Abstract

We theoretically investigate the transmission and group delay of a probe field incident on a hybrid optomechanical system, which consists of a mechanical resonator simultaneously coupled to an optical cavity and a two-level system (qubit). The cavity field is driven by a strong red-detuned control field, and a weak coherent mechanical driving field is applied to the mechanical resonator. With the assistance of additional mechanical driving field, it is shown that double optomechanically induced transparency can be switched into absorption due to destructive interference or amplification because of constructive interference, which depends on the phase difference of the applied fields. We study in detail how to control the probe transmission by tuning the parameters of the optical and mechanical driving fields. Furthermore, we find that the group delay of the transmitted probe field can be prolonged by the tuning the amplitude and phase of the mechanical driving field.

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

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2019 (2)

S. C. Wu, L. G. Qin, J. Lu, and Z. Y. Wang, “Phase-dependent double optomechanically induced transparency in a hybrid optomechanical cavity system with coherently mechanical driving,” Chin. Phys. B 28(7), 074204 (2019).
[Crossref]

T. X. Lu, Y. F. Jiao, H. L. Zhang, F. Saif, and H. Jing, “Selective optomechanically-induced amplification with driven oscillators,” Phys. Rev. A 100(1), 013813 (2019).
[Crossref]

2018 (5)

D. B. Sohn, S. Kim, and G. Bahl, “Time-reversal symmetry breaking with acoustic pumping of nanophotonic circuits,” Nat. Photonics 12(2), 91–97 (2018).
[Crossref]

C. S. Muñoz, A. Lara, J. Puebla, and F. Nori, “Hybrid systems for the generation of nonclassical mechanical states via quadratic interactions,” Phys. Rev. Lett. 121(12), 123604 (2018).
[Crossref]

H. Lü, C. Q. Wang, L. Yang, and H. Jing, “Optomechanically induced transparency at exceptional points,” Phys. Rev. Appl. 10(1), 014006 (2018).
[Crossref]

H. Zhang, F. Saif, Y. Jiao, and H. Jing, “Loss-induced transparency in optomechanics,” Opt. Express 26(19), 25199–25210 (2018).
[Crossref]

Y.-F. Jiao, T.-X. Lu, and H. Jing, “Optomechanical second-order sidebands and group delays in a Kerr resonator,” Phys. Rev. A 97(1), 013843 (2018).
[Crossref]

2017 (10)

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nat. Phys. 13(5), 465–471 (2017).
[Crossref]

H. Lü, Y. Jiang, Y. Z. Wang, and H. Jing, “Optomechanically induced transparency in a spinning resonator,” Photonics Res. 5(4), 367 (2017).
[Crossref]

L. D. Tóth, N. R. Bernier, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg, “A dissipative quantum reservoir for microwave light using a mechanical oscillator,” Nat. Phys. 13(8), 787–793 (2017).
[Crossref]

H. Lü, S. K. Özdemir, L.-M. Kuang, F. Nori, and H. Jing, “Exceptional points in random-defect phonon lasers,” Phys. Rev. Appl. 8(4), 044020 (2017).
[Crossref]

C. Jiang, L. Jiang, H. L. Yu, Y. S. Cui, X. W. Li, and G. B. Chen, “Fano resonance and slow light in hybrid optomechanics mediated by a two-level system,” Phys. Rev. A 96(5), 053821 (2017).
[Crossref]

M. Cotrufo, A. Fiore, and E. Verhagen, “Coherent atom-phonon interaction through mode field coupling in hybrid optomechanical systems,” Phys. Rev. Lett. 118(13), 133603 (2017).
[Crossref]

J. Restrepo, I. Favero, and C. Ciuti, “Fully coupled hybrid cavity optomechanics: Quantum interferences and correlations,” Phys. Rev. A 95(2), 023832 (2017).
[Crossref]

C. Bekker, R. Kalra, C. Baker, and W. P. Bowen, “Injection locking of an electro-optomechanical device,” Optica 4(10), 1196–1204 (2017).
[Crossref]

L. G. Si, H. Xiong, M. Zubairy, and Y. Wu, “Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system,” Phys. Rev. A 95(3), 033803 (2017).
[Crossref]

Y. Li, Y. Y. Huang, X. Z. Zhang, and L. Tian, “Optical directional amplification in a three-mode optomechanical system,” Opt. Express 25(16), 18907 (2017).
[Crossref]

2016 (4)

C. Jiang, Y. S. Cui, X. T. Bian, F. Zuo, H. L. Yu, and G. B. Chen, “Phase-dependent multiple optomechanically induced absorption in multimode optomechanical systems with mechanical driving,” Phys. Rev. A 94(2), 023837 (2016).
[Crossref]

C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, T. T. Heikkilä, F. Massel, and M. A. Sillanpää, “Low-noise amplification and frequency conversion with a multiport microwave optomechanical device,” Phys. Rev. X 6(4), 041024 (2016).
[Crossref]

Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10(10), 657–661 (2016).
[Crossref]

Y. Jiao, H. Lü, J. Qian, Y. Li, and H. Jing, “Nonlinear optomechanics with gain and loss: amplifying higher-order sideband and group delay,” New J. Phys. 18(8), 083034 (2016).
[Crossref]

2015 (10)

M. J. Akram, M. M. Khan, and F. Saif, “Tunable fast and slow light in a hybrid optomechanical system,” Phys. Rev. A 92(2), 023846 (2015).
[Crossref]

H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X.-Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanicallyinduced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5(1), 9663 (2015).
[Crossref]

H. Xiong, L. G. Si, X. Y. Lv, 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. Astron. 58(5), 1–13 (2015).
[Crossref]

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6(1), 5850 (2015).
[Crossref]

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

J. Y. Ma, C. You, L. G. Si, H. Xiong, J. H. Li, X. X. Yang, and Y. Wu, “Optomechanically induced transparency in the presence of an external time-harmonic-driving force,” Sci. Rep. 5(1), 11278 (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.-M. Pirkkalainen, S. U. Cho, F. Massel, J. Tuorila, T. T. Heikkilä, P. J. Hakonen, and M. A. Sillanpää, “Cavity optomechanics mediated by a quantum two-level system,” Nat. Commun. 6(1), 6981 (2015).
[Crossref]

F. Lecocq, J. D. Teufel, J. Aumentado, and R. W. Simmonds, “Resolving the vacuum fluctuations of an optomechanical system using an artificial atom,” Nat. Phys. 11(8), 635–639 (2015).
[Crossref]

H. Wang, X. Gu, Y. X. Liu, A. Miranowicz, and F. Nori, “Tunable photon blockade in a hybrid system consisting of an optomechanical device coupled to a two-level system,” Phys. Rev. A 92(3), 033806 (2015).
[Crossref]

2014 (5)

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

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

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9(10), 820–824 (2014).
[Crossref]

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(4), 043825 (2014).
[Crossref]

H. Wang, X. Gu, Y. X. 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]

2013 (5)

Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111(8), 083601 (2013).
[Crossref]

Y. X. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110(22), 223603 (2013).
[Crossref]

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

T. Ramos, V. Sudhir, K. Stannigel, P. Zoller, and T. J. Kippenberg, “Nonlinear quantum optomechanics via individual intrinsic two-level defects,” Phys. Rev. Lett. 110(19), 193602 (2013).
[Crossref]

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9(11), 712–716 (2013).
[Crossref]

2012 (6)

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335(6076), 1603–1606 (2012).
[Crossref]

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

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

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(1), 1196 (2012).
[Crossref]

H. Xiong, L. G. Si, A. S. Zheng, X. Yang, and Y. Wu, “Higher-order sidebands in optomechanically induced transparency,” Phys. Rev. A 86(1), 013815 (2012).
[Crossref]

F. Hocke, X. Zhou, A. Schliesser, T. J. Kippenberg, H. Huebl, and R. Gross, “Electromechanically induced absorption in a circuit nano-electromechanical system,” New J. Phys. 14(12), 123037 (2012).
[Crossref]

2011 (4)

J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature (London) 471(7337), 204–208 (2011).
[Crossref]

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London) 480(7377), 351–354 (2011).
[Crossref]

O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, “A single nitrogen-vacancy defect coupled to a nanomechanical oscillator,” Nat. Phys. 7(11), 879–883 (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 (London) 472(7341), 69–73 (2011).
[Crossref]

2010 (3)

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

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

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature (London) 464(7289), 697–703 (2010).
[Crossref]

2009 (3)

M. D. LaHaye, J. Suh, P. M. Echternach, K. C. Schwab, and M. L. Roukes, “Nanomechanical measurements of a superconducting qubit,” Nature (London) 459(7249), 960–964 (2009).
[Crossref]

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[Crossref]

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

2007 (1)

P. Treutlein, D. Hunger, S. Camerer, T. W. Hänsch, and J. Reichel, “Bose-Einstein Condensate coupled to a nanomechanical resonator on an atom chip,” Phys. Rev. Lett. 99(14), 140403 (2007).
[Crossref]

2005 (2)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Y. Wu and X. X. Yang, “Electromagnetically induced transparency in $V-$V−, $\Lambda -$Λ−, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71(5), 053806 (2005).
[Crossref]

2004 (1)

I. Wilson-Rae, P. Zoller, and A. Imamoglu, “Laser Cooling of a nanomechanical resonator mode to its quantum ground state,” Phys. Rev. Lett. 92(7), 075507 (2004).
[Crossref]

2002 (1)

A. D. Armour, M. P. Blencowe, and K. C. Schwab, “Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-Pair Box,” Phys. Rev. Lett. 88(14), 148301 (2002).
[Crossref]

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]

Akram, M. J.

M. J. Akram, M. M. Khan, and F. Saif, “Tunable fast and slow light in a hybrid optomechanical system,” Phys. Rev. A 92(2), 023846 (2015).
[Crossref]

Aksyuk, V.

Y. X. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110(22), 223603 (2013).
[Crossref]

Allman, M. S.

J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature (London) 471(7337), 204–208 (2011).
[Crossref]

Ansmann, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature (London) 464(7289), 697–703 (2010).
[Crossref]

Arcizet, O.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, “A single nitrogen-vacancy defect coupled to a nanomechanical oscillator,” Nat. Phys. 7(11), 879–883 (2011).
[Crossref]

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

Armour, A. D.

A. D. Armour, M. P. Blencowe, and K. C. Schwab, “Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-Pair Box,” Phys. Rev. Lett. 88(14), 148301 (2002).
[Crossref]

Aspelmeyer, M.

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

Auffèves, A.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Aumentado, J.

F. Lecocq, J. D. Teufel, J. Aumentado, and R. W. Simmonds, “Resolving the vacuum fluctuations of an optomechanical system using an artificial atom,” Nat. Phys. 11(8), 635–639 (2015).
[Crossref]

Awschalom, D. D.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9(11), 712–716 (2013).
[Crossref]

Bahl, G.

D. B. Sohn, S. Kim, and G. Bahl, “Time-reversal symmetry breaking with acoustic pumping of nanophotonic circuits,” Nat. Photonics 12(2), 91–97 (2018).
[Crossref]

Baker, C.

Bekker, C.

Bennett, S. D.

S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. G. E. Harris, and M. D. Lukin, “Coherent sensing of a mechanical resonator with a single-spin qubit,” Science 335(6076), 1603–1606 (2012).
[Crossref]

Bernier, N. R.

L. D. Tóth, N. R. Bernier, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg, “A dissipative quantum reservoir for microwave light using a mechanical oscillator,” Nat. Phys. 13(8), 787–793 (2017).
[Crossref]

Bialczak, R. C.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature (London) 464(7289), 697–703 (2010).
[Crossref]

Bian, X. T.

C. Jiang, Y. S. Cui, X. T. Bian, F. Zuo, H. L. Yu, and G. B. Chen, “Phase-dependent multiple optomechanically induced absorption in multimode optomechanical systems with mechanical driving,” Phys. Rev. A 94(2), 023837 (2016).
[Crossref]

Blanter, Y. M.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9(10), 820–824 (2014).
[Crossref]

Blencowe, M. P.

A. D. Armour, M. P. Blencowe, and K. C. Schwab, “Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-Pair Box,” Phys. Rev. Lett. 88(14), 148301 (2002).
[Crossref]

Bochmann, J.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9(11), 712–716 (2013).
[Crossref]

Bosman, S. J.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9(10), 820–824 (2014).
[Crossref]

Bowen, W. P.

Camerer, S.

P. Treutlein, D. Hunger, S. Camerer, T. W. Hänsch, and J. Reichel, “Bose-Einstein Condensate coupled to a nanomechanical resonator on an atom chip,” Phys. Rev. Lett. 99(14), 140403 (2007).
[Crossref]

Cappellaro, P.

P. Rabl, P. Cappellaro, M. V. Gurudev Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, “Strong magnetic coupling between an electronic spin qubit and a mechanical resonator,” Phys. Rev. B 79(4), 041302 (2009).
[Crossref]

Castellanos-Gomez, A.

V. Singh, S. J. Bosman, B. H. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. A. Steele, “Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity,” Nat. Nanotechnol. 9(10), 820–824 (2014).
[Crossref]

Chan, J.

J. T. Hill, A. H. Safavi-Naeini, J. Chan, and O. Painter, “Coherent optical wavelength conversion via cavity optomechanics,” Nat. Commun. 3(1), 1196 (2012).
[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 (London) 472(7341), 69–73 (2011).
[Crossref]

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 (London) 472(7341), 69–73 (2011).
[Crossref]

Chen, B.

Chen, G. B.

C. Jiang, L. Jiang, H. L. Yu, Y. S. Cui, X. W. Li, and G. B. Chen, “Fano resonance and slow light in hybrid optomechanics mediated by a two-level system,” Phys. Rev. A 96(5), 053821 (2017).
[Crossref]

C. Jiang, Y. S. Cui, X. T. Bian, F. Zuo, H. L. Yu, and G. B. Chen, “Phase-dependent multiple optomechanically induced absorption in multimode optomechanical systems with mechanical driving,” Phys. Rev. A 94(2), 023837 (2016).
[Crossref]

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

Chen, Y.

Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10(10), 657–661 (2016).
[Crossref]

Chen, Y. L.

Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111(8), 083601 (2013).
[Crossref]

Cho, S. U.

J.-M. Pirkkalainen, S. U. Cho, F. Massel, J. Tuorila, T. T. Heikkilä, P. J. Hakonen, and M. A. Sillanpää, “Cavity optomechanics mediated by a quantum two-level system,” Nat. Commun. 6(1), 6981 (2015).
[Crossref]

F. Massel, T. T. Heikkilä, J.-M. Pirkkalainen, S. U. Cho, H. Saloniemi, P. J. Hakonen, and M. A. Sillanpää, “Microwave amplification with nanomechanical resonators,” Nature (London) 480(7377), 351–354 (2011).
[Crossref]

Cicak, K.

J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, and R. W. Simmonds, “Circuit cavity electromechanics in the strong-coupling regime,” Nature (London) 471(7337), 204–208 (2011).
[Crossref]

Ciuti, C.

J. Restrepo, I. Favero, and C. Ciuti, “Fully coupled hybrid cavity optomechanics: Quantum interferences and correlations,” Phys. Rev. A 95(2), 023832 (2017).
[Crossref]

Claudon, J.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Cleland, A. N.

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9(11), 712–716 (2013).
[Crossref]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature (London) 464(7289), 697–703 (2010).
[Crossref]

Clerk, A. A.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nat. Phys. 13(5), 465–471 (2017).
[Crossref]

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

Cotrufo, M.

M. Cotrufo, A. Fiore, and E. Verhagen, “Coherent atom-phonon interaction through mode field coupling in hybrid optomechanical systems,” Phys. Rev. Lett. 118(13), 133603 (2017).
[Crossref]

Cui, Y. S.

C. Jiang, L. Jiang, H. L. Yu, Y. S. Cui, X. W. Li, and G. B. Chen, “Fano resonance and slow light in hybrid optomechanics mediated by a two-level system,” Phys. Rev. A 96(5), 053821 (2017).
[Crossref]

C. Jiang, Y. S. Cui, X. T. Bian, F. Zuo, H. L. Yu, and G. B. Chen, “Phase-dependent multiple optomechanically induced absorption in multimode optomechanical systems with mechanical driving,” Phys. Rev. A 94(2), 023837 (2016).
[Crossref]

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

Damskägg, E.

C. F. Ockeloen-Korppi, E. Damskägg, J.-M. Pirkkalainen, T. T. Heikkilä, F. Massel, and M. A. Sillanpää, “Low-noise amplification and frequency conversion with a multiport microwave optomechanical device,” Phys. Rev. X 6(4), 041024 (2016).
[Crossref]

Davanço, M.

Y. X. Liu, M. Davanço, V. Aksyuk, and K. Srinivasan, “Electromagnetically induced transparency and wideband wavelength conversion in silicon nitride microdisk optomechanical resonators,” Phys. Rev. Lett. 110(22), 223603 (2013).
[Crossref]

de Assis, P-L.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Deléglise, S.

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

Dong, C. H.

Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10(10), 657–661 (2016).
[Crossref]

Dupont-Ferrier, E.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Dupuy, E.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Echternach, P. M.

M. D. LaHaye, J. Suh, P. M. Echternach, K. C. Schwab, and M. L. Roukes, “Nanomechanical measurements of a superconducting qubit,” Nature (London) 459(7249), 960–964 (2009).
[Crossref]

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 (London) 472(7341), 69–73 (2011).
[Crossref]

Fan, L.

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6(1), 5850 (2015).
[Crossref]

Fang, K.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized nonreciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nat. Phys. 13(5), 465–471 (2017).
[Crossref]

Favero, I.

J. Restrepo, I. Favero, and C. Ciuti, “Fully coupled hybrid cavity optomechanics: Quantum interferences and correlations,” Phys. Rev. A 95(2), 023832 (2017).
[Crossref]

Feng, M.

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(4), 043825 (2014).
[Crossref]

Feofanov, A. K.

L. D. Tóth, N. R. Bernier, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg, “A dissipative quantum reservoir for microwave light using a mechanical oscillator,” Nat. Phys. 13(8), 787–793 (2017).
[Crossref]

Fiore, A.

M. Cotrufo, A. Fiore, and E. Verhagen, “Coherent atom-phonon interaction through mode field coupling in hybrid optomechanical systems,” Phys. Rev. Lett. 118(13), 133603 (2017).
[Crossref]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Fong, K. Y.

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6(1), 5850 (2015).
[Crossref]

Gavartin, E.

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

Geng, Z.

H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X.-Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanicallyinduced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5(1), 9663 (2015).
[Crossref]

Gérard, J-M.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Girvin, S. M.

F. Marquardt and S. M. Girvin, “Optomechanics,” Physics 2, 40 (2009).
[Crossref]

Gloppe, A.

I. Yeo, P-L. de Assis, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, J-M. Gérard, A. Auffèves, G. Nogues, S. Seidelin, J-Ph. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system,” Nat. Nanotechnol. 9(2), 106–110 (2014).
[Crossref]

Gong, Q.

Y. C. Liu, Y. F. Xiao, Y. L. Chen, X. C. Yu, and Q. Gong, “Parametric down-conversion and polariton pair generation in optomechanical systems,” Phys. Rev. Lett. 111(8), 083601 (2013).
[Crossref]

Gross, R.

F. Hocke, X. Zhou, A. Schliesser, T. J. Kippenberg, H. Huebl, and R. Gross, “Electromechanically induced absorption in a circuit nano-electromechanical system,” New J. Phys. 14(12), 123037 (2012).
[Crossref]

Gu, X.

H. Wang, X. Gu, Y. X. Liu, A. Miranowicz, and F. Nori, “Tunable photon blockade in a hybrid system consisting of an optomechanical device coupled to a two-level system,” Phys. Rev. A 92(3), 033806 (2015).
[Crossref]

H. Wang, X. Gu, Y. X. 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]

Guo, G. C.

Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10(10), 657–661 (2016).
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[Crossref]

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[Crossref]

Xiao, Y.

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(4), 043825 (2014).
[Crossref]

Xiao, Y. F.

Z. Shen, Y. L. Zhang, Y. Chen, C. L. Zou, Y. F. Xiao, X. B. Zou, F. W. Sun, G. C. Guo, and C. H. Dong, “Experimental realization of optomechanically induced non-reciprocity,” Nat. Photonics 10(10), 657–661 (2016).
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[Crossref]

Xiong, H.

L. G. Si, H. Xiong, M. Zubairy, and Y. Wu, “Optomechanically induced opacity and amplification in a quadratically coupled optomechanical system,” Phys. Rev. A 95(3), 033803 (2017).
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H. Xiong, L. G. Si, X. Y. Lv, 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. Astron. 58(5), 1–13 (2015).
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X. W. Xu and Y. Li, “Controllable optical output fields from an optomechanical system with mechanical driving,” Phys. Rev. A 92(2), 023855 (2015).
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H. Lü, C. Q. Wang, L. Yang, and H. Jing, “Optomechanically induced transparency at exceptional points,” Phys. Rev. Appl. 10(1), 014006 (2018).
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Figures (8)

Fig. 1.
Fig. 1. (a) Schematic diagram of the hybrid optomechanical system. One mirror of the optomechanical cavity is fixed and another vibrating mirror, treated as a mechanical resonator, is coupled to a two-level system (qubit). The cavity is driven by a strong control field at frequency $\omega _c$ and a weak probe field at frequency $\omega _p$, and $a_{\mathrm {out}}$ represents the output field of the cavity. The mechanical resonator is excited by a weak coherent mechanical driving field at frequency $\Omega =\omega _p-\omega _c$. (b) Energy-level diagram of the hybrid system where the two-level system is resonant with the mechanical resonator. A weak probe field scans the transition between $|0_a,0_m\rangle$ and $|1_a,0_m\rangle$, where the population of the mechanical mode is unchanged with $a$ and $m$ representing the cavity and mechanical modes, respectively. The coupling between the qubit and the mechanical resonator gives rise to the dressed states $|0_a,1_m+\rangle$ and $|0_a,1_m-\rangle$.
Fig. 2.
Fig. 2. Contour plot of the probe transmission $|t_p|^2$ versus the phase difference $\phi /\pi$ and probe-control field detuning $\Omega /\omega _m$. Other parameters are $\omega _m/2\pi =\omega _q/2\pi =100$ MHz, $\kappa /2\pi =8$ MHz, $\eta =0.45$, $\gamma _m/2\pi =2$ kHz, $\gamma _q/2\pi =0.1$ MHz, $g/2\pi =10$ MHz, $J/2\pi =1$ MHz, $\Delta _a=\omega _m$, $\varepsilon _c/2\pi =10$ MHz, and $r=0.2$.
Fig. 3.
Fig. 3. Plots of $|t_1|^2$, $|t_2|^2$, and $|t_p|^2$ as a function of the probe-control field detuning $\Omega /\omega _m$ when the phase difference $\phi$ equals to (a) 0 and (b) $\pi$, respectively. The inset of Fig. 3(b) shows the probe transmission $|t_p|^2$ at $\Omega =\omega _m+J$ as a function of the phase difference $\phi /\pi$. The other parameters are the same as those in Fig. 2
Fig. 4.
Fig. 4. Plots of $|t_1|^2$, $|t_2|^2$, and $|t_p|^2$ at $\Omega =\omega _m+J$ as a function of $r=\varepsilon _m/\varepsilon _p$ for (a) $\phi =0$ and (b) $\phi =\pi$. The other parameters are the same as those in Fig. 2.
Fig. 5.
Fig. 5. Probe transmission $|t_1|^2$, $|t_2|^2$, and $|t_p|^2$ at $\Omega =\omega _m+J$ as a function of the control field amplitude $\varepsilon _c/2\pi$ for different values of mechanical driving field. The other parameters are the same as those in Fig. 4.
Fig. 6.
Fig. 6. Group delay $\tau _g$ of the transmitted probe field as a function of the control field amplitude $\varepsilon _c/2\pi$ for different values of mechanical driving field. The other parameters are the same as those in Fig. 5.
Fig. 7.
Fig. 7. Group delay $\tau _g$ as a function of $r=\varepsilon _m/\varepsilon _p$ for different values of phase difference $\phi$. The inset of Fig. 7 shows the group delay $\tau _g$ versus the phase difference $\phi$ with $r=0.3$. The other parameters are the same as those in Fig. 4 except $\varepsilon _c/2\pi =4$ MHz.
Fig. 8.
Fig. 8. (a) Probe transmission $|t_p|^2$ and (b) Group delay $\tau _g$ at $\Omega =\omega _m+J$ as a function of the decay rate $\gamma _q/2\pi$ for different values of the coupling strength $J$. The other parameters are the same as those in Fig. 7 except $r=0.3$ and $\phi =\pi$.

Equations (26)

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H d r = i ε c ( a e i ω c t i ϕ c a e i ω c t + i ϕ c ) + i ε p ( a e i ω p t i ϕ p a e i ω p t + i ϕ p ) + i ε m ( b e i Ω t i ϕ m b e i Ω t + i ϕ m ) ,
H = Δ a a a + ω m b b + 2 ω q σ z + H o m + H J C + i ε c ( a a ) + i ε p ( a e i Ω t i ϕ p c a e i Ω t + i ϕ p c ) + i ε m ( b e i Ω t i ϕ m b e i Ω t + i ϕ m ) ,
a ˙ = ( κ / 2 + i Δ a ) a + i g ( b + b ) a + ε c + ε p e i Ω t i ϕ p c + κ a i n ( t ) ,
b ˙ = ( γ m / 2 + i ω m ) b + i g a a i J σ + ε m e i Ω t i ϕ m + γ m b i n ( t ) ,
σ ˙ = ( γ q / 2 + i ω q ) σ + i J b σ z + γ q c , i n ( t ) ,
σ z ˙ = γ q ( σ z + 1 ) 2 i J ( b σ + b σ ) + γ q c z , i n ( t ) ,
α = a s = ε c κ / 2 + i Δ a ,
β = b s = i g | α | 2 i J L 0 γ m / 2 + i ω m ,
L 0 = σ s = i J β W 0 γ q / 2 + i ω q ,
W 0 = σ z s = γ q 2 + 4 ω q 2 γ q 2 + 4 ω q 2 + 8 J 2 β 2 ,
| α | 2 { ( κ 2 ) 2 + [ Δ a 2 g 2 | α | 2 ( 2 ω q ϵ 1 + γ q ϵ 2 ) ϵ 1 2 + ϵ 2 2 ] 2 } = ε c 2 ,
| β | 2 ( ϵ 1 2 + ϵ 2 2 ) 2 = g 2 | α | 4 [ ( 2 ω q ϵ 1 + γ q ϵ 2 ) 2 + ( γ q ϵ 1 2 ω q ϵ 2 ) 2 ] ,
δ a ˙ = ( κ / 2 + i Δ a ) δ a + i G ( δ b + δ b ) + ε p e i Ω t i ϕ p c + κ a i n ( t ) ,
δ b ˙ = ( γ m / 2 + i ω m ) δ b + i ( G δ a + G δ a ) i J δ σ + ε m e i Ω t i ϕ m + γ m b i n ( t ) ,
δ σ ˙ = ( γ q / 2 + i ω q ) δ σ + i J ( β δ σ z + W 0 δ b ) + γ q c , i n ( t ) ,
δ σ z ˙ = γ q δ σ z 2 i J ( β δ σ + + L 0 δ b β δ σ L 0 δ b ) + γ q c z , i n ( t ) ,
δ a ˙ = Γ a δ a + i G δ b + ε p e i ϕ p c + κ a i n ( t ) ,
δ b ˙ = Γ m δ b + i G δ a i J δ σ + ε m e i ϕ m + γ m b i n ( t ) ,
δ σ ˙ = Γ δ σ + i J ( β δ σ z + W 0 δ b ) + γ q c , i n ( t ) ,
δ σ z ˙ = Γ q δ σ z 2 i J ( L 0 δ b β δ σ ) + γ q c z , i n ( t ) ,
δ a = ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) ε p e i ϕ p c + i G Θ ε m e i ϕ m Γ a ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) + | G | 2 Θ ,
t p = κ e δ a ε p e i ϕ p c ε p e i ϕ p c = t 1 + t 2
t 1 = ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) κ e Γ a ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) + | G | 2 Θ 1 ,
t 2 = i G Θ κ e r e i ϕ Γ a ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) + | G | 2 Θ ,
r | T P = | ( κ e Γ a ) ( Γ m Θ + 2 i β L 0 J 3 W 0 Γ q J 2 ) | G | 2 Θ G Θ κ e | ,
τ g = d ϕ t ( ω p ) d ω p = d { a r g [ t p ( ω p ) ] } d ω p .

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