Abstract

We study optomechanically induced transparency (OMIT) in a compound system consisting of coupled optical resonators and a mechanical mode, focusing on the unconventional role of loss. We find that optical transparency can emerge at the otherwise strongly absorptive regime in the OMIT spectrum, by using an external nanotip to enhance the optical loss. In particular, loss-induced revival of optical transparency and the associated slow-to-fast light switch can be identified in the vicinity of an exceptional point. These results open up a counterintuitive way to engineer micro-mechanical devices with tunable losses for e.g., coherent optical switch and communications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (6)

L. Midolo, A. Schliesser, and A. Fiore, “Nano-opto-electro-mechanical systems,” Nat. Nanotechnol. 13(1), 11–18 (2018).
[Crossref] [PubMed]

J. Zhang, B. Peng, Ş. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y. Liu, S. Rotter, and L. Yang, “A phonon laser operating at an exceptional point,” Nat. Photonics 12(8), 479–484 (2018).
[Crossref]

K. Ullah, H. Jing, and F. Saif, “Multiple electromechanically-induced-transparency windows and Fano resonances in hybrid nano-electro-optomechanics,” Phys. Rev. A 97(3), 033812 (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]

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and 𝒫𝒯 symmetry,” Nat. Phys. 14(1), 11–19 (2018).
[Crossref]

A. U. Hassan, H. Hodaei, D. N. Christodoulides, and M. Khajavikhan, “Exceptional points: an emerging tool for sensor applications,” Optics & Photonics News 2018(01), 20–22 (2018).

2017 (8)

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
[Crossref] [PubMed]

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
[Crossref] [PubMed]

L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11(12), 752–762 (2017).
[Crossref]

H. Jing, Ş. K. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref] [PubMed]

H. Xiong, L.-G. Si, and Y. Wu, “Precision measurement of electrical charges in an optomechanical system beyond linearized dynamics,” Appl. Phys. Lett. 110(17), 171102 (2017).
[Crossref]

H. Lü, Y. Jiang, Y. Z. Wang, and H. Jing, “Optomechanically induced transparency in a spinning resonator,” Photonics Res. 5(4), 367–371 (2017).
[Crossref]

H. Lü, Ş. 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]

Y.-C. Liu, B.-B. Li, and Y.-F. Xiao, “Electromagnetically induced transparency in optical microcavities,” Nanophotonics 6(5), 789–811 (2017).
[Crossref]

2016 (7)

Z.-P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X.-Y. Lü, C.-W. Li, L. Yang, F. Nori, and Y. Liu, “Metrology with 𝒫𝒯-symmetric cavities: Enhanced sensitivity near the 𝒫𝒯-phase transition,” Phys. Rev. Lett. 117(11), 110802 (2016).
[Crossref] [PubMed]

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, 083034 (2016).
[Crossref]

G. Li, X. Jiang, S. Hua, Y. Qin, and M. Xiao, “Optomechanically tuned electromagnetically induced transparency-like effect in coupled optical microcavities,” Appl. Phys. Lett. 109(26), 261106 (2016).
[Crossref]

H. Xu, D. Mason, L. Jiang, and J. G. E. Harris, “Topological energy transfer in an optomechanical system with exceptional points,” Nature 537(7618), 80–83 (2016).
[Crossref] [PubMed]

V. V. Konotop, J. Yang, and D. A. Zezyulin, “Nonlinear waves in 𝒫𝒯-symmetric systems,” Rev. Mod. Phys. 88(3), 035002 (2016).
[Crossref]

R. Dahan, L. L. Martin, and T. Carmon, “Droplet optomechanics,” Optica 3(2), 175–178 (2016).
[Crossref]

Z. Shen, C.-H. Dong, Y. Chen, Y.-F. Xiao, F.-W. Sun, and G.-C. Guo, “Compensation of the Kerr effect for transient optomechanically induced transparency in a silica microsphere,” Opt. Lett. 41(6), 1249–1252 (2016).
[Crossref] [PubMed]

2015 (6)

X.-Y. Lü, H. Jing, J.-Y. Ma, and Y. Wu, “𝒫𝒯-symmetry-breaking chaos in optomechanics,” Phys. Rev. Lett. 114(25), 253601 (2015).
[Crossref]

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

Y.-C. Liu, Y.-F. Xiao, X.-S. Luan, and W. C. Wei, “Optomechanically-induced-transparency cooling of massive mechanical resonators to the quantum ground state,” Sci. China-Phys. Mech. Astron. 58(5), 050305 (2015).
[Crossref]

J. Zhang, B. Peng, Ş. K. Özdemir, Y. Liu, H. Jing, X. Lü, Y. Liu, L. Yang, and F. Nori, “Giant nonlinearity via breaking parity-time symmetry: A route to low-threshold phonon diodes,” Phys. Rev. B 92(11), 115407 (2015).
[Crossref]

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

E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. C. Schwab, “Quantum squeezing of motion in a mechanical resonator,” Science 349(6251), 952–955 (2015).
[Crossref] [PubMed]

2014 (11)

H. Jing, Ş. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “𝒫𝒯-symmetric phonon laser,” Phys. Rev. Lett. 113(5), 053604 (2014).
[Crossref] [PubMed]

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]

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

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

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics 8(7), 524–529 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

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

M. Metcalfe, “Applications of cavity optomechanics,” App. Phys. Rev. 1(3), 031105 (2014).
[Crossref]

C. Dong, J. Zhang, V. Fiore, and H. Wang, “Optomechanically induced transparency and self-induced oscillations with Bogoliubov mechanical modes,” Optica 1(6), 425–428 (2014).
[Crossref]

A. A. Zyablovsky, A. P. Vinogradov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “𝒫𝒯-symmetry in optics,” Phys. Usp. 57(11), 1063–1082 (2014).
[Crossref]

2013 (7)

T. Oishi and M. Tomita, “Inverted coupled-resonator-induced transparency,” Phys. Rev. A 88(1), 013813 (2013).
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C. M. Bender, M. Gianfreda, Ş. K. Özdemir, B. Peng, and L. Yang, “Twofold transition in 𝒫𝒯-symmetric coupled oscillators,” Phys. Rev. A 88(6), 062111 (2013).
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X.-W. Xu and Y.-J. Li, “Antibunching photons in a cavity coupled to an optomechanical system,” J. Phys. B: At. Mol. Opt. Phys. 46(3), 035502 (2013).
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V. Fiore, C. Dong, M. C. Kuzyk, and H. Wang, “Optomechanical light storage in a silica microresonator,” Phys. Rev. A 87(2), 023812 (2013).
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M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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A. Kronwald and F. Marquardt, “Optomechanically induced transparency in the nonlinear quantum regime,” Phys. Rev. Lett. 111(13), 133601 (2013).
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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).
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2012 (6)

A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
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E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
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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).
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J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86(5), 053806 (2012).
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D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in finite-dimensional 𝒫𝒯-symmetric systems,” Phys. Rev. Lett. 108(21), 213906 (2012).
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J. Fan and L. Zhu, “Enhanced optomechanical interaction in coupled microresonators,” Opt. Express 20(18), 20790 (2012).
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2011 (2)

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

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 471(7337), 204–208 (2011).
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2010 (5)

G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
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S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330(6010), 1520–1523 (2010).
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P. Rabl, S. J. Kolkowitz, F. H. L. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nanoelectromechanical resonator arrays,” Nat. Phys. 6(8), 602–608 (2010).
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I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
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J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).
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2009 (1)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
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2008 (2)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
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F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science 322(5899), 235–238 (2008).
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2007 (1)

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007).
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1998 (1)

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having 𝒫𝒯 symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
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1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593 (1991).
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1985 (1)

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G. S. Agarwal and S. Huang, “Electromagnetically induced transparency in mechanical effects of light,” Phys. Rev. A 81(4), 041803 (2010).
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A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
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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 471(7337), 204–208 (2011).
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Arcizet, O.

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).
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Aspelmeyer, M.

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

M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
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B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
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C. M. Bender, M. Gianfreda, Ş. K. Özdemir, B. Peng, and L. Yang, “Twofold transition in 𝒫𝒯-symmetric coupled oscillators,” Phys. Rev. A 88(6), 062111 (2013).
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C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007).
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C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having 𝒫𝒯 symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
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M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6(11), 768–772 (2012).
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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).
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C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having 𝒫𝒯 symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
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K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593 (1991).
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T. Ojanen and K. Børkje, “Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency,” Phys. Rev. A 90(1), 013824 (2014).
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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(7341), 69–73 (2011).
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L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics 8(7), 524–529 (2014).
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A. U. Hassan, H. Hodaei, D. N. Christodoulides, and M. Khajavikhan, “Exceptional points: an emerging tool for sensor applications,” Optics & Photonics News 2018(01), 20–22 (2018).

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
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A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
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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 471(7337), 204–208 (2011).
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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).
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C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31(6), 3761–3774 (1985).
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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(6010), 1520–1523 (2010).
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M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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Dong, C.

C. Dong, J. Zhang, V. Fiore, and H. Wang, “Optomechanically induced transparency and self-induced oscillations with Bogoliubov mechanical modes,” Optica 1(6), 425–428 (2014).
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V. Fiore, C. Dong, M. C. Kuzyk, and H. Wang, “Optomechanical light storage in a silica microresonator,” Phys. Rev. A 87(2), 023812 (2013).
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Dong, C.-H.

Donner, T.

F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science 322(5899), 235–238 (2008).
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A. A. Zyablovsky, A. P. Vinogradov, A. A. Pukhov, A. V. Dorofeenko, and A. A. Lisyansky, “𝒫𝒯-symmetry in optics,” Phys. Usp. 57(11), 1063–1082 (2014).
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A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009).
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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(7341), 69–73 (2011).
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R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, “Non-Hermitian physics and 𝒫𝒯 symmetry,” Nat. Phys. 14(1), 11–19 (2018).
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L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11(12), 752–762 (2017).
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H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
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F. Brennecke, S. Ritter, T. Donner, and T. Esslinger, “Cavity optomechanics with a Bose-Einstein condensate,” Science 322(5899), 235–238 (2008).
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Fan, L.

L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
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B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
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L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11(12), 752–762 (2017).
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Feng, M.

J. Q. Zhang, Y. Li, M. Feng, and Y. Xu, “Precision measurement of electrical charge with optomechanically induced transparency,” Phys. Rev. A 86(5), 053806 (2012).
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L. Midolo, A. Schliesser, and A. Fiore, “Nano-opto-electro-mechanical systems,” Nat. Nanotechnol. 13(1), 11–18 (2018).
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C. Dong, J. Zhang, V. Fiore, and H. Wang, “Optomechanically induced transparency and self-induced oscillations with Bogoliubov mechanical modes,” Optica 1(6), 425–428 (2014).
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V. Fiore, C. Dong, M. C. Kuzyk, and H. Wang, “Optomechanical light storage in a silica microresonator,” Phys. Rev. A 87(2), 023812 (2013).
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L. Fan, K. Y. Fong, M. Poot, and H. X. Tang, “Cascaded optical transparency in multimode-cavity optomechanical systems,” Nat. Commun. 6, 5850 (2015).
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M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
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C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation,” Phys. Rev. A 31(6), 3761–3774 (1985).
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E. Gavartin, P. Verlot, and T. J. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7(8), 509–514 (2012).
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L. Feng, R. El-Ganainy, and L. Ge, “Non-Hermitian photonics based on parity-time symmetry,” Nat. Photonics 11(12), 752–762 (2017).
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C. M. Bender, M. Gianfreda, Ş. K. Özdemir, B. Peng, and L. Yang, “Twofold transition in 𝒫𝒯-symmetric coupled oscillators,” Phys. Rev. A 88(6), 062111 (2013).
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I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
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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).
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A. U. Hassan, H. Hodaei, D. N. Christodoulides, and M. Khajavikhan, “Exceptional points: an emerging tool for sensor applications,” Optics & Photonics News 2018(01), 20–22 (2018).

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
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He, L.

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(7341), 69–73 (2011).
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A. U. Hassan, H. Hodaei, D. N. Christodoulides, and M. Khajavikhan, “Exceptional points: an emerging tool for sensor applications,” Optics & Photonics News 2018(01), 20–22 (2018).

H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, “Enhanced sensitivity at higher-order exceptional points,” Nature 548(7666), 187–191 (2017).
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L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photonics 8(7), 524–529 (2014).
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Yang, J.

V. V. Konotop, J. Yang, and D. A. Zezyulin, “Nonlinear waves in 𝒫𝒯-symmetric systems,” Rev. Mod. Phys. 88(3), 035002 (2016).
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Yang, L.

J. Zhang, B. Peng, Ş. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y. Liu, S. Rotter, and L. Yang, “A phonon laser operating at an exceptional point,” Nat. Photonics 12(8), 479–484 (2018).
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W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
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Z.-P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X.-Y. Lü, C.-W. Li, L. Yang, F. Nori, and Y. Liu, “Metrology with 𝒫𝒯-symmetric cavities: Enhanced sensitivity near the 𝒫𝒯-phase transition,” Phys. Rev. Lett. 117(11), 110802 (2016).
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J. Zhang, B. Peng, Ş. K. Özdemir, Y. Liu, H. Jing, X. Lü, Y. Liu, L. Yang, and F. Nori, “Giant nonlinearity via breaking parity-time symmetry: A route to low-threshold phonon diodes,” Phys. Rev. B 92(11), 115407 (2015).
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H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 9663 (2015).
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B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
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B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
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H. Jing, Ş. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “𝒫𝒯-symmetric phonon laser,” Phys. Rev. Lett. 113(5), 053604 (2014).
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C. M. Bender, M. Gianfreda, Ş. K. Özdemir, B. Peng, and L. Yang, “Twofold transition in 𝒫𝒯-symmetric coupled oscillators,” Phys. Rev. A 88(6), 062111 (2013).
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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).
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Yilmaz, H.

B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
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Zezyulin, D. A.

V. V. Konotop, J. Yang, and D. A. Zezyulin, “Nonlinear waves in 𝒫𝒯-symmetric systems,” Rev. Mod. Phys. 88(3), 035002 (2016).
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D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in finite-dimensional 𝒫𝒯-symmetric systems,” Phys. Rev. Lett. 108(21), 213906 (2012).
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J. Zhang, B. Peng, Ş. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y. Liu, S. Rotter, and L. Yang, “A phonon laser operating at an exceptional point,” Nat. Photonics 12(8), 479–484 (2018).
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Z.-P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X.-Y. Lü, C.-W. Li, L. Yang, F. Nori, and Y. Liu, “Metrology with 𝒫𝒯-symmetric cavities: Enhanced sensitivity near the 𝒫𝒯-phase transition,” Phys. Rev. Lett. 117(11), 110802 (2016).
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H. Jing, Ş. K. Özdemir, Z. Geng, J. Zhang, X. Y. Lü, B. Peng, L. Yang, and F. Nori, “Optomechanically-induced transparency in parity-time-symmetric microresonators,” Sci. Rep. 5, 9663 (2015).
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J. Zhang, B. Peng, Ş. K. Özdemir, Y. Liu, H. Jing, X. Lü, Y. Liu, L. Yang, and F. Nori, “Giant nonlinearity via breaking parity-time symmetry: A route to low-threshold phonon diodes,” Phys. Rev. B 92(11), 115407 (2015).
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H. Jing, Ş. K. Özdemir, X. Y. Lü, J. Zhang, L. Yang, and F. Nori, “𝒫𝒯-symmetric phonon laser,” Phys. Rev. Lett. 113(5), 053604 (2014).
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W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548(7666), 192–196 (2017).
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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).
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B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
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P. Rabl, S. J. Kolkowitz, F. H. L. Koppens, J. G. E. Harris, P. Zoller, and M. D. Lukin, “A quantum spin transducer based on nanoelectromechanical resonator arrays,” Nat. Phys. 6(8), 602–608 (2010).
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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, 083034 (2016).
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Optics & Photonics News (1)

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M. Karuza, C. Biancofiore, M. Bawaj, C. Molinelli, M. Galassi, R. Natali, P. Tombesi, G. Di Giuseppe, and D. Vitali, “Optomechanically induced transparency in a membrane-in-the-middle setup at room temperature,” Phys. Rev. A 88(1), 013804 (2013).
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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).
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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).
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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).
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K. Ullah, H. Jing, and F. Saif, “Multiple electromechanically-induced-transparency windows and Fano resonances in hybrid nano-electro-optomechanics,” Phys. Rev. A 97(3), 033812 (2018).
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Phys. Rev. Appl. (1)

H. Lü, Ş. K. Özdemir, L. M. Kuang, F. Nori, and H. Jing, “Exceptional points in random-defect phonon lasers,” Phys. Rev. Appl. 8(4), 044020 (2017).
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Phys. Rev. B (1)

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of the compound COM system, with an additional optical loss γtip induced by a Cr-coated nanofiber tip on the right (i.e., purely optical) resonator [12,58,59]. (b) The frequency spectrum of the compound COM system, with the red line or the blue lines denoting the red sideband (Stokes process) or the blue sidebands (anti-Stokes process), respectively [20,21].
Fig. 2
Fig. 2 (a) Transmission rate of the coupled optical system as a function of ΔP at three selected γtip/γc. (b) Transmission rate as a function of γtip when ΔP is 0 and −11 MHz. Evolution of the real (c) and imaginary (d) parts of the eigenfrequencies of the supermodes as a function of the loss γtip. The parameters used here are γ1 = γ2 = γc = 6.43 MHz and J/γc = 2.
Fig. 3
Fig. 3 (a)–(d) Transmission rate TP of the probe light as a function of ΔP. (e) Transmission rate of OMIT as a function of γtip at different ΔP. (f) Transmission rate of OMIT as a function of γtip and ΔP. The other parameters are ωc = 193 THz, γc = 6.43 MHz, ωm = 2π × 23.4 MHz, PL = 1 mW, ΔL = ωm, g = ωc/R, R = 34.5 μm, m = 5 × 10−11 kg, J = 12.86 MHz and Γm = 0.24 MHz (see Ref. [11]).
Fig. 4
Fig. 4 (a) Group delay of the probe light as a function of γtip at different ΔP. The pump power PL is 1 mW. (b) Group delay of the probe light as a function of γtip and the pump power PL at ΔP = −3 MHz. The unit of group delay is μs.
Fig. 5
Fig. 5 (a) The efficiency of the second-order sideband process as a function of ΔP. Subfigures (b), (c) and (d) show the comparisons between transmission rate of OMIT and efficiency of the second-order sideband as a function of γtip.

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

ε L = 2 γ c P L / ω L , ε P = 2 γ c P in / ω P ,
H = H 0 + H int + H dr , H 0 = p 2 2 m + 1 2 m ω m 2 x 2 + Δ L ( a 1 a 1 + a 2 a 2 ) , H int = J ( a 1 a 2 + a 2 a 1 ) g a 1 a 1 x , H dr = i ε L ( a 1 a 1 ) + i ε P ( a 1 e i t a 1 e i t ) ,
Δ L = ω c ω L , = ω P ω L .
x ¨ = Γ m x ˙ ω m 2 x + g m a 1 a 1 , a ˙ 1 = ( i Δ L γ 1 + i g x ) a 1 + i J a 2 + ε L + ε P e i t , a ˙ 2 = ( i Δ L γ 2 + γ tip ) a 2 + i J a 1 ,
x s = g m ω m 2 | a 1 , s | 2 , a 1 , s = ε L ( i Δ L + γ 2 + γ tip ) ( i Δ L + γ 1 i g x s ) ( i Δ L + γ 2 + γ tip ) + J 2 , a 2 , s = i J ε L ( i Δ L + γ 1 i g x s ) ( i Δ L + γ 2 + γ tip ) + J 2 .
T = | a 1 out a 1 in | 2 = | 1 2 γ 1 ( i Δ 2 + γ 2 + γ tip ) ( i Δ 1 + γ 1 ) ( i Δ 2 + γ 2 + γ tip ) + J 2 | 2 ,
γ tip TP = ( i Δ 2 + γ 2 ) + ( i Δ 1 + γ 1 ) J 2 Δ 1 2 + γ 1 2 ,
ω ± = 1 2 [ ( ω 1 + ω 2 ) i ( γ 1 + γ 2 + γ tip ) ] ± 1 2 [ ( ω 1 ω 2 ) + i ( γ 2 + γ tip γ 1 ) ] 2 + 4 J 2 .
x = x s + δ x ( 1 ) + , a i = a i , s + δ a i ( 1 ) + ( i = 1 , 2 ) ,
d 2 d t 2 ( x s + δ x ( 1 ) ) = Γ m d d t ( x s + δ x ( 1 ) ) ω m 2 ( x s + δ x ( 1 ) ) + g m ( a 1 , s + δ a 1 ( 1 ) ) ( a 1 , s + δ a 1 ( 1 ) ) , d d t ( a 1 , s + δ a 1 ( 1 ) ) = [ i Δ L γ 1 + i g ( x s + δ x ( 1 ) ) ] ( a 1 , s + δ a 1 ( 1 ) ) + i J ( a 2 , s + δ a 2 ( 1 ) ) + ε L + ε P e i t , d d t ( a 2 , s + δ a 2 ( 1 ) ) = ( i Δ L γ 2 γ tip ) ( a 2 , s + δ a 2 ( 1 ) ) + i J ( a 1 , s + δ a 1 ( 1 ) ) .
( δ a i ( 1 ) δ x ( 1 ) ) = ( δ a i + ( 1 ) δ x + ( 1 ) ) e i t + ( δ a i ( 1 ) δ x ( 1 ) ) e i t ( i = 1 , 2 ) ,
δ x + ( 1 ) = g ε P a 1 , s * μ ( 1 ) 𝒜 1 ( 1 ) 𝒦 ( 1 ) 𝒜 1 ( 1 ) 𝒜 2 ( 1 ) + i g 2 | a 1 , s | 2 ( μ + ( 1 ) * 𝒜 2 ( 1 ) μ ( 1 ) 𝒜 1 ( 1 ) ) ,
δ a + ( 1 ) = ε P μ ( 1 ) ( 𝒦 ( 1 ) 𝒜 1 ( 1 ) + i g 2 | a 1 , s | 2 μ + ( 1 ) * ) 𝒦 ( 1 ) 𝒜 1 ( 1 ) 𝒜 2 ( 1 ) + i g 2 | a 1 , s | 2 ( μ + ( 1 ) * 𝒜 2 ( 1 ) μ ( 1 ) 𝒜 1 ( 1 ) ) ,
𝒦 ( 1 ) = m ( 2 i Γ m + ω m 2 ) , 𝒜 1 ( 1 ) = μ + ( 1 ) * ν + ( 1 ) * + J 2 , 𝒜 2 ( 1 ) = μ ( 1 ) ν ( 1 ) + J 2 , μ ± ( 1 ) = i Δ L + γ 2 + γ tip ± i , ν ± ( 1 ) = i Δ L + γ 1 i g x s ± i .
T p = | t P | 2 = | a 1 out a 1 in | 2 = | ε P 2 γ 1 δ a 1+ (1) ε P | 2 = | 1 2 γ 1 δ a 1+ (1) ε P | 2
( i Δ L + γ 1 i ) δ a 1 + ( 1 ) = i J δ a 2 + ( 1 ) + ε P ,
( i Δ L + γ 1 i g x s i ) δ a 1 + ( 1 ) = i g a 1 , s δ x + ( 1 ) + i J δ a 2 + ( 1 ) + ε P ,
( i Δ + γ 1 i ) δ a 1 + ( 1 ) = i J δ a 2 + ( 1 ) + ε P ,
Δ = Δ L g x s Re ( C 1 ) , γ 1 = γ 1 + Im ( C 1 ) ,
C 1 = 𝒜 1 ( 1 ) g 2 | a 1 , s | 2 𝒜 1 ( 1 ) 𝒦 ( 1 ) + i g 2 | a 1 , s | 2 ( i Δ L + γ 2 + γ tip i ) .
τ g = d arg ( T P ) d Δ P .
x = x s + δ x ( 1 ) + δ x ( 2 ) + , a i = a i , s + δ a i ( 1 ) + δ a i ( 2 ) + ( i = 1 , 2 ) ,
( δ a i ( 2 ) δ x ( 2 ) ) = ( δ a i + ( 2 ) δ x + ( 2 ) ) e 2 i t + ( δ a i ( 2 ) δ x ( 2 ) ) e 2 i t ( i = 1 , 2 ) .
δ a 1 + ( 2 ) = i g 4 a 1 , s | a 1 , s | 4 μ + ( 1 ) * μ + ( 2 ) * μ ( 2 ) δ x + ( 1 ) 2 + λ δ x + ( 1 ) δ a + ( 1 ) 𝒜 1 ( 1 ) [ 𝒦 ( 2 ) 𝒜 1 ( 2 ) 𝒜 2 ( 2 ) + i g 2 | a 1 , s | 2 ( 𝒜 2 ( 2 ) μ + ( 2 ) * 𝒜 1 ( 2 ) μ ( 2 ) ) ] ,
𝒜 1 ( 2 ) = μ + ( 2 ) * ν + ( 2 ) * + J 2 , 𝒜 2 ( 2 ) = μ ( 2 ) ν ( 2 ) + J 2 , μ ± ( 2 ) = i Δ L + γ 2 + γ tip ± 2 i , ν ± ( 2 ) = i Δ L + γ 1 i g x s ± i , λ = i g μ ( 2 ) 𝒦 ( 2 ) 𝒜 1 ( 1 ) 𝒜 1 ( 2 ) g 3 | a 1 , s | 2 μ ( 2 ) ( 𝒜 1 ( 1 ) μ + ( 2 ) * μ + ( 1 ) * 𝒜 1 ( 2 ) ) .
η = | 2 γ 1 ε P δ a 1 + ( 2 ) | .
( i Δ + γ 1 i ) δ a 1 + ( 1 ) = i J δ a 2 + ( 1 ) + ε P ,
( i Δ + γ 1 2 i ) δ a 1 + ( 2 ) = i J δ a 2 + ( 2 ) + ,
Δ = Δ L g x s Re ( C 2 ) , γ 1 = γ 1 + Im ( C 2 ) ,
C 2 = g 2 | a 1 , s | 2 𝒜 1 ( 2 ) 𝒜 1 ( 1 ) 𝒜 1 ( 2 ) 𝒜 1 ( 1 ) 𝒦 ( 2 ) + i g 2 | a 1 , s | 2 𝒜 1 ( 1 ) μ + ( 2 ) * ,
= i g 2 a 1 , s [ g 2 | a 1 , s | 2 μ + ( 2 ) * μ + ( 1 ) * δ x + ( 1 ) 2 i g 𝒜 1 ( 2 ) a 1 , s * μ + ( 1 ) * δ x + ( 1 ) δ a 1 + ( 1 ) ] 𝒜 1 ( 2 ) 𝒜 1 ( 1 ) 𝒦 ( 2 ) + i g 2 𝒜 1 ( 1 ) | a 1 , s | 2 μ + ( 2 ) * + i g δ x + ( 1 ) δ a 1 + ( 1 ) .

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