2 + Y s 2 ( 1 + ν c ) 2 ( 1 2 ν c ) Y s 2 Y c ( 1 v c 2 ) ] ,

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