Abstract

Sum sideband generation in a generic optomechanical system is discussed in the parameter configuration of optomechanically induced transparency. The nonlinear terms of the optomechanical dynamics are taken account and the features of the sum sideband generation are identified based on the analytical treatment. The nonlinear optomechanical interactions between cavity fields and the mechanical oscillation, which emerging as a new frontier in cavity optomechanics, are responsible for the generation of the frequency components at the sum sideband. We analyze in detail the influences of some parameters, including the pump power of the control field and the frequencies of the probe fields, on the sum sideband generation. The results clearly indicate that sum sideband generation can be significantly enhanced via achieving the matching conditions. The effect of sum sideband generation may be accessible in experiments and have potential application for achieving high precision measurement and on-chip manipulation of light propagation.

© 2016 Optical Society of America

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    [Crossref] [PubMed]
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  4. H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
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  5. J.-J. Li and K.-D. Zhu, “Spin-based Optomechanics with Carbon Nanotubes,” Sci. Rep. 2, 903 (2012).
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  6. Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
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  11. B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  26. Y. Sun and A. A. Sukhorukov, “Chaotic oscillations of coupled nanobeam cavities with tailored optomechanical potentials,” Opt. Lett. 39(12), 3543–3546 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  28. X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
    [Crossref] [PubMed]
  29. C. K. Law, “Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,” Phys. Rev. A 51(3), 2537 (1995).
    [Crossref] [PubMed]
  30. Z. Wang and B. Yu, “Optical bistability and multistability in polaritonic materials doped with nanoparticles,” Laser Phys. Lett. 11(11), 115903 (2014).
    [Crossref]
  31. W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
    [Crossref]
  32. X.-W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
    [Crossref]
  33. H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
    [Crossref]
  34. H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
    [Crossref] [PubMed]
  35. M. R. Mehmannavaz and H. Sattari, “A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window,” Laser Phys. Lett. 12(2), 025201 (2015).
    [Crossref]
  36. A. Chen, “Coherent manipulation of spontaneous emission spectra in coupled semiconductor quantum well structures,” Opt. Express 22(22), 26991–27000 (2014).
    [Crossref] [PubMed]
  37. X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mechan. Astron. 58(9), 594201 (2015).
    [Crossref]
  38. H. R. Hamedi, “Transient absorption and lasing without inversion in an artificial molecule via Josephson coupling energy,” Laser Phys. Lett. 12(3), 035201 (2015).
    [Crossref]

2015 (14)

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (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, 033841 (2015).
[Crossref]

S. H. Asadpour, H. R. Hamedi, and H. R. Soleimani, “Slow light propagation and bistable switching in a graphene under an external magnetic field,” Laser Phys. Lett. 12(4), 045202 (2015).
[Crossref]

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

M. R. Mehmannavaz and H. Sattari, “A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window,” Laser Phys. Lett. 12(2), 025201 (2015).
[Crossref]

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

X.-W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
[Crossref]

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

X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mechan. Astron. 58(9), 594201 (2015).
[Crossref]

H. R. Hamedi, “Transient absorption and lasing without inversion in an artificial molecule via Josephson coupling energy,” Laser Phys. Lett. 12(3), 035201 (2015).
[Crossref]

F. C. Lei, M. Gao, C. Du, Q. L. Jing, and G. L. Long, “Three-pathway electromagnetically induced transparency in coupled-cavity optomechanical system,” Opt. Express 23(9), 11508–11517 (2015).
[Crossref] [PubMed]

R.-J. Xiao, G.-X. Pan, and L. Zhou, “Analog multicolor electromagnetically induced transparency in multimode quadratic coupling quantum optomechanics,” J. Opt. Soc. Am. B 32, 1399–1405 (2015)
[Crossref]

Q. Wu, J. Q. Zhang, J. H. Wu, M. Feng, and Z. M. Zhang, “Tunable multi-channel inverse optomechanically induced transparency and its applications,” Opt. Express 23(14), 18534–18547 (2015).
[Crossref] [PubMed]

2014 (6)

Y. Sun and A. A. Sukhorukov, “Chaotic oscillations of coupled nanobeam cavities with tailored optomechanical potentials,” Opt. Lett. 39(12), 3543–3546 (2014).
[Crossref] [PubMed]

A. Chen, “Coherent manipulation of spontaneous emission spectra in coupled semiconductor quantum well structures,” Opt. Express 22(22), 26991–27000 (2014).
[Crossref] [PubMed]

Z. Wang and B. Yu, “Optical bistability and multistability in polaritonic materials doped with nanoparticles,” Laser Phys. Lett. 11(11), 115903 (2014).
[Crossref]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

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

2013 (7)

G.-F. Xu and C. K. Law, “Dark states of a moving mirror in the single-photon strong-coupling regime,” Phys. Rev. A 87(5), 053849 (2013).
[Crossref]

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

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111(13), 133601 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

C. Jiang, H. Liu, Y. Cui, X. Li, G. Chen, and B. Chen, “Electromagnetically induced transparency and slow light in two-mode optomechanics,” Opt. Express 21(10), 12165–12173 (2013).
[Crossref] [PubMed]

2012 (3)

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

J.-J. Li and K.-D. Zhu, “Spin-based Optomechanics with Carbon Nanotubes,” Sci. Rep. 2, 903 (2012).
[Crossref] [PubMed]

2011 (5)

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
[Crossref]

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

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

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

2010 (1)

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

2008 (1)

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

1995 (1)

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

Arcizet, O.

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

Asadpour, S. H.

S. H. Asadpour, H. R. Hamedi, and H. R. Soleimani, “Slow light propagation and bistable switching in a graphene under an external magnetic field,” Laser Phys. Lett. 12(4), 045202 (2015).
[Crossref]

Ashhab, S.

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

Aspelmeyer, M.

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

Børkje, K.

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Chan, J.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Chang, D. E.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Chen, A.

Chen, B.

C. Jiang, H. Liu, Y. Cui, X. Li, G. Chen, and B. Chen, “Electromagnetically induced transparency and slow light in two-mode optomechanics,” Opt. Express 21(10), 12165–12173 (2013).
[Crossref] [PubMed]

B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
[Crossref]

Chen, G.

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, 033841 (2015).
[Crossref]

Cui, Y.

Deléglise, S.

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

Ding, C.

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

Du, C.

Eichenfield, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Feng, M.

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

Q. Wu, J. Q. Zhang, J. H. Wu, M. Feng, and Z. M. Zhang, “Tunable multi-channel inverse optomechanically induced transparency and its applications,” Opt. Express 23(14), 18534–18547 (2015).
[Crossref] [PubMed]

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Gao, M.

Gavartin, E.

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

Girvin, S. M.

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Gu, W.-j.

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

Gu, X.

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

Hamedi, H. R.

S. H. Asadpour, H. R. Hamedi, and H. R. Soleimani, “Slow light propagation and bistable switching in a graphene under an external magnetic field,” Laser Phys. Lett. 12(4), 045202 (2015).
[Crossref]

H. R. Hamedi, “Transient absorption and lasing without inversion in an artificial molecule via Josephson coupling energy,” Laser Phys. Lett. 12(3), 035201 (2015).
[Crossref]

Hill, J. T.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Hou, B. P.

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

Jia, W. Z.

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

Jiang, C.

C. Jiang, H. Liu, Y. Cui, X. Li, G. Chen, and B. Chen, “Electromagnetically induced transparency and slow light in two-mode optomechanics,” Opt. Express 21(10), 12165–12173 (2013).
[Crossref] [PubMed]

B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
[Crossref]

Jing, Q. L.

Kippenberg, T. J.

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

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

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

Kronwald, A.

A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111(13), 133601 (2013).
[Crossref] [PubMed]

Law, C. K.

G.-F. Xu and C. K. Law, “Dark states of a moving mirror in the single-photon strong-coupling regime,” Phys. Rev. A 87(5), 053849 (2013).
[Crossref]

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

Lei, F. C.

Li, G.

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

Li, J.-J.

J.-J. Li and K.-D. Zhu, “Spin-based Optomechanics with Carbon Nanotubes,” Sci. Rep. 2, 903 (2012).
[Crossref] [PubMed]

Li, X.

Li, Y.

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

X.-W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
[Crossref]

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

Lin, Q.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Liu, H.

Liu, Y.

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

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, 033841 (2015).
[Crossref]

Long, G. L.

Lü, X.

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

Lü, X. Y.

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

Lü, X.-Y.

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

Luo, X. G.

X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mechan. Astron. 58(9), 594201 (2015).
[Crossref]

Ma, P. C.

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

Marquardt, F.

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

A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111(13), 133601 (2013).
[Crossref] [PubMed]

Mayer Alegre, T. P.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Mehmannavaz, M. R.

M. R. Mehmannavaz and H. Sattari, “A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window,” Laser Phys. Lett. 12(2), 025201 (2015).
[Crossref]

Miranowicz, A.

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

Nori, F.

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

Nunnenkamp, A.

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

Painter, O.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Pan, G.-X.

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, 033841 (2015).
[Crossref]

Rabl, P.

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

Rivire, R.

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

Safavi-Naeini, A. H.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Sattari, H.

M. R. Mehmannavaz and H. Sattari, “A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window,” Laser Phys. Lett. 12(2), 025201 (2015).
[Crossref]

Schliesser, A.

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

Si, L.

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

Si, L.-G.

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

Soleimani, H. R.

S. H. Asadpour, H. R. Hamedi, and H. R. Soleimani, “Slow light propagation and bistable switching in a graphene under an external magnetic field,” Laser Phys. Lett. 12(4), 045202 (2015).
[Crossref]

Sukhorukov, A. A.

Sun, Y.

Teufel, J. D.

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[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]

Wang, H.

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

Wang, Q.

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

Wang, S. J.

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

Wang, Y.-D.

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

Wang, Z.

Z. Wang and B. Yu, “Optical bistability and multistability in polaritonic materials doped with nanoparticles,” Laser Phys. Lett. 11(11), 115903 (2014).
[Crossref]

Wei, L. F.

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

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

Weis, S.

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

Winger, M.

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Wu, J. H.

Wu, L.-A.

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

Wu, Q.

Wu, Y.

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

Xiao, R.-J.

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, 033841 (2015).
[Crossref]

Xiong, H.

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

Xu, G.-F.

G.-F. Xu and C. K. Law, “Dark states of a moving mirror in the single-photon strong-coupling regime,” Phys. Rev. A 87(5), 053849 (2013).
[Crossref]

Xu, X.-W.

X.-W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
[Crossref]

Xu, Y.

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Yang, L.-P.

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

Yang, X.

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Carrier-envelope phase-dependent effect of high-order sideband generation in ultrafast driven optomechanical system,” Opt. Lett. 38, 353–356 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

Yao, C. M.

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

Yu, B.

Z. Wang and B. Yu, “Optical bistability and multistability in polaritonic materials doped with nanoparticles,” Laser Phys. Lett. 11(11), 115903 (2014).
[Crossref]

Zhang, J. Q.

Q. Wu, J. Q. Zhang, J. H. Wu, M. Feng, and Z. M. Zhang, “Tunable multi-channel inverse optomechanically induced transparency and its applications,” Opt. Express 23(14), 18534–18547 (2015).
[Crossref] [PubMed]

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

Zhang, J.-Q.

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Zhang, W. M.

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

Zhang, Z. M.

Zheng, A.-S.

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[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, 033841 (2015).
[Crossref]

Zhou, L.

Zhu, K.-D.

J.-J. Li and K.-D. Zhu, “Spin-based Optomechanics with Carbon Nanotubes,” Sci. Rep. 2, 903 (2012).
[Crossref] [PubMed]

B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
[Crossref]

Ann. Phys. (1)

H. Xiong, L.-G. Si, X.-Y. Lü, X. Yang, and Y. Wu, “Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime,” Ann. Phys. 349, 43–54 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (4)

H. R. Hamedi, “Transient absorption and lasing without inversion in an artificial molecule via Josephson coupling energy,” Laser Phys. Lett. 12(3), 035201 (2015).
[Crossref]

S. H. Asadpour, H. R. Hamedi, and H. R. Soleimani, “Slow light propagation and bistable switching in a graphene under an external magnetic field,” Laser Phys. Lett. 12(4), 045202 (2015).
[Crossref]

M. R. Mehmannavaz and H. Sattari, “A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window,” Laser Phys. Lett. 12(2), 025201 (2015).
[Crossref]

Z. Wang and B. Yu, “Optical bistability and multistability in polaritonic materials doped with nanoparticles,” Laser Phys. Lett. 11(11), 115903 (2014).
[Crossref]

Nature (1)

A. H. Safavi-Naeini, T. P. Mayer Alegre, J. Chan, M. Eichenfield, M. Winger, Q. Lin, J. T. Hill, D. E. Chang, and O. Painter, “Electromagnetically induced transparency and slow light with optomechanics,” Nature 472, 69–73 (2011).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (13)

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

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

H. Xiong, L.-G. Si, A.-S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86, 013815 (2012).
[Crossref]

H. Wang, X. Gu, Y. Liu, A. Miranowicz, and F. Nori, “Optomechanical analog of two-color electromagnetically induced transparency: photon transmission through an optomechanical device with a two-level system,” Phys. Rev. A 90(2), 023817 (2014).
[Crossref]

W. Z. Jia, L. F. Wei, Y. Li, and Y. Liu, “Phase-dependent optical response properties in an optomechanical system by coherently driving the mechanical resonator,” Phys. Rev. A 91(4), 043843 (2015).
[Crossref]

X.-W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
[Crossref]

H. Xiong, L.-G. Si, C. Ding, X. Yang, and Y. Wu, “Classical theory of cylindrical nonlinear optics: Sum- and difference-frequency generation,” Phys. Rev. A 84(4), 043841 (2011).
[Crossref]

W.-j. Gu and G. Li, “Quantum interference effects on ground-state optomechanical cooling,” Phys. Rev. A 87, 025804 (2013).
[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, 033841 (2015).
[Crossref]

G.-F. Xu and C. K. Law, “Dark states of a moving mirror in the single-photon strong-coupling regime,” Phys. Rev. A 87(5), 053849 (2013).
[Crossref]

B. Chen, C. Jiang, and K.-D. Zhu, “Slow light in a cavity optomechanical system with a Bose–Einstein condensate,” Phys. Rev. A 83, 055803 (2011).
[Crossref]

Q. Wang, J. Q. Zhang, P. C. Ma, C. M. Yao, and M. Feng, “Precision measurement of the environmental temperature by tunable double optomechanically induced transparency with a squeezed field,” Phys. Rev. A 91(6), 063827 (2015).
[Crossref]

J.-Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86, 053806 (2012).
[Crossref]

Phys. Rev. B (1)

Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, “Nondeterministic ultrafast ground-state cooling of a mechanical resonator,” Phys. Rev. B 84, 094502 (2011).
[Crossref]

Phys. Rev. Lett. (3)

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

K. Børkje, A. Nunnenkamp, J. D. Teufel, and S. M. Girvin, “Signatures of nonlinear cavity optomechanics in the weak coupling regime,” Phys. Rev. Lett. 111(5), 053603 (2013).
[Crossref] [PubMed]

A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111(13), 133601 (2013).
[Crossref] [PubMed]

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. Mechan. Astron. (2)

H. Xiong, L. Si, X. Lü, X. Yang, and Y. Wu, “Review of cavity optomechanics in the weak-coupling regime: from linearization to intrinsic nonlinear interactions,” Sci. China Phys. Mechan. Astron. 58(5), 050302 (2015).

X. G. Luo, “Principles of electromagnetic waves in metasurfaces,” Sci. China Phys. Mechan. Astron. 58(9), 594201 (2015).
[Crossref]

Sci. Rep. (3)

J.-J. Li and K.-D. Zhu, “Spin-based Optomechanics with Carbon Nanotubes,” Sci. Rep. 2, 903 (2012).
[Crossref] [PubMed]

X. Y. Lü, W. M. Zhang, S. Ashhab, Y. Wu, and F. Nori, “Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems,” Sci. Rep. 3, 2943 (2013).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, X. Yang, and Y. Wu, “Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium,” Sci. Rep. 5, 11071 (2015).
[Crossref] [PubMed]

Science (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic diagram of a double probe fields driven optomechanical system. The optomechanical system is driven by a strong control field with the frequency ωc and two relatively weak probe fields with frequencies ω1 and ω2, respectively. (b) Frequency spectrogram of sum sideband generation in the optomechanical system with double probe fields driven. The frequency of the control field is detuned by Δ̄ from the cavity resonance frequency. There are sum sideband generation (frequency components ±Ω+ in a frame rotating at ωc) in the optomechanical system due to the nonlinear terms iλ0δxδa/h̄ and λ0δa*δa with Ω+ = δ1 + δ2, δ1 = ω1ωc, and δ2 = ω2ωc. Other frequency components in the spectrogram, such as second-order sideband of each probe field, are not shown.

Fig. 2
Fig. 2

Dependencies of the efficiencies (in logarithmic form) of (a) the upper sum sideband generation log 10 η s +, (b) lower sum sideband generation log 10 η s on the pump power of the control field Pc and the frequency of the first probe field δ1 for δ2 = 0.1Ωm. (c) Calculation results of log 10 η s + and log 10 η s vary with δ1 for δ2 = −0.05Ωm, Pc = 20 μW and P1 = P2 = 1 μW. (d) The amplitude of the mechanical oscillation (in unit of femtometer) at the sum-sideband vary with δ1 and δ2. The parameters used in the calculation are m=20 ng, G/2π=−12 GHz/nm, Γm/2π=41.0 kHz, κ/2π=15.0 MHz, Ωm/2π=51.8MHz, and Δ=−Ωm. The wavelength of the control field is chosen to be 532 nm here.

Fig. 3
Fig. 3

Efficiencies (in logarithmic form) of (a) upper sum-sideband generation and (b) lower sum-sideband generation as a function of δ1 and δ2. The parameters are the same as Fig. 2.

Equations (20)

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H ^ = H ^ mech + H ^ cav + H ^ int + H ^ control + H ^ probe H ^ mech = p ^ 2 2 m + m Ω m 2 x ^ 2 2 , H ^ cav = h ¯ ω 0 a ^ a ^ , H ^ int = λ 0 x ^ a ^ a ^ , H ^ control = i h ¯ η κ ε c ( a ^ e i ω c t a ^ e i ω c t ) , H ^ probe = i h ¯ η κ ( a ^ ε 1 e i ω 1 t + a ^ ε 2 e i ω 2 t H . c . ) ,
a ^ ˙ = [ i ( Δ + λ 0 x ^ / h ¯ ) κ ] a ^ + η κ ( ε c + s in ) + a ^ in ,
x ^ ˙ = p ^ / m ,
p ^ ˙ = m Ω m 2 x ^ + λ 0 a ^ a ^ Γ m p ^ + F ^ th ,
a ˙ = ( i Δ x κ ) a + η κ ( ε c + ε 1 e i δ 1 t + ε 2 e i δ 2 t ) ,
( m d 2 d t 2 + m Γ m d d t + m Ω m 2 ) x = λ 0 a * a ,
a ¯ = η κ ε c i ( Δ + λ 0 x ¯ / h ¯ ) + κ , x ¯ = λ 0 | a ¯ | 2 m Ω m 2 ,
d d t δ a = ( i Δ ¯ κ ) δ a + i λ 0 ( a ¯ δ x + δ x δ a ) / h ¯ + η κ s in , ( m d 2 d t 2 + m Γ m d d t + m Ω m 2 ) δ x = λ 0 ( a ¯ δ a * + a * ¯ δ a + δ a * δ a ) ,
d d t δ a = ( i Δ ¯ κ ) δ a + i λ 0 a ¯ δ x h ¯ + η κ s in , ( m d 2 d t 2 + m Γ m d d t + m Ω m 2 ) δ x = λ 0 ( a ¯ δ a * + a * ¯ δ a ) ,
δ a L = a δ 1 + e i δ 1 t + a δ 1 e i δ 1 t + a δ 2 + e i δ 2 t + a δ 2 e i δ 2 t , δ x L = x δ 1 e i δ 1 t + x δ 1 * e i δ 1 t + x δ 2 e i δ 2 t + x δ 2 * e i δ 2 t ,
δ a = δ a 1 ( 1 ) + δ a 2 ( 1 ) + δ a 1 ( 2 ) + δ a 2 ( 2 ) + δ a sum ( 2 ) + , δ x = δ x 1 ( 1 ) + δ x 2 ( 1 ) + δ x 1 ( 2 ) + δ x 2 ( 2 ) + δ x sum ( 2 ) + ,
δ a 1 ( 1 ) = a δ 1 + e i δ 1 t + a δ 1 e i δ 1 t , δ a 2 ( 1 ) = a δ 2 + e i δ 2 t + a δ 1 e i δ 2 t , δ a 1 ( 2 ) = a 2 δ 1 + e 2 i δ 1 t + a 2 δ 1 + e 2 i δ 1 t , δ a 2 ( 2 ) = a 2 δ 2 + e 2 i δ 2 t + a 2 δ 2 e 2 i δ 2 t , δ x 1 ( 1 ) = x δ 1 e i δ 1 t + x δ 1 * e i δ 1 t , δ x 2 ( 1 ) = x δ 2 e i δ 2 t + x δ 2 * e i δ 2 t , δ x 1 ( 2 ) = x 2 δ 1 e 2 i δ 1 t + x 2 δ 1 * e 2 i δ 1 t , δ x 2 ( 2 ) = x 2 δ 2 e 2 i δ 2 t + x 2 δ 2 * e 2 i δ 2 t , δ a sum ( 2 ) = a s + e i Ω + t + a s e i Ω + t , δ x sum ( 2 ) = x s e i Ω + t + x s * e i Ω + t ,
δ a = a 1 + e i δ 1 t + a 1 e i δ 1 t + a 2 + e i δ 2 t + a 2 e i δ 2 t + a s + e i Ω + t + a s e i Ω + t + , δ x = x 1 e i δ 1 t + x 1 * e i δ 1 t + x 2 e i δ 2 t + x 2 * e i δ 2 t + x s e i Ω + t + x s * e i Ω + t + ,
s a 1 + i δ 1 a 1 + i λ 0 h ¯ a ¯ x 1 i λ 0 h ¯ ( a 2 x s + a s + x 2 * ) η κ ε 1 = 0 , s a 1 + i δ 1 a 1 i λ 0 h ¯ a ¯ x 1 * i λ 0 h ¯ ( a 2 + x s * + a s x 2 ) = 0 , s a 2 + i δ 2 a 2 + i λ 0 h ¯ a ¯ x 2 i λ 0 h ¯ ( a 1 x s + a s + x 1 * ) η κ ε 2 = 0 , s a 2 + i δ 2 a 2 i λ 0 h ¯ a ¯ x 2 * i λ 0 h ¯ ( a 1 + x s * + a s x 1 ) = 0 , s a s + i Ω + a s + i λ 0 h ¯ a ¯ x s i λ 0 h ¯ ( a 1 + x 2 + a 2 + x 1 ) = 0 , s a s + i Ω + a s i λ 0 h ¯ a ¯ x s * i λ 0 h ¯ ( a 1 x 2 * + a 2 x 1 * ) = 0 , m Ω m 2 x 1 m δ 1 2 x 1 i m Γ m δ 1 x 1 λ 0 [ a 2 ( a s ) * + a s + ( a 2 + ) * + a * ¯ a 1 + + a ¯ ( a 1 ) * ] = 0 , m Ω m 2 x 1 * m δ 1 2 x 1 * + i m Γ m δ 1 x 1 * λ 0 [ a 2 + ( a s + ) * + a s ( a 2 ) * + a * ¯ a 1 + a ¯ ( a 1 + ) * ] = 0 , m Ω m 2 x 2 m δ 2 2 x 2 i m Γ m δ 2 x 2 λ 0 [ a 1 ( a s ) * + a s + ( a 1 + ) * + a * ¯ a 2 + + a ¯ ( a 2 ) * ] = 0 , m Ω m 2 x 2 * m δ 2 2 x 2 * + i m Γ m δ 2 x 2 * λ 0 [ a 1 + ( a s + ) * + a s ( a 1 ) * + a * ¯ a 2 + a ¯ ( a 2 + ) * ] = 0 , m Ω m 2 x s m Ω + 2 x s i m Γ m Ω + x s λ 0 [ a 1 + ( a 2 ) * + a 2 + ( a 1 ) * + a * ¯ a s + + a ¯ ( a s ) * ] = 0 , m Ω m 2 x s * m Ω + 2 x s * + i m Γ m Ω + x s * λ 0 [ a 1 ( a 2 + ) * + a 2 ( a 1 + ) * + a * ¯ a s + a ¯ ( a s + ) * ] = 0 ,
( s i δ 1 ) a 1 + i λ 0 h ¯ a ¯ x 1 η κ ε 1 = 0 ( s + i δ 1 ) a 1 i λ 0 h ¯ a ¯ x 1 * = 0 ( m Ω m 2 m δ 1 2 i m Γ m δ 1 ) x 1 λ 0 [ a * ¯ a 1 + + a ¯ ( a 1 ) * ] = 0 .
( s i δ 2 ) a 2 + i λ 0 h ¯ a ¯ x 2 η κ ε 2 = 0 ( s + i δ 2 ) a 2 i λ 0 h ¯ a ¯ x 2 * = 0 ( m Ω m 2 m δ 2 2 i m Γ m δ 2 ) x 2 λ 0 [ a * ¯ a 2 + + a ¯ ( a 2 ) * ] = 0 .
( s i Ω + ) a s + i λ 0 h ¯ a ¯ x s i λ 0 h ¯ ( a 1 + x 2 + a 2 + x 1 ) = 0 ( s + i Ω + ) a s i λ 0 h ¯ a ¯ x s * i λ 0 h ¯ ( a 1 x 2 * + a 2 x 1 * ) = 0 ( m Ω m 2 m Ω + 2 i m Γ m Ω + ) x s λ 0 [ a 1 + ( a 2 ) * + a 2 + ( a 1 ) * + a * ¯ a s + + a ¯ ( a s ) * ] = 0 .
a 1 + = η κ ε 1 τ ( δ 1 ) θ ( δ 1 ) τ ( δ 1 ) τ , x 1 = λ 0 a * ¯ a 1 + τ ( δ 1 ) , a 1 = i λ 0 a ¯ h ¯ θ ( δ 1 ) x 1 * , a 2 + = η κ ε 2 τ ( δ 2 ) θ ( δ 2 ) τ ( δ 2 ) τ , x 2 = λ 0 a * ¯ a 2 + τ ( δ 2 ) , a 2 = i λ 0 a ¯ h ¯ θ ( δ 2 ) x 2 * , a s + = i λ 0 h ¯ λ 0 a ¯ ξ s + ( a 1 + x 2 + a 2 + x 1 ) τ ( Ω + ) τ ( Ω + ) θ ( Ω + ) α , a s = i λ 0 ( a ¯ x s * + a 1 x 2 * + a 2 x 1 * ) h ¯ θ ( Ω + ) , x s = λ 0 ( ξ s + a * ¯ a s + ) τ ( Ω + ) ,
s out = ε c η κ a ¯ + ( ε 1 η κ a 1 + ) e i δ 1 t + ( ε 2 η κ a 2 + ) e i δ 2 t η κ a 1 e i δ 1 t η κ a 2 e i δ 2 t η κ a s + e i Ω + t η κ a s e i Ω + t .
T i = 1 η κ τ ( δ i ) θ ( δ i ) τ ( δ i ) α ,

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