Abstract

The squeezing transfer from a squeezed vacuum injected in one cavity to the output spectrum of the other cavity in an optomechanical system is investigated. By calculating the noise spectrum of the output field, it is found that two squeezing dips appear symmetrically located about the resonant point. Besides the contribution from the destructive interference between the noise fluctuation of the input field and its optomechanically modified one, the major part of the squeezing is transferred from the squeezed vacuum injected in the cavity. Additionally, it is shown that the adverse effects of the environment temperature on the output spectrum can be strongly suppressed by the injected squeezed field. This study can be useful in quantum communications via the optomechanical interface.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  48. L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A 82(5), 053806(2010).
    [Crossref]
  49. Y.-D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108(15), 153603 (2012).
    [Crossref] [PubMed]
  50. J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
    [Crossref]
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    [Crossref]
  52. W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
    [Crossref]
  53. M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
    [Crossref]
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    [Crossref]

2018 (1)

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
[Crossref]

2017 (1)

M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
[Crossref]

2016 (1)

J. Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116(16), 163602 (2016).
[Crossref] [PubMed]

2015 (3)

B. P. Hou, L. F. Wei, and S. J. Wang, “Optomechanically induced transparency and absorption in hybridized optomechanical systems,” Phys. Rev. A 92(3), 033829 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91(6), 063815 (2015).
[Crossref]

Z. Li, S.-l. Ma, and F.-l. Li, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 92(2), 023856 (2015).
[Crossref]

2014 (6)

K. Qu and G. S. Agarwal, “Strong squeezing via phonon mediated spontaneous generation of photon pairs,” New J. Phys. 16, 113004 (2014).
[Crossref]

M. J. Woolley and A. A. Clerk, “Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir,” Phys. Rev. A 89(6), 063805 (2014).
[Crossref]

R. X. Adhikari, “Gravitational radiation detection with laser interferometry,” Rev. Mod, Phys. 86(1), 121–151 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, ”Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

2013 (7)

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
[Crossref]

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
[Crossref]

M. J. Woolley and A. A. Clerk, “Two-mode back-action-evading measurements in cavity optomechanics,” Phys. Rev. A 87(6), 063846 (2013).
[Crossref]

P. Meystre, ”A short walk through quantum optomechanics,” Ann. Phys. 525(3), 215–233 (2013).
[Crossref]

H. Tan, G. Li, and P. Meystre, “Dissipation-driven two-mode mechanical squeezed states in optomechanical systems,” Phys. Rev. A 87(3), 033829 (2013).
[Crossref]

2012 (5)

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108(15), 153603 (2012).
[Crossref] [PubMed]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

L. Tian, “Adiabatic state conversion and pulse transmission in optomechanical systems,” Phys. Rev. Lett. 108(15), 153604 (2012).
[Crossref] [PubMed]

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature(London) 488, 476–480 (2012).
[Crossref]

2011 (7)

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[Crossref] [PubMed]

J.-Q. Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A 83(3), 033820 (2011).
[Crossref]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, and J. Chan, ”Electromagnetically induced transparency and slow light with optomechanics,” Nature(London) 472(7341), 69–73 (2011).
[Crossref]

P. Rabl, ”Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107(6), 063601 (2011).
[Crossref] [PubMed]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, ”Single-photon optomechanics,” Phys. Rev. Lett. 107(6), 063602 (2011).
[Crossref] [PubMed]

2010 (6)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

G. S. Agarwal and S. Huang, ”Normal mode splitting and antibunching in stokes and anti-stokes processes in cavity optomechanics: radiation pressure induced four-wave mixing cavity optomechanics,” Phys. Rev. A 81(3), 033830 (2010).
[Crossref]

S. Huang and G. S. Agarwal, “Reactive coupling can beat the motional quantum limit of nanowaveguides coupled to a microdisk resonator,” Phys. Rev. A 82(3), 033811 (2010).
[Crossref]

A. A. Geraci, S. B. Papp, and J. Kitching, ”Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105(10), 101101 (2010).
[Crossref] [PubMed]

A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
[Crossref]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A 82(5), 053806(2010).
[Crossref]

2009 (2)

K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

A. Mari and J. Eisert, “Gently modulating optomechanical systems,” Phys. Rev. Lett. 103(21), 213603 (2009).
[Crossref]

2008 (2)

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78(6), 062303 (2008).
[Crossref]

A. A. Clerk, F. Marquardt, and K. Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. 10, 095010 (2008).
[Crossref]

2007 (4)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
[Crossref] [PubMed]

D. Vitali, S. Gigan, and A. Ferreira, ”Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

M. Bhattacharya and P. Meystre, ”Trapping and cooling a mirror to its quantum mechanical ground state,” Phys. Rev. Lett. 99(7), 073601 (2007).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

2006 (1)

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

2005 (1)

S. L. Braunstein and P. V. Loockand, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005).
[Crossref]

2004 (1)

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] [PubMed]

2003 (1)

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68(1), 013808 (2003).
[Crossref]

2001 (1)

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63(2), 023812 (2001).
[Crossref]

1994 (2)

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055 (1994).
[Crossref] [PubMed]

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
[Crossref] [PubMed]

1983 (1)

D. F. Walls, “Squeezed states of light,” Nature(London) 306, 141–146 (1983).
[Crossref]

1981 (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693 (1981).
[Crossref]

Adhikari, R. X.

R. X. Adhikari, “Gravitational radiation detection with laser interferometry,” Rev. Mod, Phys. 86(1), 121–151 (2014).
[Crossref]

Agarwal, G. S.

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91(6), 063815 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Strong squeezing via phonon mediated spontaneous generation of photon pairs,” New J. Phys. 16, 113004 (2014).
[Crossref]

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

S. Huang and G. S. Agarwal, “Reactive coupling can beat the motional quantum limit of nanowaveguides coupled to a microdisk resonator,” Phys. Rev. A 82(3), 033811 (2010).
[Crossref]

G. S. Agarwal and S. Huang, ”Normal mode splitting and antibunching in stokes and anti-stokes processes in cavity optomechanics: radiation pressure induced four-wave mixing cavity optomechanics,” Phys. Rev. A 81(3), 033830 (2010).
[Crossref]

Allman, M. S.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Asjad, M.

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, ”Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

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A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
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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).
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J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
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A. H. Safavi-Naeini, T. P. Mayer Alegre, and J. Chan, ”Electromagnetically induced transparency and slow light with optomechanics,” Nature(London) 472(7341), 69–73 (2011).
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J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
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T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
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T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
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M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
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M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
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A. Mari and J. Eisert, “Gently modulating optomechanical systems,” Phys. Rev. Lett. 103(21), 213603 (2009).
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M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
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C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
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D. Vitali, S. Gigan, and A. Ferreira, ”Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
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V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
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K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
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A. A. Geraci, S. B. Papp, and J. Kitching, ”Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105(10), 101101 (2010).
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C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
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D. Vitali, S. Gigan, and A. Ferreira, ”Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
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M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
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V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63(2), 023812 (2001).
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A. Nunnenkamp, K. Børkje, and S. M. Girvin, ”Single-photon optomechanics,” Phys. Rev. Lett. 107(6), 063602 (2011).
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A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
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M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
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A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
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J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
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W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
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K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
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T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
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J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
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Harris, J. G. E.

A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
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Heeck, K.

M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
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C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
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Hill, J. T.

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
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J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
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B. P. Hou, L. F. Wei, and S. J. Wang, “Optomechanically induced transparency and absorption in hybridized optomechanical systems,” Phys. Rev. A 92(3), 033829 (2015).
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D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
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G. S. Agarwal and S. Huang, ”Normal mode splitting and antibunching in stokes and anti-stokes processes in cavity optomechanics: radiation pressure induced four-wave mixing cavity optomechanics,” Phys. Rev. A 81(3), 033830 (2010).
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A. A. Clerk, F. Marquardt, and K. Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. 10, 095010 (2008).
[Crossref]

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K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
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T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

Khalili, F.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

Kim, M. S.

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

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M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, ”Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
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T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
[Crossref] [PubMed]

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A. A. Geraci, S. B. Papp, and J. Kitching, ”Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105(10), 101101 (2010).
[Crossref] [PubMed]

Krause, A.

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

Kuzyk, M. C.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[Crossref] [PubMed]

LaHaye, M. D.

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] [PubMed]

Lai, D.-G.

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
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J.-Q. Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A 83(3), 033820 (2011).
[Crossref]

Lehnert, K. W.

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

Li, D.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
[Crossref]

Li, F.-l.

Z. Li, S.-l. Ma, and F.-l. Li, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 92(2), 023856 (2015).
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Li, G.

H. Tan, G. Li, and P. Meystre, “Dissipation-driven two-mode mechanical squeezed states in optomechanical systems,” Phys. Rev. A 87(3), 033829 (2013).
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Li, G.-x.

W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
[Crossref]

Li, Z.

Z. Li, S.-l. Ma, and F.-l. Li, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 92(2), 023856 (2015).
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J. Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116(16), 163602 (2016).
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Liao, J.-Q.

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
[Crossref]

J.-Q. Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A 83(3), 033820 (2011).
[Crossref]

Loockand, P. V.

S. L. Braunstein and P. V. Loockand, “Quantum information with continuous variables,” Rev. Mod. Phys. 77(2), 513–577 (2005).
[Crossref]

Luna, F.

M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
[Crossref]

Ma, S.-l.

Z. Li, S.-l. Ma, and F.-l. Li, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 92(2), 023856 (2015).
[Crossref]

Mancini, S.

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055 (1994).
[Crossref] [PubMed]

Mari, A.

A. Mari and J. Eisert, “Gently modulating optomechanical systems,” Phys. Rev. Lett. 103(21), 213603 (2009).
[Crossref]

Marin, F.

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

Marino, F.

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, ”Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
[Crossref]

A. A. Clerk, F. Marquardt, and K. Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. 10, 095010 (2008).
[Crossref]

Mavalvala, N.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

Mayer Alegre, T. P.

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, and J. Chan, ”Electromagnetically induced transparency and slow light with optomechanics,” Nature(London) 472(7341), 69–73 (2011).
[Crossref]

Meystre, P.

P. Meystre, ”A short walk through quantum optomechanics,” Ann. Phys. 525(3), 215–233 (2013).
[Crossref]

H. Tan, G. Li, and P. Meystre, “Dissipation-driven two-mode mechanical squeezed states in optomechanical systems,” Phys. Rev. A 87(3), 033829 (2013).
[Crossref]

M. Bhattacharya and P. Meystre, ”Trapping and cooling a mirror to its quantum mechanical ground state,” Phys. Rev. Lett. 99(7), 073601 (2007).
[Crossref] [PubMed]

Milburn, G. J.

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78(6), 062303 (2008).
[Crossref]

Nunnenkamp, A.

A. Nunnenkamp, K. Børkje, and S. M. Girvin, ”Single-photon optomechanics,” Phys. Rev. Lett. 107(6), 063602 (2011).
[Crossref] [PubMed]

A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
[Crossref]

Ottaway, D.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

Painter, O.

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

Palomaki, T. A.

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

Papp, S. B.

A. A. Geraci, S. B. Papp, and J. Kitching, ”Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105(10), 101101 (2010).
[Crossref] [PubMed]

Paternostro, M.

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

Peng, K.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68(1), 013808 (2003).
[Crossref]

Peterson, R. W.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

Pinard, M.

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
[Crossref] [PubMed]

Polzik, E. S.

K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Pontin, A.

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

Prodi, G. A.

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

Purdy, T. P.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature(London) 488, 476–480 (2012).
[Crossref]

Qu, K.

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91(6), 063815 (2015).
[Crossref]

K. Qu and G. S. Agarwal, “Strong squeezing via phonon mediated spontaneous generation of photon pairs,” New J. Phys. 16, 113004 (2014).
[Crossref]

Rabl, P.

P. Rabl, ”Photon blockade effect in optomechanical systems,” Phys. Rev. Lett. 107(6), 063601 (2011).
[Crossref] [PubMed]

Regal, C. A.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

Reynaud, S.

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
[Crossref] [PubMed]

Rivière, R.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
[Crossref]

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, and J. Chan, ”Electromagnetically induced transparency and slow light with optomechanics,” Nature(London) 472(7341), 69–73 (2011).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

Schliesser, A.

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Schreppler, S.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature(London) 488, 476–480 (2012).
[Crossref]

Schwab, K. C.

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78(6), 062303 (2008).
[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] [PubMed]

Serra, E.

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

Simmonds, R. W.

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

Stamper-Kurn, D. M.

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature(London) 488, 476–480 (2012).
[Crossref]

Tan, H.

H. Tan, G. Li, and P. Meystre, “Dissipation-driven two-mode mechanical squeezed states in optomechanical systems,” Phys. Rev. A 87(3), 033829 (2013).
[Crossref]

Teufel, J. D.

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
[Crossref]

Tian, L.

J. Q. Liao and L. Tian, “Macroscopic quantum superposition in cavity optomechanics,” Phys. Rev. Lett. 116(16), 163602 (2016).
[Crossref] [PubMed]

L. Tian, “Adiabatic state conversion and pulse transmission in optomechanical systems,” Phys. Rev. Lett. 108(15), 153604 (2012).
[Crossref] [PubMed]

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[Crossref] [PubMed]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A 82(5), 053806(2010).
[Crossref]

Tombesi, P.

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055 (1994).
[Crossref] [PubMed]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
[Crossref] [PubMed]

Verhagen, E.

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

Vitali, D.

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

D. Vitali, S. Gigan, and A. Ferreira, ”Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

M. Paternostro, D. Vitali, S. Gigan, M. S. Kim, C. Brukner, J. Eisert, and M. Aspelmeyer, “Creating and probing multipartite macroscopic entanglement with light,” Phys. Rev. Lett. 99(25), 250401 (2007).
[Crossref]

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63(2), 023812 (2001).
[Crossref]

Vyatchanin, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

Wallquist, M.

K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Walls, D. F.

D. F. Walls, “Squeezed states of light,” Nature(London) 306, 141–146 (1983).
[Crossref]

Wang, H.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[Crossref] [PubMed]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A 82(5), 053806(2010).
[Crossref]

Wang, S. J.

B. P. Hou, L. F. Wei, and S. J. Wang, “Optomechanically induced transparency and absorption in hybridized optomechanical systems,” Phys. Rev. A 92(3), 033829 (2015).
[Crossref]

Wang, Y.-D.

Y.-D. Wang and A. A. Clerk, “Using interference for high fidelity quantum state transfer in optomechanics,” Phys. Rev. Lett. 108(15), 153603 (2012).
[Crossref] [PubMed]

Weaver, M. J.

M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
[Crossref]

Wei, L. F.

B. P. Hou, L. F. Wei, and S. J. Wang, “Optomechanically induced transparency and absorption in hybridized optomechanical systems,” Phys. Rev. A 92(3), 033829 (2015).
[Crossref]

Weis, S.

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
[Crossref] [PubMed]

Whitcomb, S.

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

Woolley, M. J.

M. J. Woolley and A. A. Clerk, “Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir,” Phys. Rev. A 89(6), 063805 (2014).
[Crossref]

M. J. Woolley and A. A. Clerk, “Two-mode back-action-evading measurements in cavity optomechanics,” Phys. Rev. A 87(6), 063846 (2013).
[Crossref]

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78(6), 062303 (2008).
[Crossref]

Xiao, Y.-F.

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
[Crossref]

Yang, Y.

V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107(13), 133601 (2011).
[Crossref] [PubMed]

Yang, Y.-p.

W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
[Crossref]

Yu, P.-L.

T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, “Strong optomechanical squeezing of light,” Phys. Rev. X 3(3), 031012 (2013).

Zhang, J.

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68(1), 013808 (2003).
[Crossref]

Zoller, P.

K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

Zou, F.

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
[Crossref]

Ann. Phys. (1)

P. Meystre, ”A short walk through quantum optomechanics,” Ann. Phys. 525(3), 215–233 (2013).
[Crossref]

Nat. Commun. (2)

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3, 1196 (2012).
[Crossref]

M. J. Weaver, F. Buters, F. Luna, H. Eerkens, K. Heeck, S. de Man, and D. Bouwmeester, “Coherent optomechanical state transfer between disparate mechanical resonators,” Nat. Commun. 8, 824 (2017).
[Crossref]

Nature (London) (1)

E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature (London) 482, 63–67 (2012).
[Crossref]

Nature(London) (7)

T. A. Palomaki, J. W. Harlow, J. D. Teufel, R. W. Simmonds, and K. W. Lehnert, “Coherent state transfer between itinerant microwave fields and a mechanical oscillator,” Nature(London) 495, 210–214 (2013).
[Crossref]

D. W. C. Brooks, T. Botter, S. Schreppler, T. P. Purdy, N. Brahms, and D. M. Stamper-Kurn, “Non-classical light generated by quantum-noise-driven cavity optomechanics,” Nature(London) 488, 476–480 (2012).
[Crossref]

A. H. Safavi-Naeini, S. Groblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, “Squeezed light from a silicon micromechanical resonator,” Nature(London) 500, 185–189 (2013).
[Crossref]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, and M. S. Allman, ”Sideband cooling of micromechanical motion to the quantum ground state,” Nature(London) 475(7356), 359–363 (2011).
[Crossref]

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature(London) 478(7367), 89–92 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, and J. Chan, ”Electromagnetically induced transparency and slow light with optomechanics,” Nature(London) 472(7341), 69–73 (2011).
[Crossref]

D. F. Walls, “Squeezed states of light,” Nature(London) 306, 141–146 (1983).
[Crossref]

New J. Phys. (2)

K. Qu and G. S. Agarwal, “Strong squeezing via phonon mediated spontaneous generation of photon pairs,” New J. Phys. 16, 113004 (2014).
[Crossref]

A. A. Clerk, F. Marquardt, and K. Jacobs, “Back-action evasion and squeezing of a mechanical resonator using a cavity detector,” New J. Phys. 10, 095010 (2008).
[Crossref]

Opt. Express (1)

T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
[Crossref] [PubMed]

Phys. Rev. A (22)

D.-G. Lai, F. Zou, B.-P. Hou, Y.-F. Xiao, and J.-Q. Liao, “Simultaneous cooling of coupled mechanical resonators in cavity optomechanics,” Phys. Rev. A 98(2), 023860 (2018).
[Crossref]

G. S. Agarwal and S. Huang, ”Normal mode splitting and antibunching in stokes and anti-stokes processes in cavity optomechanics: radiation pressure induced four-wave mixing cavity optomechanics,” Phys. Rev. A 81(3), 033830 (2010).
[Crossref]

B. P. Hou, L. F. Wei, and S. J. Wang, “Optomechanically induced transparency and absorption in hybridized optomechanical systems,” Phys. Rev. A 92(3), 033829 (2015).
[Crossref]

S. Huang and G. S. Agarwal, “Reactive coupling can beat the motional quantum limit of nanowaveguides coupled to a microdisk resonator,” Phys. Rev. A 82(3), 033811 (2010).
[Crossref]

J.-Q. Liao and C. K. Law, “Parametric generation of quadrature squeezing of mirrors in cavity optomechanics,” Phys. Rev. A 83(3), 033820 (2011).
[Crossref]

H. Tan, G. Li, and P. Meystre, “Dissipation-driven two-mode mechanical squeezed states in optomechanical systems,” Phys. Rev. A 87(3), 033829 (2013).
[Crossref]

M. J. Woolley and A. A. Clerk, “Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir,” Phys. Rev. A 89(6), 063805 (2014).
[Crossref]

S. Mancini and P. Tombesi, “Quantum noise reduction by radiation pressure,” Phys. Rev. A 49(5), 4055 (1994).
[Crossref] [PubMed]

C. Fabre, M. Pinard, S. Bourzeix, A. Heidmann, E. Giacobino, and S. Reynaud, “Quantum-noise reduction using a cavity with a movable mirror,” Phys. Rev. A 49(2), 1337 (1994).
[Crossref] [PubMed]

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63(2), 023812 (2001).
[Crossref]

K. Qu and G. S. Agarwal, “Generating quadrature squeezed light with dissipative optomechanical coupling,” Phys. Rev. A 91(6), 063815 (2015).
[Crossref]

Z. Li, S.-l. Ma, and F.-l. Li, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 92(2), 023856 (2015).
[Crossref]

A. Nunnenkamp, K. Borkje, J. G. E. Harris, and S. M. Girvin, “Generation of broadband two-mode squeezed light in cascaded double-cavity optomechanical systems,” Phys. Rev. A 82(2), 021806(R) (2010).
[Crossref]

M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, and D. Vitali, “Robust stationary mechanical squeezing in a kicked quadratic optomechanical system,” Phys. Rev. A 89(2), 023849 (2014).
[Crossref]

T. Corbitt, Y. Chen, F. Khalili, D. Ottaway, S. Vyatchanin, S. Whitcomb, and N. Mavalvala, “Squeezed-state source using radiation-pressure-induced rigidity,” Phys. Rev. A 73(2), 023801 (2006).
[Crossref]

M. J. Woolley, A. C. Doherty, G. J. Milburn, and K. C. Schwab, “Nanomechanical squeezing with detection via a microwave cavity,” Phys. Rev. A 78(6), 062303 (2008).
[Crossref]

A. Pontin, C. Biancofiore, E. Serra, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, M. Bonaldi, F. Marin, and D. Vitali, “Frequency-noise cancellation in optomechanical systems for ponderomotive squeezing,” Phys. Rev. A 89(3), 033810 (2014).
[Crossref]

L. Tian and H. Wang, “Optical wavelength conversion of quantum states with optomechanics,” Phys. Rev. A 82(5), 053806(2010).
[Crossref]

J. Zhang, K. Peng, and S. L. Braunstein, “Quantum-state transfer from light to macroscopic oscillators,” Phys. Rev. A 68(1), 013808 (2003).
[Crossref]

M. J. Woolley and A. A. Clerk, “Two-mode back-action-evading measurements in cavity optomechanics,” Phys. Rev. A 87(6), 063846 (2013).
[Crossref]

K. Jahne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, and P. Zoller, “Cavity-assisted squeezing of a mechanical oscillator,” Phys. Rev. A 79(6), 063819 (2009).
[Crossref]

W.-j. Gu, G.-x. Li, and Y.-p. Yang, “Generation of squeezed states in a movable mirror via dissipative optomechanical coupling,” Phys. Rev. A 88(1), 013835 (2013).
[Crossref]

Phys. Rev. D (1)

C. M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23(8), 1693 (1981).
[Crossref]

Phys. Rev. Lett. (11)

A. A. Geraci, S. B. Papp, and J. Kitching, ”Short-range force detection using optically cooled levitated microspheres,” Phys. Rev. Lett. 105(10), 101101 (2010).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic of the two-cavity optomechanical system. The system consists of two optical cavities which are coupled to a common mechanical oscillator by the radiation pressures. Two coupling fields with power Pk (k = 1, 2) and frequency ωk are used to drive the two cavities, respectively.
Fig. 2
Fig. 2 The squeezing spectra Sθ (ω) as a function of the normalized frequency ω/ωm with P2 = 1 mW and for the different powers of the left coupling field (a): P1 = 1 mW (black, solid curve); 5 mW (red, dashed curve); 10 mW (blue, dotted curve). The squeezing spectra Sθ (ω) as a function of the normalized frequency ω/ωm with P1 = 1 mW and for the different powers of the right coupling field (b): P2 = 1 mW (black, solid curve); 5 mW (red, dashed curve); 10 mW (blue, dotted curve). The values of the parameters are given by: ωm = 2π × 3.993 × 109Hz, g1 = 2π × 960 × 103, g2 = 2π × 430 × 103, T = 10K, r = 0, Qm = 87 × 103, κ1 = 2π × 520 × 106Hz, κ2 = 1.73 × 109Hz, ω1 = 2π × 205.3 × 1012Hz, ω2 = 2π × 194.1 × 1012Hz, θ = π/2.
Fig. 3
Fig. 3 The same settings are used as those in Fig. 2 except for the presence of squeezed vacuum injected in the left cavity with squeezing parameter r = 1.
Fig. 4
Fig. 4 The squeezing spectra Sθ(ω) as a function of the normalized frequency ω/ωm with P1 = 1 mW, P2 = 5 mW for the injected vacuum field r = 0 (black, solid curve), and for the injected squeezed field r = 1 (red, dashed curve). The others are set with the same values as in Fig. 2.
Fig. 5
Fig. 5 The squeezing spectra Sθ(ω) as a function of the normalized frequency ω/ωm with P1 = 1 mW, P2 = 5 mW and for different squeezing parameter r of the squeezed field injected in the left cavity: r = 0.3(black, solid curve); r = 0.6(red, dashed curve); r = 1(blue, dotted curve). The others are set with the same values as in Fig. 2.
Fig. 6
Fig. 6 The spectrum Sθ(ω) (a) as a function of the normalized frequency ω/ωm for the injected vacuum r = 0 (a) and the injected squeezed vacuum r = 1 (b) in the left-hand cavity. The temperature for the mechanical environment are given by different values: T1 = 10K (black, solid curve); 50 K (red, dashed curve); 100 K (blue, dotted curve). The others are set with the same values as in Fig. 2.
Fig. 7
Fig. 7 The spectrum Sθ(ω) (a) as a function of the normalized frequency ω/ωm for g1 = 0, r = 0 at Δ2 = ωm (a) and Δ2 = −ωm (b), and for g1 = 2π × 960 × 103, r = 1 at Δ2 = −ωm (c). The power of the right coupling field is set as: P2 = 1 mW (black, solid curve); 3 mW (red, dashed curve); 6 mW (blue, dotted curve). The others are set with the same values as in Fig. 2.

Equations (36)

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H = k = 1 , 2 Δ c k a k a ^ k + ω m b ^ b ^ ( g 1 a ^ 1 a ^ 1 g 2 a ^ 2 a ^ 2 ) ( b ^ + b ^ ) + k = 1 , 2 i E k ( a ^ k a ^ k ) .
a ^ ˙ 1 = ( i Δ c 1 + κ 1 ) a ^ 1 + i g 1 a ^ 1 ( b ^ + b ^ ) + E 1 + 2 κ 1 a ^ in , 1 ,
a ^ ˙ 2 = ( i Δ c 2 + κ 2 ) a ^ 2 i g 2 a ^ 2 ( b ^ + b ^ ) + E 2 + 2 κ 2 a ^ in , 2 ,
b ^ ˙ = ( i ω m + γ m ) b ^ + i ( g 1 a ^ 1 a ^ 1 g 2 a ^ 2 a ^ 2 ) + b ^ in
a k s = E k κ k + i Δ k , ( k = 1 , 2 )
b s = i g 1 a 1 s a 1 s * i g 2 a 2 s a 2 s * γ m + i ω m
δ a ^ ˙ k = ( i Δ k + κ k ) δ a ^ k ( 1 ) k i g k a k s ( δ b ^ + δ b ^ ) + 2 κ k δ a ^ in , k , ( k = 1 , 2 )
δ b ^ ˙ = ( i ω m + γ m ) δ b ^ + i [ g 1 ( a 1 s * δ a ^ 1 + a 1 s δ a ^ 1 ) g 2 ( a 2 s * δ a ^ 2 + a 2 s δ a ^ 2 ) ] + δ b ^ in .
δ a ^ out , 2 ( ω ) = C 1 ( ω ) δ a ^ in , 1 + C 2 ( ω ) δ a ^ in , 1 ( ω ) + V 1 ( ω ) δ a ^ in , 2 + V 2 ( ω ) δ a ^ in , 2 ( ω ) + W 1 ( ω ) δ b ^ in ( ω ) + W 2 ( ω ) δ b ^ in ( ω )
C 1 ( ω ) = 2 i g 1 g 2 a 1 s * a 2 s κ 1 κ 2 Γ m m [ κ 1 + i ( Δ 1 ω ) ] [ κ 2 + i ( Δ 2 ω ) ] ,
C 2 ( ω ) = 2 i g 1 g 2 a 1 s a 2 s κ 1 κ 2 Γ m m [ κ 1 + i ( Δ 1 ω ) ] [ κ 2 + i ( Δ 2 ω ) ] ,
V 1 ( ω ) = 2 i g 2 2 | a 2 s | 2 κ 2 Γ m m [ κ 2 + i ( Δ 2 ω ) ] [ κ 2 + i ( Δ 2 ω ) ] + 2 κ 2 κ 2 + i ( Δ 2 ω ) 1 ,
V 2 ( ω ) = 2 i g 2 2 a 2 s 2 κ 2 Γ m m [ κ 2 + i ( Δ 2 ω ) ] [ κ 2 + i ( Δ 2 + ω ) ] ,
W 1 ( ω ) = i g 2 a 2 s 2 κ 2 Γ m b κ 2 + i ( Δ 2 ω ) ,
W 2 ( ω ) = i g 2 a 2 s 2 κ 2 Γ m a κ 2 + i ( Δ 2 ω ) ,
Γ m a = Γ + Γ + Γ 2 i ω m ( Λ m + i δ m ) ,
Γ m b = Γ Γ + Γ 2 i ω m ( Λ m + i δ m ) ,
Γ m m = 2 ω m Γ + Γ 2 i ω m ( Λ m + i δ m )
S θ ( ω ) = 1 2 π d Ω δ X ^ θ out ( ω ) δ X ^ θ out ( Ω ) ,
S θ ( ω ) = M F 1 + ( N + 1 ) F 2 + N F 3 + M * F 4 + G 1 + γ m ( n b + 1 ) H 1 + γ m n b H 2 ,
F 1 = C 1 ( ω ) C 1 ( Ω 1 ) e 2 i θ + C 1 ( ω ) C 2 * ( Ω 1 ) + C 2 * ( ω ) C 1 ( Ω 1 ) + C 2 * ( ω ) C 2 * ( Ω 1 ) e 2 i θ ,
F 2 = C 1 ( ω ) C 2 ( Ω 1 ) e 2 i θ + C 1 ( ω ) C 1 * ( Ω 2 ) + C 2 * ( ω ) C 2 ( Ω 2 ) + C 2 * ( ω ) C 1 * ( Ω 2 ) e 2 i θ ,
F 3 = C 2 ( ω ) C 1 ( Ω 2 ) e 2 i θ + C 2 ( ω ) C 2 * ( Ω 2 ) + C 1 * ( ω ) C 1 ( Ω 2 ) + C 1 * ( ω ) C 2 * ( Ω 2 ) e 2 i θ ,
F 4 = C 2 ( ω ) C 2 ( Ω 3 ) e 2 i θ + C 2 ( ω ) C 1 * ( Ω 3 ) + C 1 * ( ω ) C 2 ( Ω 3 ) + C 1 * ( ω ) C 1 * ( Ω 3 ) e 2 i θ ,
G 1 = V 1 ( ω ) V 2 ( Ω 2 ) e 2 i θ + V 1 ( ω ) V 1 * ( Ω 2 ) + V 2 * ( ω ) V 2 ( Ω 2 ) + V 2 * ( ω ) V 1 * ( Ω 2 ) e 2 i θ ,
H 1 = W 1 ( ω ) W 2 ( Ω 2 ) e 2 i θ + W 1 ( ω ) W 1 * ( Ω 2 ) + W 2 * ( ω ) W 2 ( Ω 2 ) + W 2 * ( ω ) W 1 * ( Ω 2 ) e 2 i θ ,
H 2 = W 2 ( ω ) W 1 ( Ω 2 ) e 2 i θ + W 2 ( ω ) W 2 * ( Ω 2 ) + W 1 * ( ω ) W 1 ( Ω 2 ) + W 1 * ( ω ) W 2 * ( Ω 2 ) e 2 i θ
B ^ 2 ( ω ) = 2 ( κ 2 i ω ) g 2 a 2 s ( κ 2 i ω ) 2 + Δ 2 2 Q ^ ( ω ) Δ 2 2 κ 2 ( κ 2 i ω ) 2 + Δ 2 2 A ^ in , 2 + ( κ 2 i ω ) 2 κ 2 ( κ 2 i ω ) 2 + Δ 2 2 B ^ in , 2 .
Q ^ ( ω ) = 1 D ( 2 κ 1 K 1 Ω 1 A ^ in , 1 + 2 κ 1 Δ 1 Ω 1 B ^ in , 1 2 κ 2 K 2 Ω 2 A ^ in , 2 2 κ 2 Δ 2 Ω 2 B ^ in , 2 + Γ m R 1 R 2 Q ^ in + ω m R 1 R 2 P ^ in )
B ^ 2 ( ω ) = a 11 A ^ in , 1 + b 11 B ^ in , 1 + a 22 A ^ in , 2 + b 22 B ^ in , 2 + q 11 Q ^ in + p 11 P ^ in
a 11 = 1 R 2 D × 2 K 1 K 2 G 2 Ω 1 2 κ 1 ,
b 11 = 1 R 2 D × 2 Δ 1 K 2 G 2 Ω 1 2 κ 1 ,
a 22 = 1 R 2 D × 2 κ 2 ( Δ 2 D 2 K 2 2 G 2 Ω 2 ) ,
b 22 = 1 R 2 D × 2 κ 2 K 2 ( D + 2 Δ 2 2 G 2 Ω 2 ) ,
q 11 = 1 R 2 D × 2 K 2 G 2 R 1 R 2 Γ m ,
p 11 = 1 R 2 D × 2 K 2 G 2 ω m R 1 R 2 .

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