Abstract

We design a hybrid optomechanical setup, in which an ensemble of quantum emitters is coupled with a movable mirror through vacuum interaction. The optical cavity is driven along with the quantum emitters and therefore the coupling between the cavity field and the ensemble determines the dynamics of the coupled system. In particular, we investigated the influence of the vacuum coupling strength on the effective frequency and the effective damping rate of the movable mirror, which shows that the vacuum interaction enhances greatly the effective damping rate. Further, the cooling characteristics of the mechanical resonator is analyzed in detail by counting the effective phonon number in the mirror’s motion. It is found that the ground-state cooling of the mechanical motion can be approached in the bad cavity limit when the vacuum coupling is included. The dependence of the cooling of the mechanical motion on the parameters of the cavity and the quantum emitter is investigated in detail numerically.

© 2015 Optical Society of America

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References

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  1. T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
    [Crossref] [PubMed]
  2. T. J. Kippenberg and K. J. Vahala, “Cavity opto-mechanics,” Opt. Express 15(25), 17172–17205 (2007).
    [Crossref] [PubMed]
  3. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86(4), 1391–1452 (2014).
    [Crossref]
  4. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
    [Crossref] [PubMed]
  5. C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
    [Crossref]
  6. M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
    [Crossref] [PubMed]
  7. M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
    [Crossref]
  8. Y.-D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110(25), 253601 (2013).
    [Crossref] [PubMed]
  9. W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
    [Crossref]
  10. W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
    [Crossref]
  11. W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
    [Crossref]
  12. K. Jähne, 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]
  13. 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]
  14. X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
    [Crossref] [PubMed]
  15. T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
    [Crossref]
  16. D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
    [Crossref] [PubMed]
  17. Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
    [Crossref]
  18. J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
    [Crossref] [PubMed]
  19. E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
    [Crossref] [PubMed]
  20. Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
    [Crossref]
  21. M. Abdi and M. J. Hartmann, “Entangling the motion of two optically trapped objects via time-modulated driving fields,” New J. Phys. 17(1), 013056 (2015).
    [Crossref]
  22. O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
    [Crossref]
  23. H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
    [Crossref]
  24. S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
    [Crossref] [PubMed]
  25. J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
    [Crossref]
  26. K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
    [Crossref]
  27. G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
    [Crossref] [PubMed]
  28. K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
    [Crossref]
  29. S. Rips and M. J. Hartmann, “Quantum information processing with nanomechanical qubits,” Phys. Rev. Lett. 110(12), 120503 (2013).
    [Crossref] [PubMed]
  30. I. Wilson-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(9), 093901 (2007).
    [Crossref] [PubMed]
  31. 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(9), 093902 (2007).
    [Crossref] [PubMed]
  32. D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
    [Crossref] [PubMed]
  33. 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]
  34. S. Gigan, H. R. Bohm, M. Paternostro, F. Blaser, G. Langer, J. B. Hertzberg, K. C. Schwab, D. Bauerle, M. Aspelmeyer, and A. Zeilinger, “Self-cooling of a micromirror by radiation pressure,” Nature 444(7115), 67–70 (2006).
    [Crossref] [PubMed]
  35. Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
    [Crossref] [PubMed]
  36. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
    [Crossref]
  37. W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
    [Crossref]
  38. J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
    [Crossref] [PubMed]
  39. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
    [Crossref] [PubMed]
  40. K. Xia and J. Evers, “Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103(22), 227203 (2009).
    [Crossref]
  41. C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
    [Crossref]
  42. S. Zhang, J.-Q. Zhang, J. Zhang, C.-W. Wu, W. Wu, and P.-X. Chen, “Ground state cooling of an optomechanical resonator assisted by a Λ-type atom,” Opt. Express 22(23), 28118–28131 (2014).
    [Crossref] [PubMed]
  43. Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
    [Crossref]
  44. F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
    [Crossref]
  45. T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
    [Crossref]
  46. D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
    [Crossref] [PubMed]
  47. C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
    [Crossref] [PubMed]
  48. M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
    [Crossref] [PubMed]
  49. C. K. Law, “Interaction between a moving mirror and radiation pressure: a hamiltonian formulation,” Phys. Rev. A 51(3), 2537–2541 (1995).
    [Crossref] [PubMed]
  50. S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
    [Crossref]
  51. S. Y. Buhmann and D.-G. Welsch, “Dispersion forces in macroscopic quantum electrodynamics,” Prog. Quant. Electron. 31(2), 51–130 (2007).
    [Crossref]
  52. C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
    [Crossref] [PubMed]
  53. A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
    [Crossref]
  54. T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
    [Crossref]
  55. H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
    [Crossref]
  56. S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
    [Crossref] [PubMed]
  57. 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]
  58. G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
    [Crossref]
  59. E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35(12), 5288–5290 (1987).
    [Crossref] [PubMed]
  60. A. Lambrecht and S. Reynaud, “Casimir force between metallic mirrors,” Eur. Phys. J. D 8(3), 309–318 (2000).
    [Crossref]
  61. T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
    [Crossref] [PubMed]
  62. X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
    [Crossref]
  63. W.-J. Gu and G.-X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87(2), 025804 (2013).
    [Crossref]

2015 (4)

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

M. Abdi and M. J. Hartmann, “Entangling the motion of two optically trapped objects via time-modulated driving fields,” New J. Phys. 17(1), 013056 (2015).
[Crossref]

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

2014 (14)

S. Zhang, J.-Q. Zhang, J. Zhang, C.-W. Wu, W. Wu, and P.-X. Chen, “Ground state cooling of an optomechanical resonator assisted by a Λ-type atom,” Opt. Express 22(23), 28118–28131 (2014).
[Crossref] [PubMed]

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
[Crossref]

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
[Crossref]

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

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

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

2013 (9)

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
[Crossref]

Y.-D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110(25), 253601 (2013).
[Crossref] [PubMed]

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]

Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
[Crossref]

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

S. Rips and M. J. Hartmann, “Quantum information processing with nanomechanical qubits,” Phys. Rev. Lett. 110(12), 120503 (2013).
[Crossref] [PubMed]

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[Crossref] [PubMed]

W.-J. Gu and G.-X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87(2), 025804 (2013).
[Crossref]

2012 (3)

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

2011 (5)

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
[Crossref]

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

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

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
[Crossref]

2010 (5)

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
[Crossref]

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[Crossref]

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

2009 (3)

K. Jähne, 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]

K. Xia and J. Evers, “Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103(22), 227203 (2009).
[Crossref]

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

2008 (5)

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

2007 (7)

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “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]

I. Wilson-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(9), 093901 (2007).
[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(9), 093902 (2007).
[Crossref] [PubMed]

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

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

S. Y. Buhmann and D.-G. Welsch, “Dispersion forces in macroscopic quantum electrodynamics,” Prog. Quant. Electron. 31(2), 51–130 (2007).
[Crossref]

2006 (2)

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
[Crossref] [PubMed]

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

2004 (1)

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

2003 (1)

C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
[Crossref] [PubMed]

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]

2000 (1)

A. Lambrecht and S. Reynaud, “Casimir force between metallic mirrors,” Eur. Phys. J. D 8(3), 309–318 (2000).
[Crossref]

1995 (1)

C. K. Law, “Interaction between a moving mirror and radiation pressure: a hamiltonian formulation,” Phys. Rev. A 51(3), 2537–2541 (1995).
[Crossref] [PubMed]

1987 (1)

E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35(12), 5288–5290 (1987).
[Crossref] [PubMed]

Abdi, M.

M. Abdi and M. J. Hartmann, “Entangling the motion of two optically trapped objects via time-modulated driving fields,” New J. Phys. 17(1), 013056 (2015).
[Crossref]

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

Agarwal, G. S.

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
[Crossref]

Al-Amri, M.

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

Alegre, T. P. M.

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

Alhambra, A. M.

A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
[Crossref]

Allman, M. S.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Antezza, M.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Aspelmeyer, M.

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

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

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

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

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

Bachtold, A.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

Bariani, F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

Barzanjeh, S.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

Bauerle, D.

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

Bhattacharya, M.

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[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]

Blaser, F.

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

Bohm, H. R.

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

Böhm, H. R.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Børkje, K.

T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
[Crossref]

Bouwmeester, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
[Crossref] [PubMed]

Braggio, C.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Bruder, C.

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

Buchmann, L. F.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

Buhmann, S. Y.

S. Y. Buhmann and D.-G. Welsch, “Dispersion forces in macroscopic quantum electrodynamics,” Prog. Quant. Electron. 31(2), 51–130 (2007).
[Crossref]

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

Carugno, G.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Chan, J.

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

Chang, D. E.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[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(9), 093902 (2007).
[Crossref] [PubMed]

Chen, P.-X.

Chen, W.

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[Crossref]

Chen, X.

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

Chen, Y.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Cicak, K.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Cirac, J. I.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Ciuti, C.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

Clerk, A. A.

Y.-D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110(25), 253601 (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(9), 093902 (2007).
[Crossref] [PubMed]

Corbitt, T.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

D. Donner, T.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[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(5), 051801 (2011).
[Crossref]

DeJesus, E. X.

E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35(12), 5288–5290 (1987).
[Crossref] [PubMed]

Deleglise, S.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

Drewsen, M.

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
[Crossref]

Dung, H. T.

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

Evers, J.

K. Xia and J. Evers, “Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103(22), 227203 (2009).
[Crossref]

Favero, I.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

Ferreira, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Ge, W.

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

Genes, C.

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
[Crossref]

K. Jähne, 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]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

Geraci, A. A.

Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
[Crossref]

Gigan, S.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

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

Giovannetti, V.

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]

Girvin, S. M.

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(9), 093902 (2007).
[Crossref] [PubMed]

Grebogi, C.

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

Groblacher, S.

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

Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

Gu, W.-J.

W.-J. Gu and G.-X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87(2), 025804 (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]

Guerreiro, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Guo, Y. J.

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

Hammerer, K.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

K. Jähne, 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]

Harlow, J. W.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Hartmann, M. J.

M. Abdi and M. J. Hartmann, “Entangling the motion of two optically trapped objects via time-modulated driving fields,” New J. Phys. 17(1), 013056 (2015).
[Crossref]

S. Rips and M. J. Hartmann, “Quantum information processing with nanomechanical qubits,” Phys. Rev. Lett. 110(12), 120503 (2013).
[Crossref] [PubMed]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

Hertzberg, J. B.

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

Hill, J. T.

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

Huang, L.

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

Huang, S.

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
[Crossref]

Innerhofer, E.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Jähne, K.

K. Jähne, 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]

Jing, H.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

Johansson, J. R.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

Juan, M. L.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Kaufman, C.

E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35(12), 5288–5290 (1987).
[Crossref] [PubMed]

Kempf, A.

A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
[Crossref]

Kheifets, S.

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
[Crossref]

Kiesel, N.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Kimble, H. J.

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Kippenberg, T. J.

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

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

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

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99(9), 093901 (2007).
[Crossref] [PubMed]

Kleckner, D.

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
[Crossref] [PubMed]

Knöll, L.

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

Koppens, F. H. L.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

Krause, A.

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

Kuzyk, M. C.

M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
[Crossref]

L’u, X. Y

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

Lai, Y.-C.

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

Lambrecht, A.

A. Lambrecht and S. Reynaud, “Casimir force between metallic mirrors,” Eur. Phys. J. D 8(3), 309–318 (2000).
[Crossref]

Lan, Y.

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

Lan, Y. H.

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

Langer, G.

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

Law, C. K.

C. K. Law, “Interaction between a moving mirror and radiation pressure: a hamiltonian formulation,” Phys. Rev. A 51(3), 2537–2541 (1995).
[Crossref] [PubMed]

Lehnert, K. W.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Lewenstein, M.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

Li,

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Li, G.-X.

W.-J. Gu and G.-X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87(2), 025804 (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]

Li, J.

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Li, K.

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

Li, T.

Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
[Crossref]

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
[Crossref]

Li, Y.

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
[Crossref] [PubMed]

Liu, X. F.

C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
[Crossref] [PubMed]

Liu, Y.-C.

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[Crossref] [PubMed]

Lü, X.-Y.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

Luan, X.

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[Crossref] [PubMed]

Lukin, M. D.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

Ma, J.

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Mari, A.

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

Marquardt, F.

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

F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, “Quantum theory of cavity-assisted sideband cooling of mechanical motion,” Phys. Rev. Lett. 99(9), 093902 (2007).
[Crossref] [PubMed]

Martín-Martínez, E.

A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
[Crossref]

Mavalvala, N.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Meystre, P.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[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.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

Moulieras, S.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

Müller-Ebhardt, H.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Muschik, C. A.

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

Nha, H.

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

Nie, W.

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

Nie, W. J.

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

Nooshi, N.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99(9), 093901 (2007).
[Crossref] [PubMed]

Nori, F.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

Noto, A.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Ojanen, T.

T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
[Crossref]

Ottaway, D.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Painter, O.

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

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Pan, S.

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

Papp, S. B.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Passante, R.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Paternostro, M.

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

Peng, P.

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

Pflanzer, A. C.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Plenio, M. B.

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

Polzik, E. S.

K. Jähne, 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]

Quidant, R.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Rabl, P.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

Raizen, M. G.

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
[Crossref]

Regal, C. A.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Rehbein, H.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Restrepo, J.

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

Reynaud, S.

A. Lambrecht and S. Reynaud, “Casimir force between metallic mirrors,” Eur. Phys. J. D 8(3), 309–318 (2000).
[Crossref]

Rips, S.

S. Rips and M. J. Hartmann, “Quantum information processing with nanomechanical qubits,” Phys. Rev. Lett. 110(12), 120503 (2013).
[Crossref] [PubMed]

Ritsch, H.

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
[Crossref]

Rizzuto, L.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Romero-Isart, O.

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

Ruoso, G.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Safavi-Naeini, A. H.

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

Schliesser, A.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

Schwab, K. C.

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

Shao, X.

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

Si, L. G.

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

Si, L.-G.

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Sigg, D.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Simmonds, R. W.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Singh, S.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

Sinha, K.

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

Sirois, A. J.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Sørensen, A. S.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

Spagnolo, S.

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

Stannigel, K.

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

Sun, C. P.

C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
[Crossref] [PubMed]

Taylor, J. M.

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

Teufel, J. D.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Tian, T.

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

Tombesi, P.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

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

van Enk, S. J.

M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
[Crossref]

Vanner, M. R.

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

Vedral, V.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

Vengalattore, M.

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

Verhagen, E.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

Vitali, D.

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[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]

Wallquist, M.

K. Jähne, 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]

Wang, G.

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

Wang, H.

M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
[Crossref]

Wang, Y.-D.

Y.-D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110(25), 253601 (2013).
[Crossref] [PubMed]

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

Wang, Z. H.

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

Weis, S.

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

Welsch, D.-G.

S. Y. Buhmann and D.-G. Welsch, “Dispersion forces in macroscopic quantum electrodynamics,” Prog. Quant. Electron. 31(2), 51–130 (2007).
[Crossref]

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

Whitcomb, S.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Whittaker, J. D.

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

Wilson, D. J.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Wilson-Rae, I.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99(9), 093901 (2007).
[Crossref] [PubMed]

Wipf, C.

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

Wong, C. W.

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[Crossref] [PubMed]

Wu, C.-W.

Wu, W.

Wu, Y.

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Xia, K.

K. Xia and J. Evers, “Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103(22), 227203 (2009).
[Crossref]

Xiao, Y.-F.

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[Crossref] [PubMed]

Xiong, H.

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Xue, F.

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

Yang, H.

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

Yang, X.

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Yang, X. X.

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

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]

Ye, J.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Yin, Z.-q.

Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
[Crossref]

You, C.

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

Zeilinger, A.

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

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

Zhang, J.

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

S. Zhang, J.-Q. Zhang, J. Zhang, C.-W. Wu, W. Wu, and P.-X. Chen, “Ground state cooling of an optomechanical resonator assisted by a Λ-type atom,” Opt. Express 22(23), 28118–28131 (2014).
[Crossref] [PubMed]

Zhang, J.-Q.

Zhang, K.

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[Crossref]

Zhang, S.

Zhang, X.

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

Zheng, T.

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

Zheng, T. Y.

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

Zhi, Y.

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

Zhu, S.

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

Zhu, S. Y.

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

Zoller, P.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

K. Jähne, 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]

Zubairy, M. S.

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

Zwerger, W.

I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, “Theory of ground state cooling of a mechanical oscillator using dynamical backaction,” Phys. Rev. Lett. 99(9), 093901 (2007).
[Crossref] [PubMed]

Ann. Phys. (1)

H. Yang, T. Zheng, X. Zhang, X. Shao, and S. Pan, “Dynamical Casimir-Polder force on a partially dressed atom in a cavity comprising a dielectric,” Ann. Phys. 344, 69–77 (2014).
[Crossref]

Eur. Phys. J. D (1)

A. Lambrecht and S. Reynaud, “Casimir force between metallic mirrors,” Eur. Phys. J. D 8(3), 309–318 (2000).
[Crossref]

Int. J. Mod. Phys. B (1)

Z.-q. Yin, A. A. Geraci, and T. Li, “Optomechanics of levitated dielectric particles,” Int. J. Mod. Phys. B 27(26), 1330018 (2013).
[Crossref]

Nat. Commun. (1)

D. E. Chang, K. Sinha, J. M. Taylor, and H. J. Kimble, “Trapping atoms using nanoscale quantum vacuum forces,” Nat. Commun. 5, 4343 (2014).
[Crossref] [PubMed]

Nat. Physics (1)

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Physics 7(7), 527–530 (2011).
[Crossref]

Nature (6)

E. Verhagen, S. Deleglise, S. Weis, A. Schliesser, and T. J. Kippenberg, “Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode,” Nature 482(7383), 63–67 (2012).
[Crossref] [PubMed]

D. Kleckner and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444(7115), 75–78 (2006).
[Crossref] [PubMed]

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

J. D. Teufel, T. D. Donner, 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(7356), 359–363 (2011).
[Crossref] [PubMed]

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

S. Gröblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460(7256), 724–727 (2009).
[Crossref] [PubMed]

New J. Phys. (1)

M. Abdi and M. J. Hartmann, “Entangling the motion of two optically trapped objects via time-modulated driving fields,” New J. Phys. 17(1), 013056 (2015).
[Crossref]

Opt. Express (2)

Phys. Rev. A (24)

X. Chen, Y.-C. Liu, P. Peng, Y. Zhi, and Y.-F. Xiao, “Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems,” Phys. Rev. A 92(3), 033841 (2015).
[Crossref]

W.-J. Gu and G.-X. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87(2), 025804 (2013).
[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]

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
[Crossref]

E. X. DeJesus and C. Kaufman, “Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations,” Phys. Rev. A 35(12), 5288–5290 (1987).
[Crossref] [PubMed]

A. M. Alhambra, A. Kempf, and E. Martín-Martínez, “Casimir forces on atoms in optical cavities,” Phys. Rev. A 89(3), 033835 (2014).
[Crossref]

T. Tian, T. Y. Zheng, Z. H. Wang, and X. Zhang, “Dynamical Casimir-Polder force in a one-dimensional cavity with quasimodes,” Phys. Rev. A 82(1), 013810 (2010).
[Crossref]

C. K. Law, “Interaction between a moving mirror and radiation pressure: a hamiltonian formulation,” Phys. Rev. A 51(3), 2537–2541 (1995).
[Crossref] [PubMed]

S. Y. Buhmann, L. Knöll, D.-G. Welsch, and H. T. Dung, “Casimir-Polder forces: a nonperturbative approach,” Phys. Rev. A 70(5), 052117 (2004).
[Crossref]

C. Genes, H. Ritsch, M. Drewsen, and A. Dantan, “Atom-membrane cooling and entanglement using cavity electromagnetically induced transparency,” Phys. Rev. A 84(5), 051801 (2011).
[Crossref]

Y. J. Guo, K. Li, W. J. Nie, and Y. Li, “Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system,” Phys. Rev. A 90(5), 053841 (2014).
[Crossref]

F. Bariani, S. Singh, L. F. Buchmann, M. Vengalattore, and P. Meystre, “Hybrid optomechanical cooling by atomic Λ systems,” Phys. Rev. A 90(3), 033838 (2014).
[Crossref]

T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
[Crossref]

O. Romero-Isart, A. C. Pflanzer, M. L. Juan, R. Quidant, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, “Optically levitating dielectrics in the quantum regime: theory and protocols,” Phys. Rev. A 83(1), 013803 (2011).
[Crossref]

J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, “Formation and manipulation of optomechanical chaos via a bichromatic driving,” Phys. Rev. A 90(4), 043839 (2014).
[Crossref]

K. Zhang, W. Chen, M. Bhattacharya, and P. Meystre, “Hamiltonian chaos in a coupled BEC-optomechanical-cavity system,” Phys. Rev. A 81(1), 013802 (2010).
[Crossref]

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77(3), 033804 (2008).
[Crossref]

W. Nie, Y. Lan, Y. Li, and S. Zhu, “Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction,” Phys. Rev. A 88(6), 063849 (2013).
[Crossref]

W. Ge, M. Al-Amri, H. Nha, and M. S. Zubairy, “Entanglement of movable mirrors in a correlated-emission laser,” Phys. Rev. A 88(2), 022338 (2013).
[Crossref]

K. Jähne, 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]

C. Genes, A. Mari, P. Tombesi, and D. Vitali, “Robust entanglement of a micromechanical resonator with output optical fields,” Phys. Rev. A 78(3), 032316 (2008).
[Crossref]

M. C. Kuzyk, S. J. van Enk, and H. Wang, “Generating robust optical entanglement in weak-coupling optomechanical systems,” Phys. Rev. A 88(6), 062341 (2013).
[Crossref]

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Effect of the Casimir force on the entanglement between a levitated nanosphere and cavity modes,” Phys. Rev. A 86(6), 063809 (2012).
[Crossref]

Phys. Rev. B (1)

Y. Li, Y.-D. Wang, F. Xue, and C. Bruder, “Quantum theory of transmission line resonator-assisted cooling of a micromechanical resonator,” Phys. Rev. B 78(13), 134301 (2008).
[Crossref]

Phys. Rev. Lett. (18)

G. Wang, L. Huang, Y.-C. Lai, and C. Grebogi, “Nonlinear dynamics and quantum entanglement in optomechanical systems,” Phys. Rev. Lett. 112(11), 110406 (2014).
[Crossref] [PubMed]

K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, “Optomechanical transducers for long-distance quantum communication,” Phys. Rev. Lett. 105(22), 220501 (2010).
[Crossref]

S. Rips and M. J. Hartmann, “Quantum information processing with nanomechanical qubits,” Phys. Rev. Lett. 110(12), 120503 (2013).
[Crossref] [PubMed]

I. Wilson-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(9), 093901 (2007).
[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(9), 093902 (2007).
[Crossref] [PubMed]

K. Xia and J. Evers, “Ground state cooling of a nanomechanical resonator in the nonresolved regime via quantum interference,” Phys. Rev. Lett. 103(22), 227203 (2009).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X. Luan, and C. W. Wong, “Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics,” Phys. Rev. Lett. 110(15), 153606 (2013).
[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]

Y.-D. Wang and A. A. Clerk, “Reservoir-engineered entanglement in optomechanical systems,” Phys. Rev. Lett. 110(25), 253601 (2013).
[Crossref] [PubMed]

M. J. Hartmann and M. B. Plenio, “Steady state entanglement in the mechanical vibrations of two dielectric membranes,” Phys. Rev. Lett. 101(20), 200503 (2008).
[Crossref] [PubMed]

D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, “Optomechanical entanglement between a movable mirror and a cavity field,” Phys. Rev. Lett. 98(3), 030405 (2007).
[Crossref] [PubMed]

X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, “Squeezed optomechanics with phase-matched amplification and dissipation,” Phys. Rev. Lett. 114(9), 093602 (2015).
[Crossref] [PubMed]

J. Restrepo, C. Ciuti, and I. Favero, “Single-polariton optomechanics,” Phys. Rev. Lett. 112(1), 013601 (2014).
[Crossref] [PubMed]

C. A. Muschik, S. Moulieras, A. Bachtold, F. H. L. Koppens, M. Lewenstein, and D. E. Chang, “Harnessing vacuum forces for quantum sensing of graphene motion,” Phys. Rev. Lett. 112(22), 223601 (2014).
[Crossref] [PubMed]

M. Antezza, C. Braggio, G. Carugno, A. Noto, R. Passante, L. Rizzuto, G. Ruoso, and S. Spagnolo, “Optomechanical Rydberg-atom excitation via dynamic Casimir-Polder coupling,” Phys. Rev. Lett. 113(2), 023601 (2014).
[Crossref] [PubMed]

S. Barzanjeh, M. Abdi, G. J. Milburn, P. Tombesi, and D. Vitali, “Reversible optical-to-microwave quantum interface,” Phys. Rev. Lett. 109(13), 130503 (2012).
[Crossref] [PubMed]

C. P. Sun, Y. Li, and X. F. Liu, “Quasi-spin-wave quantum memories with a dynamical symmetry,” Phys. Rev. Lett. 91(14), 147903 (2003).
[Crossref] [PubMed]

T. Corbitt, Y. Chen, E. Innerhofer, H. Müller-Ebhardt, D. Ottaway, H. Rehbein, D. Sigg, S. Whitcomb, C. Wipf, and N. Mavalvala, “An all-optical trap for a gram-scale mirror,” Phys. Rev. Lett. 98(15), 150802 (2007).
[Crossref] [PubMed]

PNAS (1)

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” PNAS 107(3), 1005–1010 (2010).
[Crossref] [PubMed]

Prog. Quant. Electron. (1)

S. Y. Buhmann and D.-G. Welsch, “Dispersion forces in macroscopic quantum electrodynamics,” Prog. Quant. Electron. 31(2), 51–130 (2007).
[Crossref]

Rev. Mod. Phys. (1)

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

Sci. China Phys. Mech. (2)

W. J. Nie, Y. H. Lan, Y. Li, and S. Y. Zhu, “Generating large steady-state optomechanical entanglement by the action of Casimir force,” Sci. China Phys. Mech. 57(12), 2276–2284 (2014).
[Crossref]

H. Xiong, L. G. Si, X. Y L’u, X. X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mech. 58(5), 1–13 (2015).
[Crossref]

Science (1)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 A hybrid optomechanical system model. An ensemble of quantum emitters is positioned inside a standard optomechanical cavity, which is modeled by a two-level system with the excited-state |e〉 and ground-state |g〉 and driven by an external field with frequency ωf. The motion of the mirror nearby the quantum emitter changes its transition rate via vacuum fluctuation and therefore leads to the coupling between the quantum emitter and the mechanical mode.
Fig. 2
Fig. 2 The normalized effective oscillation frequency ωeffm and the normalized effective damping rate γeffm are plotted as a function of the normalized frequency ω/ωm with different distances. We use the plasma wavelength λP = 136 nm of copper corresponding to the plasma frequency ωP = 2πc/λP and γ = 0.0033 ωP to calculate the coupling strength between the quantum emitter and the nearby mirror. Other parameters are, respectively, ωm = 2π × 2 × 106 Hz, m = 5 ng, γm = 2π × 100 Hz, Δc = −ωm, Δa = −ωm, κ = 5ωm, Γ0 = 0.1ωm and L = 0.01 m. In addition, the quantum emitter is driven by a laser with wavelength λL = 1064 nm and the collective coupling strength |η| = 1012 Hz. The collective coupling strength G = ωm.
Fig. 3
Fig. 3 The effective phonon number Nph is plotted as a function of the dimensionless effective cavity detuning Δcm with different distances d. The collective coupling strength |η| = 0.8 × 1012 Hz and the temperature of the movable mirror is selected as T = 0.1 K. Other parameter values are the same as those in Fig. 2.
Fig. 4
Fig. 4 Plot the energy level diagram in the hybrid optomechanical system, where |n, na, m〉 denotes the state of n photons in optical mode, na atomic excitations in collective excitation mode and m phonons in mechanical mode. The black double arrow denotes the coupling between states |n, na + 1, m + 1〉 and |n + 1, na, m + 1〉 through the atom-field coupling. The black solid (dashed) arrow denotes the cooling (heating) process of the mechanical mode through the radiation pressure coupling and the red solid (dashed) arrow denotes the cooling (heating) process of the mechanical mode through vacuum coupling.
Fig. 5
Fig. 5 The effective phonon number Nph is plotted as a function of the dimensionless effective detuning of the emitter Δam with different distances d. The effective detuning Δc = −ωm. Other parameter values are the same as those in Fig. 3.
Fig. 6
Fig. 6 The effective phonon number Nph is plotted as a function of the collective coupling strength g in absence and presence of the vacuum coupling (ω0d/c = 0.1). The effective detuning Δc = −ωm. Other parameter values are the same as those in Fig. 3.
Fig. 7
Fig. 7 The effective phonon number Nph is plotted as a function of the free-space spontaneous emission rate of the quantum emitter Γ0 in the absence and presence of the vacuum coupling (ω0d/c = 0.1). Other parameter values are the same as those in Fig. 6.

Equations (16)

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H = h ¯ ω c a a + p 2 2 m + 1 2 m ω m 2 x 2 + 1 2 h ¯ ω a ( d + x ) i = 1 N σ z ( i ) + h ¯ g ( a i = 1 N σ + ( i ) + a i = 1 N σ ( i ) ) h ¯ χ c a a x + h ¯ ( Ω i = 1 N σ + ( i ) e i ω f t + Ω * i = 1 N σ ( i ) e i ω f t )
Δ ω a ( r ) = δ ω ae ( r ) δ ω ag ( r ) ,
δ ω ag ( r ) = 3 c Γ 0 ω 0 2 0 d u u 2 ω 0 2 + u 2 Tr { G ( r , r , i u ) } ,
δ ω ae ( r ) = δ ω ag ( r ) 3 π c Γ 0 ω 0 Tr Re { G ( r , r , ω 0 ) } ,
λ 0 ( d ) = 2 c 3 Γ 0 π ω 0 2 0 d u ω 0 2 + u 2 0 d k k e 2 i d K 0 [ ( ω c ) 2 r s + ( k 2 K 0 2 ) r p ] + Re { c 3 Γ 0 2 ω 0 3 0 d k k e 2 i d ( ω 0 c ) 2 k 2 [ ( ω 0 c ) 2 r s + ( 2 k 2 ( ω 0 c ) 2 ) r p ] } .
H = h ¯ Δ c 0 a a + 1 2 h ¯ ω m ( p 2 + q 2 ) + h ¯ ( Δ a 0 + λ q ) S + S + h ¯ g N ( a S + + a S ) h ¯ χ a a q + h ¯ N ( Ω S + + Ω * S ) ,
q ˙ = ω m p , p ˙ = ω m q λ N / 2 + χ a a γ m p + ξ ( t ) , a ˙ = ( κ + i Δ c 0 ) a + i χ aq i GS + 2 κ a in ( t ) , S ˙ = ( Γ a + i Δ a 0 ) S i Ga i λ q S i η + 2 Γ a Γ ( t ) ,
p s = 0 , q s = χ | α s | 2 λ N / 2 ω m , α s = i GS s κ + i Δ c , S s = i η Γ a + G 2 κ κ 2 + Δ c 2 + i ( Δ a G 2 Δ c κ 2 + Δ c 2 ) ,
δ q ˙ = ω m δ p , δ p ˙ = ω m δ q + χ ( α s * δ a + α s δ a ) γ m p + ξ ( t ) , δ a ˙ = ( κ + i Δ c ) δ a + i χ α s δ q i G δ S + 2 κ a in ( t ) , δ S ˙ = ( Γ a + i Δ a ) δ S i G δ a i λ S s δ q + 2 Γ a Γ ( t ) ,
J = ( 0 ω m 0 0 0 0 ω m γ m χ p χ n 0 0 χ n 0 κ Δ c 0 G χ p 0 Δ c κ G 0 G n 0 0 G Γ a Δ a G p 0 G 0 Δ a Γ a ) ,
ω eff = ω m Re [ A ( ω ) + B ( ω ) + C ( ω ) D ( ω ) ]
γ eff = γ m + ω m ω Im [ A ( ω ) + B ( ω ) + C ( ω ) D ( ω ) ] ,
D ( ω ) = [ G 2 Γ a κ i ( Γ a + κ ) ω + ω 2 ] 2 + 2 G 2 Δ a Δ c + ( Γ a + i ω ) 2 Δ c 2 + Δ a 2 β 1 , A ( ω ) = G 2 β 3 ( Γ a + i ω ) + ( Γ a + i ω ) 2 [ β 1 ω m Δ c ( χ n 2 + χ p 2 ) ] , B ( ω ) = Δ a [ ( G 2 Δ c + β 1 Δ a ) ω m ( G 2 + Δ a Δ c ) χ n 2 Δ c Δ c χ p 2 G G p β 2 ] , C ( ω ) = G ( Γ a + i ω ) ( G β 4 + G p β 5 ) + G 2 [ G 2 ω m G G p χ p + Δ a ( Δ c ω m χ p 2 ) ] , β 1 ( ω ) = ( κ + i ω ) 2 + Δ c 2 , β 2 ( ω ) = ( κ + i ω ) χ n + Δ c χ p , β 3 ( ω ) = ( κ + i ω ) ω m + χ n χ p , β 4 ( ω ) = χ n χ p ( κ + i ω ) ω m , β 5 ( ω ) = ( κ + i ω ) χ p χ n Δ c .
N ph = ( δ p 2 + ( δ q 2 ) 1 ) / 2 ,
S q ( ω ) = | χ ( ω ) | 2 [ S t ( ω ) + S f ( ω ) + S a ( ω ) ] ,
S t ( ω ) = γ m ω ω m ( 1 + coth h ¯ ω 2 k B T ) , S f ( ω ) = 2 κ | D ( ω ) | 2 [ | h 1 ( ω ) | 2 + | h 2 ( ω ) | 2 ] , S a ( ω ) = 2 Γ a | D ( ω ) | 2 [ | h 3 ( ω ) | 2 + | h 4 ( ω ) | 2 ] , h 1 ( ω ) = ( G 2 Δ a + β 6 Δ c ) χ n + [ ( Γ 1 + i ω ) β 7 + ( κ + i ω ) Δ a 2 ] χ p , h 2 ( ω ) = ( G 2 Δ a + β 6 Δ c ) χ p + [ ( Γ a + i ω ) β 7 ( κ + i ω ) Δ a 2 ] χ n , h 3 ( ω ) = G β 8 χ n G χ p [ ( κ + i ω ) Δ a + ( Γ a + i ω ) Δ c ] , h 4 ( ω ) = G [ ( Γ a + i ω ) β 5 G 2 χ p Δ a β 2 ] , β 6 ( ω ) = ( κ + i ω ) 2 + Δ a 2 , β 7 ( ω ) = G 2 + ( ω i Γ a ) ( ω i κ ) , β 8 ( ω ) = G 2 Γ a κ i ω ( Γ a + κ ) + ω 2 + Δ a Δ c .

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