Abstract

We investigate a hybrid quantum system combining cavity quantum electrodynamics and optomechanics, where a photon mode is coupled to a four-level tripod atom and to a mechanical mode via radiation pressure. We find that within the single-photon optomechanics and Lamb-Dicke limit, the presence of the tripod atom alters the optical properties of the cavity radiation field drastically, and gives rise to completely quantum destructive interference effects in the optical scattering. The heating rate can be dramatically suppressed via utilizing the completely destructive interference involving atom, photon and phonon, and the obtained result is analogous to that of the resolved sideband regime. The heating process is only connected to the scattering of cavity damping path, which is also far-off resonance. Meanwhile, the cooling rate assisted by the atomic transitions can be significantly enhanced, where the cooling process occurs through the cavity and atomic dissipation paths. Finally, the ground-state cooling of the movable mirror is achievable and even more robust to heating process and thermal noise.

© 2014 Optical Society of America

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References

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  31. M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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2014 (2)

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

2013 (5)

Z. Yi, G. X. Li, and Y. P. Yang, “Cavity-mediated cooling of a trapped -type three-level atom using a standing-wave laser field,” Phys. Rev. A 87, 053408 (2013).
[Crossref]

W. J. Gu and G. X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87, 025804 (2013).
[Crossref]

M. A. Lemonde, N. Didier, and A. A. Clerk, “Nonlinear interaction effects in a strongly driven optomechanical cavity,” Phys. Rev. Lett. 111, 053602 (2013).
[Crossref] [PubMed]

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111, 053603 (2013).
[Crossref] [PubMed]

Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. H. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111, 083601 (2013).
[Crossref] [PubMed]

2012 (9)

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

L. H. Sun, G. X. Li, and Z. Ficek, “First-order coherence versus entanglement in a nanomechanical cavity,” Phys. Rev. A 85, 022327 (2012).
[Crossref]

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
[Crossref]

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

M. Ludwig, A. H. Safavi-Naeini, O. Painter, and F. Marquardt, “Enhanced quantum nonlinearities in a two-mode optomechanical system,” Phys. Rev. Lett. 109, 063601 (2012).
[Crossref] [PubMed]

J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
[Crossref]

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

2011 (6)

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
[Crossref]

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

A. Schliesser and T. J. Kippenberg, “Hybrid atom-optomechanics,” Physics 4, 97 (2011).
[Crossref]

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

J. 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]

Y. Li, L.-A. Wu, and Z. D. Wang, “Fast ground-state cooling of mechanical resonators with time-dependent optical cavities,” Phys. Rev. A 83, 043804 (2011).
[Crossref]

2010 (5)

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

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101(R) (2010).
[Crossref]

T. Kumar, A. B. Bhattacherjee, and ManMohan, “Dynamics of a movable micromirror in a nonlinear optical cavity,” Phys. Rev. A 81, 013835 (2010).
[Crossref]

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758(2010).
[Crossref] [PubMed]

J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
[Crossref]

2009 (3)

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803(R) (2009).
[Crossref]

S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79, 013821 (2009).
[Crossref]

J. Zhang, Y.-X. Liu, and F. Nori, “Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control,” Phys. Rev. A 79, 052102 (2009).
[Crossref]

2008 (2)

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

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

2007 (2)

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

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

2006 (1)

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref] [PubMed]

2002 (1)

S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A 65, 063804 (2002).
[Crossref]

2001 (1)

Y. Wu and X. X. Yang, “Algebraic method for solving a class of coupled-channel cavity QED models,” Phys. Rev. A 63, 043816 (2001).
[Crossref]

1992 (1)

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Agarwal, G. S.

S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79, 013821 (2009).
[Crossref]

Allman, M. S.

J. 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]

Arcizet, O.

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

Baker, C.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

Bariani, F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” arXiv:1407.1073.

Bennett, S. D.

K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
[Crossref] [PubMed]

Bhattacherjee, A. B.

T. Kumar, A. B. Bhattacherjee, and ManMohan, “Dynamics of a movable micromirror in a nonlinear optical cavity,” Phys. Rev. A 81, 013835 (2010).
[Crossref]

Bienert, M.

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
[Crossref]

Blatt, R.

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Bochmann, J.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758(2010).
[Crossref] [PubMed]

Børkje, K.

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111, 053603 (2013).
[Crossref] [PubMed]

A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
[Crossref]

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

Bouwmeester, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006).
[Crossref] [PubMed]

Breyer, D.

D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
[Crossref]

Buchmann, L. F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” arXiv:1407.1073.

Chan, J.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, T. P. Mayer Alegre, A. Krause, and O. Painter, “Observation of quantum motion of a nanomechanical resonator,” Phys. Rev. Lett. 108, 033602 (2012).
[Crossref] [PubMed]

Chang, D. E.

K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
[Crossref] [PubMed]

Chen, J. P.

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

Chen, P. X.

S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
[Crossref]

Chen, Y. L.

Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. H. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111, 083601 (2013).
[Crossref] [PubMed]

Cicak, K.

J. 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]

Cirac, J. I.

J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, “Laser cooling of trapped ions in a standing wave,” Phys. Rev. A 46, 2668–2681 (1992).
[Crossref] [PubMed]

Ciuti, C.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
[Crossref] [PubMed]

Clerk, A. A.

M. A. Lemonde, N. Didier, and A. A. Clerk, “Nonlinear interaction effects in a strongly driven optomechanical cavity,” Phys. Rev. Lett. 111, 053602 (2013).
[Crossref] [PubMed]

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

Dantan, A.

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
[Crossref]

De Chiara, G.

B. Rogers, N. Lo Gullo, G. De Chiara, G. M. Palma, and M. Paternostro, “Hybrid optomechanics for quantum technologies,” arXiv:1402.1195.

Deléglise, S.

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

Didier, N.

M. A. Lemonde, N. Didier, and A. A. Clerk, “Nonlinear interaction effects in a strongly driven optomechanical cavity,” Phys. Rev. Lett. 111, 053602 (2013).
[Crossref] [PubMed]

Ding, L.

L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
[Crossref]

Donner, T.

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Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101(R) (2010).
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Taniyama, H.

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101(R) (2010).
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J. 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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K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111, 053603 (2013).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
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F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” arXiv:1407.1073.

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M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758(2010).
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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, 1520–1523 (2010).
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J. 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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K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
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S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
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S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
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Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. H. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111, 083601 (2013).
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J. Zhang, Y.-X. Liu, and F. Nori, “Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control,” Phys. Rev. A 79, 052102 (2009).
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S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
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J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
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K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
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I. Wilso-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
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L. Ding, C. Baker, P. Senellart, A. Lemaitre, S. Ducci, G. Leo, and I. Favero, “Wavelength-sized GaAs optomechanical resonators with gigahertz frequency,” Appl. Phys. Lett. 98, 113108 (2011).
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C. A. Regal, J. D. Teufel, and K. W. Lehnert, “Measuring nanomechanical motion with a microwave cavity interferometer,” Nat. Phys. 4, 555–560 (2008).
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J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. E. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature 452, 72–75 (2008).
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J. 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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M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature 465, 755–758(2010).
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M. Bienert and G. Morigi, “Cavity cooling of a trapped atom using electromagnetically induced transparency,” New J. Phys. 14, 023002 (2012).
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Phys. Rev. A (17)

Z. Yi, G. X. Li, and Y. P. Yang, “Cavity-mediated cooling of a trapped -type three-level atom using a standing-wave laser field,” Phys. Rev. A 87, 053408 (2013).
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J. Hofer, A. Schliesser, and T. J. Kippenberg, “Cavity optomechanics with ultrahigh-Q crystalline microresonators,” Phys. Rev. A 82, 031804 (2010).
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Y. Wu and X. X. Yang, “Algebraic method for solving a class of coupled-channel cavity QED models,” Phys. Rev. A 63, 043816 (2001).
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S. Zhang, Q. H. Duan, C. Guo, C. W. Wu, W. Wu, and P. X. Chen, “Cavity-assisted cooling of a trapped atom using cavity-induced transparency,” Phys. Rev. A 89, 013402 (2014).
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J. P. Zhu and G. X. Li, “Ground-state cooling of a nanomechanical resonator with a triple quantum dot via quantum interference,” Phys. Rev. A 86, 053828 (2012).
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S. Huang and G. S. Agarwal, “Enhancement of cavity cooling of a micromechanical mirror using parametric interactions,” Phys. Rev. A 79, 013821 (2009).
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T. Kumar, A. B. Bhattacherjee, and ManMohan, “Dynamics of a movable micromirror in a nonlinear optical cavity,” Phys. Rev. A 81, 013835 (2010).
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S. Rebić, A. S. Parkins, and S. M. Tan, “Photon statistics of a single-atom intracavity system involving electromagnetically induced transparency,” Phys. Rev. A 65, 063804 (2002).
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A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Cooling in the single-photon strong-coupling regime of cavity optomechanics,” Phys. Rev. A 85, 051803(R) (2012).
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L. H. Sun, G. X. Li, and Z. Ficek, “First-order coherence versus entanglement in a nanomechanical cavity,” Phys. Rev. A 85, 022327 (2012).
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W. J. Gu and G. X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87, 025804 (2013).
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J. Zhang, Y.-X. Liu, and F. Nori, “Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control,” Phys. Rev. A 79, 052102 (2009).
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Y. Li, L.-A. Wu, and Z. D. Wang, “Fast ground-state cooling of mechanical resonators with time-dependent optical cavities,” Phys. Rev. A 83, 043804 (2011).
[Crossref]

C. Genes, H. Ritsch, and D. Vitali, “Micromechanical oscillator ground-state cooling via resonant intracavity optical gain or absorption,” Phys. Rev. A 80, 061803(R) (2009).
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C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84, 051801(R) (2011).
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D. Breyer and M. Bienert, “Light scattering in an optomechanical cavity coupled to a single atom,” Phys. Rev. A 86, 053819 (2012).
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Phys. Rev. B (1)

Y.-G. Roh, T. Tanabe, A. Shinya, H. Taniyama, E. Kuramochi, S. Matsuo, T. Sato, and M. Notomi, “Strong optomechanical interaction in a bilayer photonic crystal,” Phys. Rev. B 81, 121101(R) (2010).
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J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112, 013601 (2014).
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A. Nunnenkamp, K. Børkje, and S. M. Girvin, “Single-photon optomechanics,” Phys. Rev. Lett. 107, 063602 (2011).
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K.-K. Ni, R. Norte, D. J. Wilson, J. D. Hood, D. E. Chang, O. Painter, and H. J. Kimble, “Enhancement of mechanical Q factors by optical trapping,” Phys. Rev. Lett. 108, 214302 (2012).
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F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99, 093902 (2007).
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I. Wilso-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99, 093901 (2007).
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K. Stannigel, P. Komar, S. J. M. Habraken, S. D. Bennett, M. D. Lukin, P. Zoller, and P. Rabl, “Optomechanical quantum information processing with photons and phonons,” Phys. Rev. Lett. 109, 013603 (2012).
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K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111, 053603 (2013).
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Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. H. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111, 083601 (2013).
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Physics (1)

A. Schliesser and T. J. Kippenberg, “Hybrid atom-optomechanics,” Physics 4, 97 (2011).
[Crossref]

Science (1)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” arXiv:1407.1073.

B. Rogers, N. Lo Gullo, G. De Chiara, G. M. Palma, and M. Paternostro, “Hybrid optomechanics for quantum technologies,” arXiv:1402.1195.

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[Crossref]

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Figures (3)

Fig. 1
Fig. 1

Sketch of the hybrid atom-optomechanical setup, consisting of a cavity coupled to a mechanical oscillator by radiation pressure with an atom in tripod configuration placed inside the cavity.

Fig. 2
Fig. 2

Sketch of the suppression of heating processes. The phonon number states are |n〉 in (a) and |n + 1〉 in (b). Through the completely quantum destructive interference between excitation paths |g3, n〉 → |1, n〉 → |e, n〉 and |g1, n〉 → |e, n〉 shown in (a) by the green lines, the carrier transition into |e, n〉 is prohibited. By use of the completely quantum destructive interferences between excitation paths |g2, n + 1〉 → |e, n + 1〉 and |g3, n〉 → |1, n〉 → |e, n + 1〉 shown in (b) by the solid blue lines, and between excitation paths |g2, n + 1〉 → |e, n + 1〉 and |g3, n〉 → |1, n + 1〉 → |e, n + 1〉 shown in (b) by the dashed blue lines, the phonon-increased transitions are significantly suppressed.

Fig. 3
Fig. 3

Steady-state phonon number 〈st and cooling rate W/η2 as functions of detunings δ1 and δ2 with parameters in units of ν: Ω1 = Ω2 = 6ν, κ = 0.1ν, Δ = −2ν, γ = 10ν, Ωp = ν, g = 6ν, δc3 = δ1 − Δ.

Equations (54)

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H ^ = H ^ osc + H ^ at + H ^ cav + H ^ cav-at + H ^ L-at + H ^ L-cav + F ^ x ^ ,
H ^ osc = ν b ^ b ^
H ^ at = δ c 3 | e e | + j ( δ j δ c 3 ) | g j g j | + Δ | g 3 g 3 | , H ^ cav = Δ a ^ a ^ , H ^ cav-at = g ( | e g 3 | a ^ + | g 3 e | a ^ ) , H ^ L-at = j Ω j 2 ( | e g j | + | g j e | ) , H ^ L-cav = Ω p 2 ( a ^ + a ^ )
x ^ = ξ ( b ^ + b ^ ) , p ^ = 1 2 i ξ ( b ^ b ^ ) ,
F ^ x ^ = χ a ^ a ^ ( b ^ + b ^ ) ,
d d t ρ ^ = i [ H ^ , ρ ^ ] + ^ ρ ^ + 𝒦 ^ ρ ^ + ^ m ρ ^ ,
^ ρ ^ = i γ i 2 ( 2 | g i e | ρ ^ | e g i | | e e | ρ ^ ρ ^ | e e | ) , 𝒦 ^ ρ ^ = κ 2 ( 2 a ^ ρ ^ a ^ a ^ a ^ ρ ^ ρ ^ a ^ a ^ ) ,
^ m ρ ^ = γ m 2 ( n ¯ th + 1 ) ( 2 b ^ ρ ^ b ^ b ^ b ^ ρ ^ ρ ^ b ^ b ^ ) + γ m 2 n ¯ th ( 2 b ^ ρ ^ b ^ b ^ b ^ ρ ^ ρ ^ b ^ b ^ ) ,
H ^ osc + F ^ x ^ = ν b ^ b ^ η χ ( a ^ a ^ ) 2 ,
H ^ cav-at = g [ | e g 3 | a ^ e η ( b ^ b ^ ) + | g 3 e | a ^ e η ( b ^ b ^ ) ] , H ^ L-cav = Ω p 2 [ a ^ e η ( b ^ b ^ ) + a ^ e η ( b ^ b ^ ) ] .
𝒦 ^ ρ ^ = κ 2 [ 2 a ^ e η ( b ^ b ^ ) ρ ^ a ^ e η ( b ^ b ^ ) a ^ a ^ ρ ^ ρ ^ a ^ a ^ ] .
{ | e , 0 , g 1 , 0 | , | g 2 , 0 , g 3 , 0 | , | g 3 , 1 } .
H ^ osc + F ^ x ^ = ν b ^ b ^ η χ | 1 1 | , H ^ cav-at = g [ | e 1 | e η ( b ^ b ^ ) + | 1 e | e η ( b ^ b ^ ) ] , H ^ L-cav = Ω p 2 [ | g 3 1 | e η ( b ^ b ^ ) + | 1 g 3 | e η ( b ^ b ^ ) ] ,
𝒦 ^ ρ ^ = κ 2 [ 2 | g 3 1 | e η ( b ^ b ^ ) ρ ^ | 1 g 3 | e η ( b ^ b ^ ) | 1 1 | ρ ^ ρ ^ | 1 1 | ] .
e η ( b ^ b ^ ) = 1 + η ( b ^ b ^ ) + O ( η 2 ) .
H ^ free a-c = δ c 3 | e e | + j ( δ j δ c 3 ) | g j g j | + Δ | g 3 g 3 | + j Ω j 2 ( | e g j | + | g j e | ) + g ( | e 1 | + | 1 e | ) + Ω p 2 ( | g 3 1 | + | 1 g 3 | ) ,
V ^ 1 = i η [ g | e 1 | + Ω p 2 | g 3 1 | ] + H . c . .
d d t ρ ^ = ( 𝒮 ^ 0 + 𝒮 ^ 1 + 𝒮 ^ 2 ) ρ ^ .
𝒮 ^ 0 ρ ^ = i [ H ^ free a-c , ρ ^ ] + ^ ρ ^ + 𝒦 ^ 0 ρ ^ ,
𝒦 ^ 0 ρ ^ = κ 2 ( 2 | g 3 1 | ρ ^ | 1 g 3 | | 1 1 | ρ ^ ρ ^ | 1 1 | ) .
𝒮 ^ 2 ρ ^ = i [ H ^ osc , ρ ^ ] + ^ m ρ ^ .
𝒮 ^ 1 ρ ^ = i [ H ^ 1 , ρ ^ ] + 𝒦 ^ 2 ρ ^ ,
𝒦 ^ 2 ρ ^ = κ | g 3 1 | [ η ( b ^ b ^ ) ρ ^ + η 2 2 ( b ^ ρ ^ b ^ + b ^ ρ ^ b ^ b ^ b ^ ρ ^ b ^ b ^ ρ ^ ) + H . c . ] | 1 g 3 | .
d d t μ ^ = Tr a-c { [ 𝒫 ^ 𝒮 ^ 2 𝒫 ^ + 𝒫 ^ 𝒮 ^ 1 ( 𝒮 ^ 0 ) 1 𝒮 ^ 1 𝒫 ^ ] ρ ^ } ,
d d t μ ^ = S ( ν ) ( b ^ μ ^ b ^ b ^ b ^ μ ^ ) + S ( ν ) ( b ^ μ ^ b ^ b ^ b ^ μ ^ ) + H . c . + ^ m μ ^ ,
S ( ν ) = 0 d t e i ν t V ^ 1 ( t ) V ^ 1 ( 0 ) st .
n ^ ˙ = ( A A + + γ m ) n ^ + A + + γ m n ¯ th ,
A ± = 2 Re { S ( ν ) }
n ^ st = A + + γ m n ¯ th A A + + γ m , W = A A + + γ m .
ρ ˙ e e = γ ρ e e + i ( Ω 1 2 ρ e g 1 + Ω 2 2 ρ e g 2 + g ρ e 1 ) + c . c . , ρ ˙ g j g j = γ j ρ e e i Ω j 2 ( ρ e g j ρ g j e ) , ρ ˙ 11 = κ ρ 11 + i ( Ω p 2 ρ 1 g 3 g ρ e 1 ) + c . c . , ρ ˙ e g 1 = ( i δ 1 γ 2 ) ρ e g 1 + i Ω 1 2 ( ρ e e ρ g 1 g 1 ) i Ω 2 2 ρ g 2 g 1 i g ρ 1 g 1 , ρ ˙ e g 2 = ( i δ 2 γ 2 ) ρ e g 2 + i Ω 2 2 ( ρ e e ρ g 2 g 2 ) i Ω 1 2 ρ g 1 g 2 i g ρ 1 g 2 , ρ ˙ e 1 = ( i δ c 3 γ + κ 2 ) ρ e 1 + i g ( ρ e e ρ 11 ) i j Ω j 2 ρ g j 1 + i Ω p 2 ρ e g 3 , ρ ˙ g 1 g 2 = i ( δ 2 δ 1 ) ρ g 1 g 2 i Ω 1 2 ρ e g 2 + i Ω 2 2 ρ g 1 e , ρ ˙ g 1 1 = [ i ( δ c 3 δ 1 ) κ 2 ] ρ g 1 1 i Ω 1 2 ρ e 1 + i g ρ g 1 e + i Ω p 2 ρ g 1 g 3 , ρ ˙ g 2 1 = [ i ( δ c 3 δ 2 ) κ 2 ] ρ g 2 1 i Ω 2 2 ρ e 1 + i g ρ g 2 e + i Ω p 2 ρ g 2 g 3 , ρ ˙ e g 3 = [ i ( δ c 3 + Δ ) γ 2 ] ρ e g 3 i j Ω j 2 ρ g j g 3 i g ρ 1 g 3 + i Ω p 2 ρ e 1 , ρ ˙ g 1 g 3 = i ( δ c 3 + Δ δ 1 ) ρ g 1 g 3 i Ω 1 2 ρ e g 3 + i Ω p 2 ρ g 1 1 , ρ ˙ g 2 g 3 = i ( δ c 3 + Δ δ 2 ) ρ g 2 g 3 i Ω 2 2 ρ e g 3 + i Ω p 2 ρ g 2 1 , ρ ˙ 1 g 3 = ( i Δ κ 2 ) ρ 1 g 3 i g ρ e g 3 i Ω p 2 ( ρ g 3 g 3 ρ 11 ) .
A ± / η 2 = γ | 𝒯 2 ± | 2 + κ | g 𝒯 2 ± + g 𝒯 1 + Ω p / 2 Δ ν + i κ / 2 | 2 ,
𝒯 1 = g Ω p / 2 f ( Δ ) ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) , 𝒯 2 ± = ± ν g Ω p / 2 f ( Δ ) f ( Δ ν ) γ ( Δ ) ( δ c 3 + Δ ν δ 1 ) ( δ c 3 + Δ ν δ 2 ) ,
f ( Δ ) = ( Δ + i κ / 2 ) γ ( Δ ) g 2 ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) , γ ( Δ ) = ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ + i γ / 2 ) ( Ω 1 / 2 ) 2 ( δ c 3 + Δ δ 2 ) ( Ω 2 / 2 ) 2 ( δ c 3 + Δ δ 1 ) .
δ c 3 + Δ δ 1 = 0 or δ c 3 + Δ δ 2 = 0 .
δ c 3 + Δ ν δ 2 = 0 ,
A + / η 2 = κ ( Ω p / 2 ) 2 ( Δ ν ) 2 + ( κ / 2 ) 2 ,
𝒯 2 = ν g ε ( Δ + ν + i κ 2 ) ( i γ 2 + δ 1 + ν Ω 1 2 4 ν Ω 2 2 8 ν ) g 2 .
δ 1 = Ω 1 2 4 ν + Ω 2 2 8 ν + g 2 + κ γ / 4 Δ + ν ν ,
𝒯 2 = i ν g ε κ 2 g 2 + κ γ / 4 Δ + ν + γ 2 ( Δ + ν ) ,
A / η 2 = κ ( Ω p / 2 ) 2 + g 2 | 𝒯 2 | 2 ( Δ + ν ) 2 + ( κ / 2 ) 2 + γ | 𝒯 2 | 2 .
A / η 2 4 g 2 | ε | 2 / γ , A + / η 2 4 κ | ε | 2 / 9 ,
n ^ A + / A 4 9 C ,
A ± / η 2 = κ ( Ω p / 2 ) 2 ( Δ ν ) 2 + ( κ / 2 ) 2 ,
𝒯 1 = g Ω p / 2 D ( Δ ) , 𝒯 2 ± = ± ν g Ω p / 2 ( δ c 3 + Δ + i γ / 2 ) D ( Δ ) D ( Δ ν ) ,
D ( Δ ) = ( Δ + i κ / 2 ) ( δ c 3 + Δ + i γ / 2 ) g 2 .
A ± / η 2 = | Ω p / 2 ( δ c 3 + Δ + i γ / 2 ) D ( Δ ) D ( Δ ν ) | 2 [ γ ν 2 g 2 + κ | D ( Δ ) ν ( Δ + i κ / 2 ) | 2 ] ,
ρ ( i ) ( s ) = 0 e s t ρ ( i ) ( t ) d t , ( i = 0 , 1 , 2 ) .
ρ ˙ g 3 g 3 ( 0 ) = γ ρ e e ( 0 ) .
ρ ˙ e g 3 ( 1 ) = [ i ( δ c 3 + Δ ) γ 2 ] ρ e g 3 ( 1 ) i j Ω j 2 ρ g j g 3 ( 1 ) i g ρ 1 g 3 ( 1 ) , ρ ˙ g 1 g 3 ( 1 ) = i ( δ c 3 + Δ δ 1 ) ρ g 1 g 3 ( 1 ) i Ω 1 2 ρ e g 3 ( 1 ) , ρ ˙ g 2 g 3 ( 1 ) = i ( δ c 3 + Δ δ 2 ) ρ g 2 g 3 ( 1 ) i Ω 2 2 ρ e g 3 ( 1 ) , ρ ˙ 1 g 3 ( 1 ) = ( i Δ κ 2 ) ρ 1 g 3 ( 1 ) i g ρ e g 3 ( 1 ) i Ω p 2 ρ g 3 g 3 ( 0 ) ,
ρ ( 1 ) ( s ) = 1 s L ( 1 ) ρ ( 1 ) ( ) ,
ρ ˙ e e ( 2 ) = γ ρ e e ( 2 ) + i ( Ω 1 2 ρ e g 1 ( 2 ) + Ω 2 2 ρ e g 2 ( 2 ) + g ρ e 1 ( 2 ) ) + c . c . , ρ ˙ g j g j ( 2 ) = γ j ρ e e ( 2 ) i Ω j 2 ( ρ e g j ( 2 ) ρ g j e ( 2 ) ) , ρ ˙ 11 ( 2 ) = κ ρ 11 ( 2 ) + i ( Ω p 2 ρ 1 g 3 ( 1 ) g ρ e 1 ( 2 ) ) + c . c . , ρ ˙ e g 1 ( 2 ) = ( i δ 1 γ 2 ) ρ e g 1 ( 2 ) + i Ω 1 2 ( ρ e e ( 2 ) ρ g 1 g 1 ( 2 ) ) i Ω 2 2 ρ g 2 g 1 ( 2 ) i g ρ 1 g 1 ( 2 ) , ρ ˙ e g 2 ( 2 ) = ( i δ 2 γ 2 ) ρ e g 2 ( 2 ) + i Ω 2 2 ( ρ e e ( 2 ) ρ g 2 g 2 ( 2 ) ) i Ω 1 2 ρ g 1 g 2 ( 2 ) i g ρ 1 g 2 ( 2 ) , ρ ˙ e 1 ( 2 ) = ( i δ c 3 γ + κ 2 ) ρ e 1 ( 2 ) + i g ( ρ e e ( 2 ) ρ 11 ( 2 ) ) i j Ω j 2 ρ g j 1 ( 2 ) + i Ω p 2 ρ e g 3 ( 1 ) , ρ ˙ g 1 g 2 ( 2 ) = i ( δ 2 δ 1 ) ρ g 1 g 2 ( 2 ) i Ω 1 2 ρ e g 2 ( 2 ) + i Ω 2 2 ρ g 1 e ( 2 ) , ρ ˙ g 1 1 ( 2 ) = [ i ( δ c 3 δ 1 ) κ 2 ] ρ g 1 1 ( 2 ) i Ω 1 2 ρ e 1 ( 2 ) + i g ρ g 1 e ( 2 ) + i Ω p 2 ρ g 1 g 3 ( 1 ) , ρ ˙ g 2 1 ( 2 ) = [ i ( δ c 3 δ 2 ) κ 2 ] ρ g 2 1 ( 2 ) i Ω 2 2 ρ e 1 ( 2 ) + i g ρ g 2 e ( 2 ) + i Ω p 2 ρ g 2 g 3 ( 1 ) ,
ρ e e ( 2 ) ( ) = ( Ω p / 2 ) 2 | f ( Δ ) | 2 g 2 ( δ c 3 + Δ δ 1 ) 2 ( δ c 3 + Δ δ 2 ) 2 ,
f ( Δ ) = ( i κ 2 + Δ ) [ ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) ( δ c 3 + Δ + i γ 2 ) ( δ c 3 + Δ δ 2 ) Ω 1 2 / 4 ( δ c 3 + Δ δ 1 ) Ω 2 2 / 4 ] g 2 ( δ c 3 + Δ δ 1 ) ( δ c 3 + Δ δ 2 ) .
ρ ( 2 ) ( s ) = 1 s L ( 2 ) [ ρ ( 2 ) ( ) + 1 s L ( 1 ) ρ ( 1 ) ( ) ] ,

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