Abstract

Recent research on parity-time- (𝒫𝒯-) symmetric optical structures have exhibited great potential for achieving distinctive optical behaviour which is unattainable with ordinary optical systems. Here we propose a 𝒫𝒯-symmetric cavity-magnon system consisting of active cavity mode strongly interacting with magnon to study magnon-induced transparency (MIT) and amplification (MIA) by exploiting recent microwave-cavity-engineered ferromagnetic magnons. We find that (i) due to the gain-induced enhancement of coherent coupling between the cavity field and the magnon, the transmitted probe power is remarkably enhanced about four orders of magnitude and the bandwidth also becomes much narrower, compared to passive cavity system. (ii) More importantly, the light transmission can be well controlled by adjusting the applied magnetic field without changing other parameters, and a Lorentzian-like spectra can be established between the transmitted probe power and the external magnetic field, which provides an additional degree of freedom to realize the coherent manipulation of optical transparency and amplification. Our results may offer an approach to make a low-power magnetic-field-controlled optical amplifier in 𝒫𝒯-symmetric cavity-magnon system.

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

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References

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2018 (1)

Y.-P. Wang, G.-Q. Zhang, D. Zhang, T.-F. Li, C.-M. Hu, and J. Q. You, “Bistability of Cavity Magnon Polaritons,” Phys. Rev. Lett. 120, 057202 (2018).
[Crossref] [PubMed]

2017 (6)

W. J Chen, Ş. K. Özdemir, G. M Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature. 548, 23281 (2017).
[Crossref]

H. Hodaei, A. U. Hassan, G. M Zhao, S. Wittek, H. Garcia-Gracia, and R. El-Ganainy, “Enhanced sensitivity at higher-order exceptional points,” Nature 548, 23280 (2017).
[Crossref]

D. Zhang, X.-Q. Luo, Y.-P. Wang, T.-F. Li, and J.Q. You, “Observation of the exceptional point in cavity magnon-polaritons,” Nat. Commun. 8, 1368 (2017).
[Crossref] [PubMed]

W.-X. Yang, A.-X. Chen, X.-T. Xie, and L. Ni, “Enhanced generation of higher-order sidebands in a single-quantum-dot-cavity system coupled to a 𝒫𝒯-symmetric double cavity,” Phys. Rev. A 96, 013802 (2017).
[Crossref]

H. Xiong, J. H. Gan, and Y. Wu, “Kuznetsov-Ma Soliton Dynamics Based on the Mechanical Effect of Light,” Phys. Rev. Lett. 119, 153901 (2017).
[Crossref] [PubMed]

M. N. Winchester, M. A. Norcia, J. R. K. Cline, and J. K. Thompson,“ Magnetically Induced Optical Transparency on a Forbidden Transition in Strontium for Cavity-Enhanced Spectroscopy,” Phys. Rev. Lett. 118, 263601 (2017).
[Crossref] [PubMed]

2016 (9)

Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, “Magnon Kerr effect in a strongly coupled cavity-magnon system,” Phys. Rev. B 94, 224410 (2016).
[Crossref]

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

K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, “Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization,” Phys. Rev. X 6, 021007 (2016).

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, 110802 (2016).
[Crossref]

Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, “Magnon Kerr effect in a strongly coupled cavity-magnon system,” Physical Review B 94, 224410 (2016).
[Crossref]

X. Zhang, N. Zhu, C.-L. Zou, and H. X. Tang, “Optomagnonic Whispering Gallery Microresonators,” Phys. Rev. Lett. 117, 123605 (2016).
[Crossref] [PubMed]

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Cavity magnomechanics,” Sci. Adv. 2, e1501286 (2016).
[Crossref] [PubMed]

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref] [PubMed]

J. Li, J. Li, Q. Xiao, and Y. Wu, “Giant enhancement of optical high-order sideband generation and their control in a dimer of two cavities with gain and loss,” Phys. Rev. A 93, 063814 (2016).
[Crossref]

2015 (6)

D. Zhang, X.-M. Wang, T.-F. Li, X.-Q. Luo, W. Wu, F. Nori, and J. Q. You, “Cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet sphere,” npj Quantum Inf. 1, 15014 (2015).
[Crossref]

Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Coherent coupling between a ferromagnetic magnon and a superconducting qubit,” Science 10, 3693 (2015).

L. Bai, M. Harder, Y. P. Chen, X. Fan, J. Q. Xiao, and C.-M. Hu, “Spin Pumping in Electrodynamically Coupled Magnon-Photon Systems,” Phys. Rev. Lett. 114, 227201 (2015).
[Crossref] [PubMed]

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]

X.-Y. Lü, H. Jing, J. Ma, and Y. Wu, “𝒫𝒯-Symmetry-Breaking Chaos in Optomechanics,” Phys. Rev. Lett. 114, 253601 (2015).
[Crossref]

A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, “Magnon spintronics,” Nat. Phys. 11, 453–461 (2015).
[Crossref]

2014 (7)

B.-I. Popa and S. A. Cummer, “Non-Reciprocal and Highly Nonlinear Active Acoustic Metamaterials,” Nat. Commun. 5, 3398 (2014).
[Crossref] [PubMed]

Y. Sun, W. Tan, H. Li, J. Li, and H Chen, “Experimental Demonstration of a Coherent Perfect Absorber with PT Phase Transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

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. Photon. 8, 524–529 (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, 394–398 (2014).
[Crossref]

H. Jing, S. K. özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, “PT-Symmetric Phonon Laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref] [PubMed]

Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, “Hybridizing Ferromagnetic Magnons and Microwave Photons in the Quantum Limit,” Phys. Rev. Lett. 113, 083603 (2014).
[Crossref] [PubMed]

X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, “Strongly Coupled Magnons and Cavity Microwave Photons,” Phys. Rev. Lett. 113, 156401 (2014).
[Crossref] [PubMed]

2013 (2)

H. Huebl, C.W. Zollitsch, J. Lotze, F. Hocke, M. Greifenstein, A. Marx, R. Gross, and S. T. B. Goennenwein, “High Cooperativity in Coupled Microwave Resonator Ferrimagnetic Insulator Hybrids,” Phys. Rev. Lett. 111, 127003 (2013).
[Crossref] [PubMed]

D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Ya. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, “Deterministic entanglement of superconducting qubits by parity measurement and feedback,” Nature 502, 350–354 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

Y. D. Chong, L. Ge, and A. D. Stone, “PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref] [PubMed]

2010 (1)

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature (London) 465, 755–758 (2010).
[Crossref]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

1962 (1)

K. Sinha and U. Upadhyaya, “Phonon-Magnon Interaction in Magnetic Crystals,” Phys. Rev. 127, 432–439 (1962).
[Crossref]

1960 (1)

E. H. Turner, “Interaction of phonons and spin waves in yttrium iron garnet,” Phys. Rev. Lett. 5, 100–101 (1960).
[Crossref]

Akamatsu, D.

Bai, L.

L. Bai, M. Harder, Y. P. Chen, X. Fan, J. Q. Xiao, and C.-M. Hu, “Spin Pumping in Electrodynamically Coupled Magnon-Photon Systems,” Phys. Rev. Lett. 114, 227201 (2015).
[Crossref] [PubMed]

Bender, C. M.

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, 394–398 (2014).
[Crossref]

Blanter, Ya. M.

D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Ya. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, “Deterministic entanglement of superconducting qubits by parity measurement and feedback,” Nature 502, 350–354 (2013).
[Crossref] [PubMed]

Bochmann, J.

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature (London) 465, 755–758 (2010).
[Crossref]

Chan, C. T.

K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, “Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization,” Phys. Rev. X 6, 021007 (2016).

Chang, L.

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. Photon. 8, 524–529 (2014).
[Crossref]

Chen, A.-X.

W.-X. Yang, A.-X. Chen, X.-T. Xie, and L. Ni, “Enhanced generation of higher-order sidebands in a single-quantum-dot-cavity system coupled to a 𝒫𝒯-symmetric double cavity,” Phys. Rev. A 96, 013802 (2017).
[Crossref]

Chen, H

Y. Sun, W. Tan, H. Li, J. Li, and H Chen, “Experimental Demonstration of a Coherent Perfect Absorber with PT Phase Transition,” Phys. Rev. Lett. 112, 143903 (2014).
[Crossref] [PubMed]

Chen, W. J

W. J Chen, Ş. K. Özdemir, G. M Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature. 548, 23281 (2017).
[Crossref]

Chen, Y. P.

L. Bai, M. Harder, Y. P. Chen, X. Fan, J. Q. Xiao, and C.-M. Hu, “Spin Pumping in Electrodynamically Coupled Magnon-Photon Systems,” Phys. Rev. Lett. 114, 227201 (2015).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems,” Phys. Rev. Lett. 106, 093902 (2011).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. Zhang, Y. Zhang, J. Sheng, L. Yang, M.-A. Miri, D. N. Christodoulides, B. He, Y. Zhang, and M. Xiao, “Observation of Parity-Time Symmetry in Optically Induced Atomic Lattices,” Phys. Rev. Lett. 117, 123601 (2016).
[Crossref] [PubMed]

Chumak, A. V.

A. V. Chumak, V. I. Vasyuchka, A. A. Serga, and B. Hillebrands, “Magnon spintronics,” Nat. Phys. 11, 453–461 (2015).
[Crossref]

Cline, J. R. K.

M. N. Winchester, M. A. Norcia, J. R. K. Cline, and J. K. Thompson,“ Magnetically Induced Optical Transparency on a Forbidden Transition in Strontium for Cavity-Enhanced Spectroscopy,” Phys. Rev. Lett. 118, 263601 (2017).
[Crossref] [PubMed]

Cummer, S. A.

B.-I. Popa and S. A. Cummer, “Non-Reciprocal and Highly Nonlinear Active Acoustic Metamaterials,” Nat. Commun. 5, 3398 (2014).
[Crossref] [PubMed]

de Lange, G.

D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Ya. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, “Deterministic entanglement of superconducting qubits by parity measurement and feedback,” Nature 502, 350–354 (2013).
[Crossref] [PubMed]

DiCarlo, L.

D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Ya. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, “Deterministic entanglement of superconducting qubits by parity measurement and feedback,” Nature 502, 350–354 (2013).
[Crossref] [PubMed]

Ding, K.

K. Ding, G. Ma, M. Xiao, Z. Q. Zhang, and C. T. Chan, “Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization,” Phys. Rev. X 6, 021007 (2016).

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref] [PubMed]

Dukalski, M.

D. Ristè, M. Dukalski, C. A. Watson, G. de Lange, M. J. Tiggelman, Ya. M. Blanter, K. W. Lehnert, R. N. Schouten, and L. DiCarlo, “Deterministic entanglement of superconducting qubits by parity measurement and feedback,” Nature 502, 350–354 (2013).
[Crossref] [PubMed]

El-Ganainy, R.

H. Hodaei, A. U. Hassan, G. M Zhao, S. Wittek, H. Garcia-Gracia, and R. El-Ganainy, “Enhanced sensitivity at higher-order exceptional points,” Nature 548, 23280 (2017).
[Crossref]

Fan, S.

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, 394–398 (2014).
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D. Zhang, X.-Q. Luo, Y.-P. Wang, T.-F. Li, and J.Q. You, “Observation of the exceptional point in cavity magnon-polaritons,” Nat. Commun. 8, 1368 (2017).
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Nat. Photon. (1)

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. Photon. 8, 524–529 (2014).
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Nat. Phys. (2)

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, 394–398 (2014).
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Nature (3)

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Nature (London) (1)

M. Mücke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, “Electromagnetically induced transparency with single atoms in a cavity,” Nature (London) 465, 755–758 (2010).
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Nature. (1)

W. J Chen, Ş. K. Özdemir, G. M Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature. 548, 23281 (2017).
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New J. Phys. (1)

Y. Jiao, H. Lü, J. Qian, Y. Li, and H. Jing, “Nonlinear optomechanics with gain and loss: amplifying higherorder sideband and group delay,” New J. Phys. 18, 083034 (2016).
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npj Quantum Inf. (1)

D. Zhang, X.-M. Wang, T.-F. Li, X.-Q. Luo, W. Wu, F. Nori, and J. Q. You, “Cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet sphere,” npj Quantum Inf. 1, 15014 (2015).
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Opt. Express (1)

Phys. Rev. (1)

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Phys. Rev. A (2)

J. Li, J. Li, Q. Xiao, and Y. Wu, “Giant enhancement of optical high-order sideband generation and their control in a dimer of two cavities with gain and loss,” Phys. Rev. A 93, 063814 (2016).
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W.-X. Yang, A.-X. Chen, X.-T. Xie, and L. Ni, “Enhanced generation of higher-order sidebands in a single-quantum-dot-cavity system coupled to a 𝒫𝒯-symmetric double cavity,” Phys. Rev. A 96, 013802 (2017).
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Phys. Rev. B (1)

Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, “Magnon Kerr effect in a strongly coupled cavity-magnon system,” Phys. Rev. B 94, 224410 (2016).
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Phys. Rev. Lett. (15)

H. Xiong, J. H. Gan, and Y. Wu, “Kuznetsov-Ma Soliton Dynamics Based on the Mechanical Effect of Light,” Phys. Rev. Lett. 119, 153901 (2017).
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Physical Review B (1)

Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, “Magnon Kerr effect in a strongly coupled cavity-magnon system,” Physical Review B 94, 224410 (2016).
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Science (1)

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H. Xiong and Y. Wu, “Optomechanical Akhmediev Breathers,” https://arXiv:1805.04229 (2018).
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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of ����-symmetric cavity-magnon system, which includes an active rectangular 3D cavity and a small YIG sphere. κ is the cavity gain. B0 denotes the applied static magnetic field, which is parallel to the long edge of the cavity and is perpendicular to the microwave magnetic field at the YIG sphere. The system is pumped by a probe field ωp. (b) The energy-level diagram of the cavity-magnon coupling scheme, where |a〉, |b〉 denote the number states of the cavity photon and magnon, respectively. The probe field sp can make a single-photon transition from |0, 0〉a,b to |1, 0〉a,b, |1, 0〉a,b to |2, 0〉a,b and |0, 1〉a,b to |1, 1〉a,b.
Fig. 2
Fig. 2 The logarithm of the transmitted probe power |PT|2 varies with the applied static magnetic field and the coupling strength Jm when (a) κ/2π = −8.75 MHz and (c) κ/2π = 8.75 MHz. We use the parameters here are ωc/2π = ωm/2π = 10.1 GHz, and γm/2π = 8.75 MHz [9]. (b) The logarithm of the |PT |2 varies with the coupling strength Jm and frequency detuning δ with the passive cavity, i.e., κ = γm, other parameters are the same as (a). Inset: |PT|2 varies with frequency detuning δ at the case of Jm = 12.9 MHz. (d) The logarithm of the |PT|2 varies with the coupling strength Jm and frequency detuning δ, with the active cavity, i.e., κ = γm, other parameters are the same as (c). Inset: |PT|2 varies with frequency detuning δ at the case of Jm = 12.9 MHz. All the parameters are chosen based on the recent experiment and can be achieved under the currently existing experimental technique.
Fig. 3
Fig. 3 The logarithm of the |PT|2 versus the gain-loss ratio κ/γm and the applied magnetic field B0. The other parameters are Jm/2π = 24.6 MHz and γm/2π = 8.75 MHz and the frequency detuning δc = δm = γm.
Fig. 4
Fig. 4 Calculated transmission spectrum of the probe light as a function of the frequency detuning δ under different cavity gain κ. Jm/2π = 4.1 MHz and γm/2π = 8.75 MHz. Inset: |PT|2 varies with frequency detuning δ at the case of κ = −γm.
Fig. 5
Fig. 5 The change of transmission spectrum |PT|2 with adjusted magnetic field. We use the parameters here are Jm/2π = 11.3 MHz, δc = δm = γm, γm/2π = 8.75 MHz and κ = γm. Blue area denotes |PT|2 ≤ 1.

Equations (9)

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H = H c + H m + H 1
˙ = + 𝒟 + ϱ
= ( i δ c + κ / 2 i J m i J m i δ m γ m / 2 ) , 𝒟 = ( η κ s p 0 )
a ( δ ) = η κ s p / Θ ( δ )
H ^ m = ( a ^ b ^ ) ( ω c + i κ / 2 J m J m ω m i γ m / 2 ) ( a ^ b ^ )
R = ( ω c + i κ / 2 J m J m ω m i γ m / 2 )
R = ( ω c + i γ + 0 0 ω + i γ )
H ^ m = ( B ^ 1 B ^ 2 ) ( ω + + i γ + 0 0 ω + i γ ) ( B ^ 1 B ^ 2 )
ω ± = ω c + ω m 2 ± Re J m 2 [ i ( ω c ω m ) 2 + κ + γ m 4 ] 2 γ ± = ( κ γ m ) 4 ± Im J m 2 [ i ( ω c ω m ) 2 + κ + γ m 4 ] 2

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