Abstract

Multiple-path interference plays a fundamental role in classical and quantum physics. In this work, we propose two general schemes to realize multiple electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) in coupled microresonators and optomechanical systems. We give explicit physical descriptions and find out that these two schemes are essentially equivalent to each other. More importantly, we experimentally demonstrate both multiple EIT and EIA by coupling a microtoroid to a microsphere that supports multiple high Q optical modes with dense modes distributions. The theory fits well with the experimental results. We believe that our study and experimental results lay a foundation for realizing arbitrary multiple pathways interference in applications.

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

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (4)

H. Xiong and Y. Wu, “Fundamentals and applications of optomechanically induced transparency,” Appl. Phys. Rev. 5, 031305 (2018).
[Crossref]

T. Wang, X.-F. Liu, Y. Hu, G. Qin, D. Ruan, and G.-L. Long, “Rapid and high precision measurement of opto-thermal relaxation with pump-probe method,” Sci. Bull. 63, 287–292 (2018).
[Crossref]

W. Chen, J. Zhang, B. Peng, Ş. K. Özdemir, X. Fan, and L. Yang, “Parity-time-symmetric whispering-gallery mode nanoparticle sensor,” Photonics Res. 6, A23–A30 (2018).
[Crossref]

T. Wang, M. Wang, Y.-Q. Hu, and G.-L. Long, “Optothermal control of the raman gain enhanced ringing in microresonators,” Europhys. Lett. 124, 14002 (2018).
[Crossref]

2017 (4)

Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
[Crossref] [PubMed]

A. Sohail, Y. Zhang, M. Usman, and C. Yu, “Controllable optomechanically induced transparency in coupled optomechanical systems,” The Eur. Phys. J. D 71, 103 (2017).
[Crossref]

C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-q microtoroid cavities,” Laser Photonics Rev. 11, 1600178 (2017).
[Crossref]

C. Yang, Y. Hu, X. Jiang, and M. Xiao, “Analysis of a triple-cavity photonic molecule based on coupled-mode theory,” Phys. Rev. A 95, 033847 (2017).
[Crossref]

2016 (3)

A. Sohail, Y. Zhang, J. Zhang, and C.-S. Yu, “Optomechanically induced transparency in multi-cavity optomechanical system with and without one two-level atom,” Sci. Rep. 6, 28830 (2016).
[Crossref]

X.-F. Liu, F. Lei, M. Gao, X. Yang, G.-Q. Qin, and G.-L. Long, “Fabrication of a microtoroidal resonator with picometer precise resonant wavelength,” Opt. Lett. 41, 3603–3606 (2016).
[Crossref] [PubMed]

M. Gao, F. Lei, C. Du, and G. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime,” Sci. China Physics, Mech. & Astron. 59, 610301 (2016).
[Crossref]

2015 (3)

F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
[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, 063827 (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, 11508–11517 (2015).
[Crossref] [PubMed]

2014 (5)

P.-C. Ma, J.-Q. Zhang, Y. Xiao, M. Feng, and Z.-M. Zhang, “Tunable double optomechanically induced transparency in an optomechanical system,” Phys. Rev. A 90, 043825 (2014).
[Crossref]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
[Crossref] [PubMed]

A. Naweed, D. Goldberg, and V. M. Menon, “All-optical electromagnetically induced transparency using one-dimensional coupled microcavities,” Opt. Express 22, 18818–18823 (2014).
[Crossref] [PubMed]

B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
[Crossref] [PubMed]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

2013 (3)

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
[Crossref] [PubMed]

S. Shahidani, M. Naderi, and M. Soltanolkotabi, “Control and manipulation of electromagnetically induced transparency in a nonlinear optomechanical system with two movable mirrors,” Phys. Rev. A 88, 053813 (2013).
[Crossref]

K. Qu and G. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2013).
[Crossref]

2012 (4)

F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
[Crossref] [PubMed]

B. Peng, Ş. K. Özdemir, J. Zhu, and L. Yang, “Photonic molecules formed by coupled hybrid resonators,” Opt. Lett. 37, 3435–3437 (2012).
[Crossref]

J. Chen, C. Wang, R. Zhang, and J. Xiao, “Multiple plasmon-induced transparencies in coupled-resonator systems,” Opt. Lett. 37, 5133–5135 (2012).
[Crossref] [PubMed]

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

2011 (1)

D. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
[Crossref]

2010 (2)

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
[Crossref]

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

2009 (4)

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-q microresonator,” Nat. Photonics 4, 122 (2009).
[Crossref]

M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, “Tunable fano interference effect in coupled-microsphere resonator-induced transparency,” J. The Opt. Soc. Am. B Opt. Phys. 26, 813–818 (2009).
[Crossref]

Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
[Crossref]

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phy. B: At. Mol. Opt. Phys. 42, 215401 (2009).
[Crossref]

2007 (4)

R. Ma, A. Schliesser, P. Del’Haye, A. Dabirian, G. Anetsberger, and T. J. Kippenberg, “Radiation-pressure-driven vibrational modes in ultrahigh-q silica microspheres,” Opt. Lett. 32, 2200–2202 (2007).
[Crossref] [PubMed]

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

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[Crossref]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).
[Crossref] [PubMed]

2006 (3)

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[Crossref] [PubMed]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

B. Wang, Y. Han, J. Xiao, X. Yang, C. Xie, H. Wang, and M. Xiao, “Multi-dark-state resonances in cold multi-zeeman-sublevel atoms,” Opt. Lett. 31, 3647–3649 (2006).
[Crossref] [PubMed]

2005 (2)

A. Naweed, G. Farca, S. Shopova, and A. Rosenberger, “Induced transparency and absorption in coupled whispering-gallery microresonators,” Phys. Rev. A 71, 043804 (2005).
[Crossref]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

2004 (3)

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
[Crossref]

L. Maleki, A. Matsko, A. Savchenkov, and V. Ilchenko, “Tunable delay line with interacting whispering-gallery-mode resonators,” Opt. Lett. 29, 626–628 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (1)

E. Paspalakis and P. Knight, “Electromagnetically induced transparency and controlled group velocity in a multilevel system,” Phys. Rev. A 66, 015802 (2002).
[Crossref]

2001 (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

1999 (1)

S. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[Crossref]

1998 (1)

J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
[Crossref]

1996 (1)

1990 (1)

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

Agarwal, G.

K. Qu and G. Agarwal, “Phonon-mediated electromagnetically induced absorption in hybrid opto-electromechanical systems,” Phys. Rev. A 87, 031802 (2013).
[Crossref]

Anetsberger, G.

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
[Crossref] [PubMed]

Arcizet, O.

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

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Bowen, W. P.

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J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-q microresonator,” Nat. Photonics 4, 122 (2009).
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Chen, W.

W. Chen, J. Zhang, B. Peng, Ş. K. Özdemir, X. Fan, and L. Yang, “Parity-time-symmetric whispering-gallery mode nanoparticle sensor,” Photonics Res. 6, A23–A30 (2018).
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C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-q microtoroid cavities,” Laser Photonics Rev. 11, 1600178 (2017).
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Chen, Y.-L.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
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F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
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C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phy. B: At. Mol. Opt. Phys. 42, 215401 (2009).
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Dayan, B.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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Deléglise, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
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C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phy. B: At. Mol. Opt. Phys. 42, 215401 (2009).
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M. Gao, F. Lei, C. Du, and G. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime,” Sci. China Physics, Mech. & Astron. 59, 610301 (2016).
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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, 11508–11517 (2015).
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F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
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C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
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Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
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W. Chen, J. Zhang, B. Peng, Ş. K. Özdemir, X. Fan, and L. Yang, “Parity-time-symmetric whispering-gallery mode nanoparticle sensor,” Photonics Res. 6, A23–A30 (2018).
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S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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D. D. Smith, H. Chang, K. A. Fuller, A. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).
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Gao, M.

M. Gao, F. Lei, C. Du, and G. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime,” Sci. China Physics, Mech. & Astron. 59, 610301 (2016).
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X.-F. Liu, F. Lei, M. Gao, X. Yang, G.-Q. Qin, and G.-L. Long, “Fabrication of a microtoroidal resonator with picometer precise resonant wavelength,” Opt. Lett. 41, 3603–3606 (2016).
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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, 11508–11517 (2015).
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F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
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Gavartin, E.

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

Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
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Goldberg, D.

Gong, Q.

Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
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B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
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Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
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Guo, G.-C.

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phy. B: At. Mol. Opt. Phys. 42, 215401 (2009).
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Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
[Crossref]

Hafezi, M.

D. Chang, A. H. Safavi-Naeini, M. Hafezi, and O. Painter, “Slowing and stopping light using an optomechanical crystal array,” New J. Phys. 13, 023003 (2011).
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F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
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G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
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Han, Z.-F.

C.-H. Dong, C.-L. Zou, Y.-F. Xiao, J.-M. Cui, Z.-F. Han, and G.-C. Guo, “Modified transmission spectrum induced by two-mode interference in a single silica microsphere,” J. Phy. B: At. Mol. Opt. Phys. 42, 215401 (2009).
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M. Tomita, K. Totsuka, R. Hanamura, and T. Matsumoto, “Tunable fano interference effect in coupled-microsphere resonator-induced transparency,” J. The Opt. Soc. Am. B Opt. Phys. 26, 813–818 (2009).
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S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
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Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
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S. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
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He, L.

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
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J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-q microresonator,” Nat. Photonics 4, 122 (2009).
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F. Massel, S. U. Cho, J.-M. Pirkkalainen, P. J. Hakonen, T. T. Heikkilä, and M. A. Sillanpää, “Multimode circuit optomechanics near the quantum limit,” Nat. Commun. 3, 987 (2012).
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G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
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F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
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Hu, Y.

T. Wang, X.-F. Liu, Y. Hu, G. Qin, D. Ruan, and G.-L. Long, “Rapid and high precision measurement of opto-thermal relaxation with pump-probe method,” Sci. Bull. 63, 287–292 (2018).
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C. Yang, Y. Hu, X. Jiang, and M. Xiao, “Analysis of a triple-cavity photonic molecule based on coupled-mode theory,” Phys. Rev. A 95, 033847 (2017).
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T. Wang, M. Wang, Y.-Q. Hu, and G.-L. Long, “Optothermal control of the raman gain enhanced ringing in microresonators,” Europhys. Lett. 124, 14002 (2018).
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C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-q microtoroid cavities,” Laser Photonics Rev. 11, 1600178 (2017).
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C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-q microtoroid cavities,” Laser Photonics Rev. 11, 1600178 (2017).
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S. Huang and M. Tsang, “Electromagnetically induced transparency and optical memories in an optomechanical system with n membranes,” arXiv 1403.1340 (2014).

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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
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Hubrich, C.

G. Heinze, C. Hubrich, and T. Halfmann, “Stopped light and image storage by electromagnetically induced transparency up to the regime of one minute,” Phys. Rev. Lett. 111, 033601 (2013).
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Ilchenko, V.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
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Jiang, W.

Y.-F. Xiao, X.-B. Zou, W. Jiang, Y.-L. Chen, and G.-C. Guo, “Analog to multiple electromagnetically induced transparency in all-optical drop-filter systems,” Phys. Rev. A 75, 063833 (2007).
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Jiang, X.

C. Yang, X. Jiang, Q. Hua, S. Hua, Y. Chen, J. Ma, and M. Xiao, “Realization of controllable photonic molecule based on three ultrahigh-q microtoroid cavities,” Laser Photonics Rev. 11, 1600178 (2017).
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C. Yang, Y. Hu, X. Jiang, and M. Xiao, “Analysis of a triple-cavity photonic molecule based on coupled-mode theory,” Phys. Rev. A 95, 033847 (2017).
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Jiang, X.-F.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
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Jing, H.

Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
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Jing, Q.-L.

Kimble, H. J.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443, 671–674 (2006).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
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M. Gao, F. Lei, C. Du, and G. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime,” Sci. China Physics, Mech. & Astron. 59, 610301 (2016).
[Crossref]

F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
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F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
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Lei, F.-C.

Li, B.-B.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
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Li, L.

J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-q microresonator,” Nat. Photonics 4, 122 (2009).
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Li, M.

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
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Li, Y.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
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Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
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Lipson, M.

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).
[Crossref] [PubMed]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[Crossref] [PubMed]

Liu, R.

Q. Cao, H. Wang, C. Dong, H. Jing, R. Liu, X. Chen, L. Ge, Q. Gong, and Y. Xiao, “Experimental demonstration of spontaneous chirality in a nonlinear microresonator,” Phys. Rev. Lett. 118, 033901 (2017).
[Crossref] [PubMed]

Liu, X.-F.

T. Wang, X.-F. Liu, Y. Hu, G. Qin, D. Ruan, and G.-L. Long, “Rapid and high precision measurement of opto-thermal relaxation with pump-probe method,” Sci. Bull. 63, 287–292 (2018).
[Crossref]

X.-F. Liu, F. Lei, M. Gao, X. Yang, G.-Q. Qin, and G.-L. Long, “Fabrication of a microtoroidal resonator with picometer precise resonant wavelength,” Opt. Lett. 41, 3603–3606 (2016).
[Crossref] [PubMed]

Liu, Y.-C.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012).
[Crossref]

Y.-F. Xiao, M. Li, Y.-C. Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).
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Long, G.

M. Gao, F. Lei, C. Du, and G. Long, “Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime,” Sci. China Physics, Mech. & Astron. 59, 610301 (2016).
[Crossref]

Long, G. L.

F. Lei, M. Gao, C. Du, S.-Y. Hou, X. Yang, and G. L. Long, “Engineering optomechanical normal modes for single-phonon transfer and entanglement preparation,” J. The Opt. Soc. Am. B-optical Phys. 32, 588–594 (2015).
[Crossref]

F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
[Crossref] [PubMed]

Long, G.-L.

T. Wang, M. Wang, Y.-Q. Hu, and G.-L. Long, “Optothermal control of the raman gain enhanced ringing in microresonators,” Europhys. Lett. 124, 14002 (2018).
[Crossref]

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C. Yang, Y. Hu, X. Jiang, and M. Xiao, “Analysis of a triple-cavity photonic molecule based on coupled-mode theory,” Phys. Rev. A 95, 033847 (2017).
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W. Chen, J. Zhang, B. Peng, Ş. K. Özdemir, X. Fan, and L. Yang, “Parity-time-symmetric whispering-gallery mode nanoparticle sensor,” Photonics Res. 6, A23–A30 (2018).
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B. Peng, Ş. K. Özdemir, W. Chen, F. Nori, and L. Yang, “What is and what is not electromagnetically induced transparency in whispering-gallery microcavities,” Nat. Commun. 5, 5082 (2014).
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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
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F. Lei, B. Peng, Ş. K. Özdemir, G. L. Long, and L. Yang, “Dynamic fano-like resonances in erbium-doped whispering-gallery-mode microresonators,” Appl. Phys. Lett. 105, 101112 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, J. Zhu, and L. Yang, “Photonic molecules formed by coupled hybrid resonators,” Opt. Lett. 37, 3435–3437 (2012).
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Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009).
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J. Zhu, Ş. K. Özdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-q microresonator,” Nat. Photonics 4, 122 (2009).
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M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93, 233903 (2004).
[Crossref] [PubMed]

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, 063827 (2015).
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Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery raman microlaser,” Proc. Natl. Acad. Sci. 111, E3836–E3844 (2014).
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A. Sohail, Y. Zhang, M. Usman, and C. Yu, “Controllable optomechanically induced transparency in coupled optomechanical systems,” The Eur. Phys. J. D 71, 103 (2017).
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Yu, C.-S.

A. Sohail, Y. Zhang, J. Zhang, and C.-S. Yu, “Optomechanically induced transparency in multi-cavity optomechanical system with and without one two-level atom,” Sci. Rep. 6, 28830 (2016).
[Crossref]

Zhang, J.

W. Chen, J. Zhang, B. Peng, Ş. K. Özdemir, X. Fan, and L. Yang, “Parity-time-symmetric whispering-gallery mode nanoparticle sensor,” Photonics Res. 6, A23–A30 (2018).
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A. Sohail, Y. Zhang, J. Zhang, and C.-S. Yu, “Optomechanically induced transparency in multi-cavity optomechanical system with and without one two-level atom,” Sci. Rep. 6, 28830 (2016).
[Crossref]

Zhang, J.-Q.

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Figures (5)

Fig. 1
Fig. 1 The schematic of the considered systems. (a) One master microcavity a0 and N slave microcavities are directly coupled via evanescent fields. And there are no interactions between neighboring slave microcavities. A fiber waveguide is side-coupled with the master microcavity for input and output. (b) Light is input and collected from the top fixed mirror. The optical mode simultaneously interacts with N movable highly refractive mirrors.
Fig. 2
Fig. 2 Sketched multiple level diagrams. (a) stands for the multiple coupled microcavities as in Fig. 1(a). The coupling lines means the interations between the master microcavity and slave microcavities. (b) represents the multiple mechanical oscillators coupling with the red detuned pump field and probe field as in Fig. 1(b). (c) shows the equivalence between (a) and (b) in the dressed states picture.
Fig. 3
Fig. 3 Illustration of experimental setup. PC, polarization controller; PD, photo detector. a0 and a1,, a2,, a3 represent the optical modes in microtoroid and microsphere respectively.
Fig. 4
Fig. 4 Observation of multiple EIT effects. The blue lines represent the experimental results. The red lines represent the numerical results. (d)-(f) are the imagine part of the transmission calculated from the theories in (a)-(c). The input wavelength is about 1541.2nm. The parameters of (a) are [Δ1, γ1, g1, k]/γ0 = [−0.028, 0.028, 0.097, 0.19], γ0 = 0.379 GHz. The parameters of (b) are [(Δ1, Δ2), (γ1, γ2), (g1, g2), k]/γ0 = [(−0.09, 0.172), (0.0217, 0.017), (0.058, 0.073), 0.25], γ0 = 0.624 GHz. The parameters of (c) are [(Δ1, Δ2, Δ3), (γ1, γ2, γ3), (g1, g2, g3), k]/γ0 = [(−0.15, 0.068, 0.394), (0.026, 0.02, 0.005), (0.056, 0.07, 0.1), 0.3], γ0 = 0.52 GHz.
Fig. 5
Fig. 5 Multiple EIA effects. the blue lines represent the experimental results. The red lines represent the numerical results.(a) stands for the EIA for N = 1 (b) stands for multiple EIA for N = 4. The parameters of (a) are [Δ1, g1, γ1, κ]/γ0=[0, 0.018, 0.017, 0.85], γ0=0.581 GHz. The parameters of (b) are [(Δ1, Δ2, Δ3, Δ4), (g1, g2, g3, g4), (γ1, γ2, γ3, γ4), κ]/γ0=[(-0.14, -0.024, 0.024, 0.096), (0.0086, 0.0048, 0.086, 0.021), (0.017, 0.0034, 0.0052, 0.0086), 0.881], γ0=0.58 GHz.

Equations (20)

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H = H 0 + H d
H 0 = j = 0 N ω j a j a j + j = 1 N g j ( a 0 a j + a 0 a j )
H d = i κ a i n a 0 e i ω t + H . c .
d a 0 d t = ( i Δ 0 γ 0 2 ) a 0 i j = 1 N g j a j κ a i n
d a j d t = ( i Δ j γ j 2 ) a j i g j a 0
t = a o u t a i n = 1 + κ i Δ 0 γ 0 / 2 + j = 1 N g j 2 i Δ j γ j / 2
H = H 0 + H d
H 0 = ω 0 a 0 a 0 + j = 1 N ( p j 2 2 m j + 1 2 m j ω j 2 q j 2 ) + j = 1 N g j a 0 a 0 q j + H d
H d = i κ Ω a 0 e i ω L t + i κ a i n a 0 e i ω s t + H . c .
d q j d t = p j m j
d p j d t = γ j p j m j ω j 2 q j g j | a 0 | 2
d a 0 d t = ( i Δ 0 κ 0 2 ) a 0 i j = 1 N g j q j a 0 κ Ω κ a i n e i δ t
m j ( d 2 d t 2 + γ j d d t + ω j 2 ) q j = g j ( a ¯ 0 * a 0 + a 0 * a ¯ 0 )
d a 0 d t = ( i Δ ¯ κ 0 2 ) a 0 i a ¯ 0 j = 1 N g j q j κ a i n e i δ t
a 0 = A e i δ t + A e i δ t
q j = X j e i δ t + X j * e i δ t
t = 1 + 1 + i ( j = 1 N f j ) i ( Δ ¯ + δ ) κ 0 / 2 2 Δ ¯ ( j = 1 N f j ) κ
f j = g j 2 | a ¯ 0 | 2 m j ( δ 2 i δ γ j + ω j 2 ) 1 i ( Δ ¯ δ ) + κ 0 / 2
t = 1 + κ i ( Δ ¯ + δ ) κ 0 / 2 + j = 1 N G j 2 i ( δ ω j ) γ j / 2
t = 1 + κ i ( Δ ¯ + δ ) κ 0 / 2 + G 0 2 i ( δ ω ) γ / 2

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