Abstract

Starting from the semiclassical theory of light–matter interaction, we have theoretically investigated the substantial influences of two coherent driving fields on manipulating the single-photon transmission probability in the extensively studied atom-cavity-waveguide coupled system. The results strictly demonstrate that under the relatively large photon-cavity detuning and moderately strong driving fields, the single-photon transmission probability increases remarkably from the original 0 to 1 by controlling the coherent fields in the nondissipative environment, which manifests the manipulation of the coherent fields as a sort of highly controllable external tool to efficiently act as an experimentally available all-optical quantum switching. In contrast, the behavior independent from variation of coherent fields and characterized by the stationary transmission spectrum appears under the photon-atom on-resonance condition. Similar properties can also be observed in the dissipative environment. These distinct characteristics essentially reveal some significant functionalities of coherent field control in influencing the single-photon transmission spectrum, which may have potential applications in designing efficient photonic devices.

© 2013 Optical Society of America

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2012 (6)

M. G. Genoni, A. Serafini, M. S. Kim, and D. Burgarth, “Dynamic recurrence and the quantum control of coupled oscillators,” Phys. Rev. Lett. 108, 150501 (2012).
[CrossRef]

E. Kyoseva, A. Beige, and L. C. Kwek, “Coherent cavity networks with complete connectivity,” New J. Phys. 14, 023023 (2012).
[CrossRef]

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Strongly correlated photons generated by coupling a three- or four-level system to waveguide,” Phys. Rev. A 85, 043832(2012).
[CrossRef]

W. B. Yan, Q. B. Fan, and L. Zhou, “Control of correlated two-photon transport in a one-dimensional waveguide,” Phys. Rev. A 85, 015803 (2012).
[CrossRef]

2011 (5)

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
[CrossRef]

D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparence,” Phys. Rev. Lett. 106, 053601 (2011).
[CrossRef]

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

2010 (9)

K. Zhang and Z. Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

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

L. M. Duan and C. Monroe, “Quantum networks with trapped ions,” Rev. Mod. Phys. 82, 1209–1224 (2010).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

E. E. Hach, A. W. Elshaari, and S. F. Preble, “Fully quantum-mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator,” Phys. Rev. A 82, 063839 (2010).
[CrossRef]

X. Y. Yu and L. H. Li, “Phase manipulation of entanglement and quantum discord,” Europhys. Lett. 92, 40002(2010).
[CrossRef]

X. Y. Yu and L. H. Li, “Coherent and ultrafast manipulation of entanglement sudden death and recurrence,” Opt. Lett. 35, 2744–2746 (2010).
[CrossRef]

W. M. Zhang, M. H. Wu, C. U. Lei, and H. N. Xiong, “Non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystals,” Opt. Express 18, 18407–18418 (2010).
[CrossRef]

D. Witthaut and A. S. Sorensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New. J. Phys. 12, 043052 (2010).
[CrossRef]

2009 (4)

P. Longo, P. Schmitteckert, and K. Busch, “Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems,” J. Opt. A 11, 114009 (2009).
[CrossRef]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

2008 (3)

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

2007 (3)

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (2007).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

2006 (3)

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

V. S. Malinovsky and I. R. Sola, “Phase-controlled collapse and revival of entanglement of two interacting qubits,” Phys. Rev. Lett. 96, 050502 (2006).
[CrossRef]

2000 (1)

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

1998 (2)

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Abdumalikov, A.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Badolato, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Baranger, H. U.

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Strongly correlated photons generated by coupling a three- or four-level system to waveguide,” Phys. Rev. A 85, 043832(2012).
[CrossRef]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
[CrossRef]

Baur, M.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Beige, A.

E. Kyoseva, A. Beige, and L. C. Kwek, “Coherent cavity networks with complete connectivity,” New J. Phys. 14, 023023 (2012).
[CrossRef]

Bermel, P.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Boas, C. J.

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

Bochmann, J.

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

Bose, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Bozyigit, D.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Burgarth, D.

M. G. Genoni, A. Serafini, M. S. Kim, and D. Burgarth, “Dynamic recurrence and the quantum control of coupled oscillators,” Phys. Rev. Lett. 108, 150501 (2012).
[CrossRef]

Busch, K.

P. Longo, P. Schmitteckert, and K. Busch, “Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems,” J. Opt. A 11, 114009 (2009).
[CrossRef]

Chang, D. E.

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

Chen, X. H.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Demler, E.

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

Duan, L. M.

L. M. Duan and C. Monroe, “Quantum networks with trapped ions,” Rev. Mod. Phys. 82, 1209–1224 (2010).
[CrossRef]

Eichler, C.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Elshaari, A. W.

E. E. Hach, A. W. Elshaari, and S. F. Preble, “Fully quantum-mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator,” Phys. Rev. A 82, 063839 (2010).
[CrossRef]

Englund, D.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Fan, Q. B.

W. B. Yan, Q. B. Fan, and L. Zhou, “Control of correlated two-photon transport in a one-dimensional waveguide,” Phys. Rev. A 85, 015803 (2012).
[CrossRef]

Fan, S. H.

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (2007).
[CrossRef]

Faraon, A.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Fazio, R.

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Feng, M.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

Figueroa, E.

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

Fink, J. M.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Fushman, L.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Gauthier, D. J.

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Strongly correlated photons generated by coupling a three- or four-level system to waveguide,” Phys. Rev. A 85, 043832(2012).
[CrossRef]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
[CrossRef]

Genoni, M. G.

M. G. Genoni, A. Serafini, M. S. Kim, and D. Burgarth, “Dynamic recurrence and the quantum control of coupled oscillators,” Phys. Rev. Lett. 108, 150501 (2012).
[CrossRef]

Gerace, D.

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Giovannetti, V.

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Gong, Q. H.

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

Gong, Z. R.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Gritsev, V.

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

Gu, L. M.

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Gu, Y.

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

Guo, G. C.

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

Hach, E. E.

E. E. Hach, A. W. Elshaari, and S. F. Preble, “Fully quantum-mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator,” Phys. Rev. A 82, 063839 (2010).
[CrossRef]

Hafezi, M.

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

Hahn, C.

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

Han, X. F.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Hennessy, K. J.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Hu, E. L.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Imamoglu, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Joannopoulos, J. D.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Johnson, S. G.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Kim, M. S.

M. G. Genoni, A. Serafini, M. S. Kim, and D. Burgarth, “Dynamic recurrence and the quantum control of coupled oscillators,” Phys. Rev. Lett. 108, 150501 (2012).
[CrossRef]

Kimble, H. J.

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

Knight, P. L.

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Kwek, L. C.

E. Kyoseva, A. Beige, and L. C. Kwek, “Coherent cavity networks with complete connectivity,” New J. Phys. 14, 023023 (2012).
[CrossRef]

Kyoseva, E.

E. Kyoseva, A. Beige, and L. C. Kwek, “Coherent cavity networks with complete connectivity,” New J. Phys. 14, 023023 (2012).
[CrossRef]

Lang, C.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Lang, J. H.

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Lei, C. U.

Li, L. H.

X. Y. Yu and L. H. Li, “Coherent and ultrafast manipulation of entanglement sudden death and recurrence,” Opt. Lett. 35, 2744–2746 (2010).
[CrossRef]

X. Y. Yu and L. H. Li, “Phase manipulation of entanglement and quantum discord,” Europhys. Lett. 92, 40002(2010).
[CrossRef]

Li, P. B.

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

Li, Q.

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Li, W. L.

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Li, Z. Y.

K. Zhang and Z. Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

Liao, J. Q.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

Liu, Y. X.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Longo, P.

P. Longo, P. Schmitteckert, and K. Busch, “Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems,” J. Opt. A 11, 114009 (2009).
[CrossRef]

Lukin, M. D.

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

Luo, K. H.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Luo, Q.

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Luo, Y. Q.

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Ma, X. S.

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Malinovsky, V. S.

V. S. Malinovsky and I. R. Sola, “Phase-controlled collapse and revival of entanglement of two interacting qubits,” Phys. Rev. Lett. 96, 050502 (2006).
[CrossRef]

Mancini, S.

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Monroe, C.

L. M. Duan and C. Monroe, “Quantum networks with trapped ions,” Rev. Mod. Phys. 82, 1209–1224 (2010).
[CrossRef]

Mucke, M.

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

Murr, K.

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

Nori, F.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Oh, C. H.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

Paspalakis, E.

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Petroff, P.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Preble, S. F.

E. E. Hach, A. W. Elshaari, and S. F. Preble, “Fully quantum-mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator,” Phys. Rev. A 82, 063839 (2010).
[CrossRef]

Qiu, Z. R.

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Reinhard, A.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Rempe, G.

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

Ritter, S.

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

Rodriguez, A.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Roy, D.

D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparence,” Phys. Rev. Lett. 106, 053601 (2011).
[CrossRef]

Schmitteckert, P.

P. Longo, P. Schmitteckert, and K. Busch, “Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems,” J. Opt. A 11, 114009 (2009).
[CrossRef]

Scully, M. O.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Serafini, A.

M. G. Genoni, A. Serafini, M. S. Kim, and D. Burgarth, “Dynamic recurrence and the quantum control of coupled oscillators,” Phys. Rev. Lett. 108, 150501 (2012).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

Shen, J. T.

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (2007).
[CrossRef]

Sola, I. R.

V. S. Malinovsky and I. R. Sola, “Phase-controlled collapse and revival of entanglement of two interacting qubits,” Phys. Rev. Lett. 96, 050502 (2006).
[CrossRef]

Soljacic, M.

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

Song, Y. Y.

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Sorensen, A. S.

D. Witthaut and A. S. Sorensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New. J. Phys. 12, 043052 (2010).
[CrossRef]

Steffen, L.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Stoltz, N.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Sun, C. P.

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Tureci, H. E.

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Volz, T.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Vuckovic, J.

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

Walllraff, A.

C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. Abdumalikov, M. Baur, and A. Walllraff, “Observation of resonant photon blockade at microwave frequencies using correlation function measurements,” Phys. Rev. Lett. 106, 243601 (2011).
[CrossRef]

Wang, R.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Weng, Y. X.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Winger, M.

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Witthaut, D.

D. Witthaut and A. S. Sorensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New. J. Phys. 12, 043052 (2010).
[CrossRef]

Wu, L. A.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Wu, M. H.

Xiong, H. N.

Xu, Z. Y.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

Yan, W. B.

W. B. Yan, Q. B. Fan, and L. Zhou, “Control of correlated two-photon transport in a one-dimensional waveguide,” Phys. Rev. A 85, 015803 (2012).
[CrossRef]

Yang, W. L.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

Yin, Z. Q.

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

Yu, X. Y.

X. Y. Yu and L. H. Li, “Coherent and ultrafast manipulation of entanglement sudden death and recurrence,” Opt. Lett. 35, 2744–2746 (2010).
[CrossRef]

X. Y. Yu and L. H. Li, “Phase manipulation of entanglement and quantum discord,” Europhys. Lett. 92, 40002(2010).
[CrossRef]

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Zhang, K.

K. Zhang and Z. Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

Zhang, W. M.

Zhao, J. M.

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

Zheng, H. X.

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Strongly correlated photons generated by coupling a three- or four-level system to waveguide,” Phys. Rev. A 85, 043832(2012).
[CrossRef]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Cavity-free photon blockade induced by many-body bound states,” Phys. Rev. Lett. 107, 223601 (2011).
[CrossRef]

Zheng, S. B.

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

Zhou, J. Y.

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Zhou, L.

W. B. Yan, Q. B. Fan, and L. Zhou, “Control of correlated two-photon transport in a one-dimensional waveguide,” Phys. Rev. A 85, 015803 (2012).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Appl. Phys. Lett. (2)

X. F. Han, Y. X. Weng, R. Wang, X. H. Chen, K. H. Luo, L. A. Wu, and J. M. Zhao, “Single-photon level ultrafast all-optical switching,” Appl. Phys. Lett. 92, 151109 (2008).
[CrossRef]

X. Y. Yu, Q. Luo, W. L. Li, Q. Li, Z. R. Qiu, and J. Y. Zhou, “Ultrafast phase dynamics of coherent carriers in GaAs,” Appl. Phys. Lett. 73, 3321–3323 (1998).
[CrossRef]

Chin. Phys. Lett. (1)

Y. Q. Luo, Y. Y. Song, L. M. Gu, J. H. Lang, and X. S. Ma, “Voltage-controlled scattering of single photons in a one-dimensional waveguide,” Chin. Phys. Lett. 28, 074209 (2011).
[CrossRef]

Europhys. Lett. (1)

X. Y. Yu and L. H. Li, “Phase manipulation of entanglement and quantum discord,” Europhys. Lett. 92, 40002(2010).
[CrossRef]

J. Opt. A (1)

P. Longo, P. Schmitteckert, and K. Busch, “Dynamics of photon transport through quantum impurities in dispersion-engineered one-dimensional systems,” J. Opt. A 11, 114009 (2009).
[CrossRef]

Nat. Photonics (1)

T. Volz, A. Reinhard, M. Winger, A. Badolato, K. J. Hennessy, E. L. Hu, and A. Imamoglu, “Ultrafast all-optical switching by single photon,” Nat. Photonics 6, 605–609 (2012).
[CrossRef]

Nat. Phys. (1)

D. Gerace, H. E. Tureci, A. Imamoglu, V. Giovannetti, and R. Fazio, “The quantum-optical Josephson interferometer,” Nat. Phys. 5, 281–284 (2009).
[CrossRef]

Nature (3)

D. Englund, A. Faraon, L. Fushman, N. Stoltz, P. Petroff, and J. Vuckovic, “Controlling cavity reflectivity with a single quantum dot,” Nature 450, 857–861 (2007).
[CrossRef]

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[CrossRef]

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

New J. Phys. (1)

E. Kyoseva, A. Beige, and L. C. Kwek, “Coherent cavity networks with complete connectivity,” New J. Phys. 14, 023023 (2012).
[CrossRef]

New. J. Phys. (1)

D. Witthaut and A. S. Sorensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New. J. Phys. 12, 043052 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (11)

P. Bermel, A. Rodriguez, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Single-photon all-optical switching using waveguide-cavity quantum electrodynamics,” Phys. Rev. A 74, 043818 (2006).
[CrossRef]

M. Hafezi, D. E. Chang, V. Gritsev, E. Demler, and M. D. Lukin, “Quantum transport of strongly interaction photons in a one-dimensional nonlinear waveguide,” Phys. Rev. A 85, 013822 (2012).
[CrossRef]

H. X. Zheng, D. J. Gauthier, and H. U. Baranger, “Strongly correlated photons generated by coupling a three- or four-level system to waveguide,” Phys. Rev. A 85, 043832(2012).
[CrossRef]

K. Zhang and Z. Y. Li, “Transfer behavior of quantum states between atoms in photonic crystal coupled cavities,” Phys. Rev. A 81, 033843 (2010).
[CrossRef]

W. L. Yang, Z. Q. Yin, Z. Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

P. B. Li, Y. Gu, Q. H. Gong, and G. C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009).
[CrossRef]

E. E. Hach, A. W. Elshaari, and S. F. Preble, “Fully quantum-mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator,” Phys. Rev. A 82, 063839 (2010).
[CrossRef]

W. B. Yan, Q. B. Fan, and L. Zhou, “Control of correlated two-photon transport in a one-dimensional waveguide,” Phys. Rev. A 85, 015803 (2012).
[CrossRef]

J. T. Shen and S. H. Fan, “Theory of single-photon transport in a single-mode waveguide. I. Coupling to a cavity containing a two-level atom,” Phys. Rev. A 79, 023837 (2009).
[CrossRef]

J. T. Shen and S. H. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (2007).
[CrossRef]

J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A 81, 042304 (2010).
[CrossRef]

Phys. Rev. Lett. (10)

J. T. Shen and S. H. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98, 153003 (2007).
[CrossRef]

L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. 101, 100501 (2008).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. 96, 010503 (2006).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic configuration of the composite system consisting of the cavity-waveguide coupled system in which a four-level N-type atom is embedded. ga and gb represent the coupling strength of the atomic electronic dipole moment with the corresponding cavity modes with oscillation frequency ωa and ωb, respectively; Δa=ωaω31 (Δb=ωbω42) denotes the corresponding cavity-atom detuning. Two classical and coherent driving fields differentiated by the phase difference are employed to induce the particle transition between the excited energy levels |3 and |2. Here, the fundamental effect of coherent field control on the single-photon transmission spectrum will be our underlying interest.

Fig. 2.
Fig. 2.

Transmission probability as a function of the phase difference of the coherent driving fields in the nondissipative environment (Γ3=0, Γ4=0). For (a-1) and (a-8), Δa,b=0; for (b-1) and (b-8), Δa,b=0.1ga. The other parameters are chosen as follows: gb=ga, V2/υg=1.8ga, and ωb=ωa.

Fig. 3.
Fig. 3.

Same as Fig. 2, except Γ3=0.05ga and Γ4=0.05ga.

Equations (17)

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E(t)=(E˜1+E˜2eiθ)eiωLt+c.c,
Heff=dx[CR(x)(iυgx+ωa)CR(x)+CL(x)(iυgxωa)CL(x)]+Vdxδ(x){[CR(x)+CL(x)]aa+aa[CR(x)+CL(x)]}+(ω31ωaiΓ3)σ33+(ω42ωbiΓ4)σ44+ga(aaσ31+aaσ13)+gb(abσ42+abσ24)+(Ω1+Ω2eiθ)σ23+(Ω1+Ω2eiθ)σ32,
ϕR(x)=eiqx[ϑ(x)+tϑ(x)],
ϕL(x)=reiqxϑ(x),
|Ek={dx[ϕR(x)CR+(x)+ϕL(x)CL+(x)]+Pcaa+P3σ31+P2σ21+P4abσ21}|0,0,1,1,
(ωaωiV2υg1)Pc+gaP3=V,
(ωaωΔaiΓ3)P3+gaPc+(Ω1+Ω2eiθ)P2=0,
(ωaω)P2+(Ω1+Ω2eiθ)P3+gbP4=0,
(ωaωΔbiΓ4)P4+gbP2=0.
Pc=V[Ω2D+(gbCD)B]·M1,
P3=Vga(CDgb2)·M1,
P2=ga(Ω1+Ω2eiθ)VD·M1,
P4=gagb(Ω1+Ω2eiθ)V·M1,
t={M+iV2υg1[Ω2D+(gbCD)B]}·M1,
r=iV2υg1[Ω2D+(gbCD)B]·M1.
θT=0=arccos[(CDgb)B2Ω12D1],θT=1=arccos(λ6+λ624λ52λ724Ω12λ521),
arccos(λ6λ624λ52λ724Ω12λ521),

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