Abstract

We note that most of the studies of the single photon scattering inside a one-dimensional coupled resonator waveguide are based on the waveguide coupling with the atom systems. In this paper, we will study the single photon scattering enabled by another system, i.e., the second-order nonlinearity, which can act as a single photon switch to control the single photon transmission and reflection inside the one-dimensional coupled resonator waveguide. The transmission rate is calculated to analyze the single-photon scattering properties. In addition, a more complicated second-order nonlinear form, i.e., three-wave mixing, is discussed to control single photon transmission inside the one-dimensional coupled resonator waveguide.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  57. X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117(12), 123902 (2016).
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  58. X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency,” Optica 3(10), 1126–1131 (2016).
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    [Crossref]
  60. M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
    [Crossref]

2018 (4)

H. Z. Shen, S. Xu, Y. H.Zhou, G. Wang, and X. X. Yi, “Unconventional photon blockade from bimodal driving and dissipations in coupled semiconductor microcavities,” J. Phys. B 51(3), 035503 (2018).
[Crossref]

H. Z. Shen, C. Shang, Y. H. Zhou, and X. X. Yi, “Unconventional single-photon blockade in non-Markovian systems,” Phys. Rev. A 98(2), 023856 (2018).
[Crossref]

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. I. Formalism,” Phys. Rev. A 97(4), 043837 (2018).
[Crossref]

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. II. Application to emitters coupled to a one-dimensional waveguide,” Phys. Rev. A 97(4), 043838 (2018).
[Crossref]

2017 (7)

C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X.-F. Ren, G.-C. Guo, and M. Lončar, “Second harmonic generation in nano-structured thin-film lithium niobate waveguides,” Opt. Express 25(6), 6963–6973 (2017).
[Crossref]

N. Sinclair, D. Oblak, C. W. Thiel, R. L. Cone, and W. Tittel, “Properties of a Rare-Earth-Ion-Doped Waveguide at Sub-Kelvin Temperatures for Quantum Signal Processing,” Phys. Rev. Lett. 118(10), 100504 (2017).
[Crossref]

Y. H. Zhou, H. Z. Shen, X. Y. Luo, Y. Wang, F. Gao, and C. Y. Xin, “Tunable three-wave-mixing-induced transparency,” Phys. Rev. A 96(6), 063815 (2017).
[Crossref]

Y. H. Zhou, S. S. Zhang, H. Z. Shen, and X. X. Yi, “Second-order nonlinearity induced transparency,” Opt. Lett. 42(7), 1289–1292 (2017).
[Crossref]

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light: Sci. Appl. 6(5), e16249 (2017).
[Crossref]

S. L. Su, Y. Z. Tian, H. Z. Shen, H. P. Zang, E. J. Liang, and S. Zhang, “Applications of the modified Rydberg antiblockade regime with simultaneous driving,” Phys. Rev. A 96(4), 042335 (2017).
[Crossref]

S. L.Su, Y. Gao, E. J. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95(2), 022319 (2017).
[Crossref]

2016 (4)

S. L. Su, E. J Liang, S. Zhang, J. J. Wen, L. L. Sun, Z. Jin, and A. D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93(1), 012306 (2016).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117(12), 123902 (2016).
[Crossref]

X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency,” Optica 3(10), 1126–1131 (2016).
[Crossref]

Y. H. Zhou, H. Z. Shen, X. Q. Shao, and X. X. Yi, “Strong photon antibunching with weak second-order nonlinearity under dissipation and coherent driving,” Opt. Express 24(15), 17332–17344 (2016).
[Crossref]

2015 (4)

Y. H. Zhou, H. Z. Shen, and X. X. Yi, “Unconventional photon blockade with second-order nonlinearity,” Phys. Rev. A 92(2), 023838 (2015).
[Crossref]

Z. H. Wang, C. P. Sun, and Y. Li, “Microwave degenerate parametric down-conversion with a single cyclic three-level system in a circuit-QED setup,” Phys. Rev. A 91(4), 043801 (2015).
[Crossref]

H. Z. Shen, Y. H. Zhou, H. D. Liu, G. C. Wang, and X. X. Yi, “Exact optimal control of photon blockade with weakly nonlinear coupled,” Opt. Express 23(25), 32835 (2015).
[Crossref]

H. Z. Shen, Y. H. Zhou, and X. X. Yi, “Tunable photon blockade in coupled semiconductor cavities,” Phys. Rev. A 91(6), 063808 (2015).
[Crossref]

2014 (2)

P. S. Kuo, J. Bravo-Abad, and G. S. Solomon, “Second-harmonic generation using-quasi-phasematching in a GaAs whispering-gallery-mode microcavity,” Nat. Commun. 5(1), 3109 (2014).
[Crossref]

H. Z. Shen, Y. H. Zhou, and X. X. Yi, “Quantum optical diode with semiconductor microcavities,” Phys. Rev. A 90(2), 023849 (2014).
[Crossref]

2013 (3)

A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87(23), 235319 (2013).
[Crossref]

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013).
[Crossref]

Z.-Y. Zhang, Y.-L. Dong, S.-L. Zhang, and S.-Q. Zhu, “Polarization-dependent photon switch in a one-dimensional coupled-resonator waveguide,” Opt. Express 21(18), 20786–20799 (2013).
[Crossref]

2012 (2)

M.-T. Cheng, X.-S. Ma, M.-T. Ding, Y.-Q. Luo, and G.-X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal coupling to a nanocavity containing a two-level system,” Phys. Rev. A 85(5), 053840 (2012).
[Crossref]

Z.-F. Bi, A. W. Rodriguez, H. Hashemi, D. Duchesne, M. Loncar, K.-M. Wang, and S. G. Johnson, “High-efficiency second-harmonic generation in doubly-resonant χ2 microring resonators,” Opt. Express 20(7), 7526–7543 (2012).
[Crossref]

2011 (7)

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett. 107(17), 173902 (2011).
[Crossref]

D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency,” Phys. Rev. Lett. 106(5), 053601 (2011).
[Crossref]

E. Rephaeli, S. E. Kocabas, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A 84(6), 063832 (2011).
[Crossref]

I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, “Demonstration of a Single-Photon Router in the Microwave Regime,” Phys. Rev. Lett. 107(7), 073601 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

D. Roy, “Correlated few-photon transport in one-dimensional waveguides: Linear and nonlinear dispersions,” Phys. Rev. A 83(4), 043823 (2011).
[Crossref]

2010 (6)

M. Alexanian, “Scattering of two coherent photons inside a one-dimensional coupled-resonator waveguide,” Phys. Rev. A 81(1), 015805 (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(4), 042304 (2010).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. 12(4), 043052 (2010).
[Crossref]

D. Roy, “Few-photon optical diode,” Phys. Rev. B 81(15), 155117 (2010).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

2009 (3)

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A 80(3), 033823 (2009).
[Crossref]

J.-Q. Liao, J.-F. Huang, Y.-X. Liu, L.-M. Kuang, and C. P. Sun, “Quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator array,” Phys. Rev. A 80(1), 014301 (2009).
[Crossref]

T. Shi and C. P. Sun, “Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays,” Phys. Rev. B 79(20), 205111 (2009).
[Crossref]

2008 (7)

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(10), 100501 (2008).
[Crossref]

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A 77(1), 013831 (2008).
[Crossref]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78(6), 063827 (2008).
[Crossref]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A 78(5), 053806 (2008).
[Crossref]

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A 78(6), 063832 (2008).
[Crossref]

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savelev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80(4), 1201–1213 (2008).
[Crossref]

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
[Crossref]

2007 (3)

A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
[Crossref]

J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98(15), 153003 (2007).
[Crossref]

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

2006 (3)

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref]

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

2005 (2)

J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with super-conducting quantum bits,” Phys. Rev. Lett. 95(21), 213001 (2005).
[Crossref]

J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30(15), 2001–2003 (2005).
[Crossref]

2004 (1)

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

2003 (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425(6961), 944–947 (2003).
[Crossref]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425(6961), 944–947 (2003).
[Crossref]

Alexanian, M.

M. Alexanian, “Scattering of two coherent photons inside a one-dimensional coupled-resonator waveguide,” Phys. Rev. A 81(1), 015805 (2010).
[Crossref]

Andrade, N.

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425(6961), 944–947 (2003).
[Crossref]

Bauch, T.

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
[Crossref]

Bi, Z.-F.

Blais, A.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savelev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80(4), 1201–1213 (2008).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savelev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80(4), 1201–1213 (2008).
[Crossref]

Bouwmeester, D.

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

Bradford, M.

Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett. 107(17), 173902 (2011).
[Crossref]

Bravo-Abad, J.

P. S. Kuo, J. Bravo-Abad, and G. S. Solomon, “Second-harmonic generation using-quasi-phasematching in a GaAs whispering-gallery-mode microcavity,” Nat. Commun. 5(1), 3109 (2014).
[Crossref]

Busch, K.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

Chang, D. E.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref]

Cheng, M.-T.

M.-T. Cheng, X.-S. Ma, M.-T. Ding, Y.-Q. Luo, and G.-X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal coupling to a nanocavity containing a two-level system,” Phys. Rev. A 85(5), 053840 (2012).
[Crossref]

Cheng, R.

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light: Sci. Appl. 6(5), e16249 (2017).
[Crossref]

Cone, R. L.

N. Sinclair, D. Oblak, C. W. Thiel, R. L. Cone, and W. Tittel, “Properties of a Rare-Earth-Ion-Doped Waveguide at Sub-Kelvin Temperatures for Quantum Signal Processing,” Phys. Rev. Lett. 118(10), 100504 (2017).
[Crossref]

Das, S.

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. II. Application to emitters coupled to a one-dimensional waveguide,” Phys. Rev. A 97(4), 043838 (2018).
[Crossref]

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. I. Formalism,” Phys. Rev. A 97(4), 043837 (2018).
[Crossref]

Delsing, P.

I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, “Demonstration of a Single-Photon Router in the Microwave Regime,” Phys. Rev. Lett. 107(7), 073601 (2011).
[Crossref]

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
[Crossref]

Ding, M.-T.

M.-T. Cheng, X.-S. Ma, M.-T. Ding, Y.-Q. Luo, and G.-X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal coupling to a nanocavity containing a two-level system,” Phys. Rev. A 85(5), 053840 (2012).
[Crossref]

Dong, H.

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78(6), 063827 (2008).
[Crossref]

Dong, Y.-L.

Duchesne, D.

Duty, T.

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
[Crossref]

Elfving, V. E.

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. II. Application to emitters coupled to a one-dimensional waveguide,” Phys. Rev. A 97(4), 043838 (2018).
[Crossref]

S. Das, V. E. Elfving, F. Reiter, and A. S. Sørensen, “Photon scattering from a system of multilevel quantum emitters. I. Formalism,” Phys. Rev. A 97(4), 043837 (2018).
[Crossref]

Englund, D.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

Fan, S.

E. Rephaeli, S. E. Kocabas, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A 84(6), 063832 (2011).
[Crossref]

J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98(15), 153003 (2007).
[Crossref]

J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30(15), 2001–2003 (2005).
[Crossref]

J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with super-conducting quantum bits,” Phys. Rev. Lett. 95(21), 213001 (2005).
[Crossref]

Faraon, A.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

Freilikher, V.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savelev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80(4), 1201–1213 (2008).
[Crossref]

Frunzio, L.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

Fushman, I.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

Gao, F.

Y. H. Zhou, H. Z. Shen, X. Y. Luo, Y. Wang, F. Gao, and C. Y. Xin, “Tunable three-wave-mixing-induced transparency,” Phys. Rev. A 96(6), 063815 (2017).
[Crossref]

Gao, R.

K. Wang, J. Li, R. Gao, and Z. Qi, “LiNbO3 waveguide Based Fourier Transform Spectrometer with Algorithmic Enhancement of Spectral Resolution,” in Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), OSA Techncail Digest (online) (Optical Society of America, 2018), paper JTu6D.1.

Gao, Y.

S. L.Su, Y. Gao, E. J. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95(2), 022319 (2017).
[Crossref]

Gao, Y. B.

L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A 77(1), 013831 (2008).
[Crossref]

Gerace, D.

A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87(23), 235319 (2013).
[Crossref]

Girvin, S. M.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[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(4), 042304 (2010).
[Crossref]

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A 78(5), 053806 (2008).
[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(10), 100501 (2008).
[Crossref]

Guo, G.-C.

Guo, X.

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light: Sci. Appl. 6(5), e16249 (2017).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117(12), 123902 (2016).
[Crossref]

X. Guo, C.-L. Zou, and H. X. Tang, “Second-harmonic generation in aluminum nitride microrings with 2500%/W conversion efficiency,” Optica 3(10), 1126–1131 (2016).
[Crossref]

H.Zhou, Y.

H. Z. Shen, S. Xu, Y. H.Zhou, G. Wang, and X. X. Yi, “Unconventional photon blockade from bimodal driving and dissipations in coupled semiconductor microcavities,” J. Phys. B 51(3), 035503 (2018).
[Crossref]

Hashemi, H.

Hemmer, P. R.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref]

Hennessy, K.

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

Hoi, I. C.

I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, “Demonstration of a Single-Photon Router in the Microwave Regime,” Phys. Rev. Lett. 107(7), 073601 (2011).
[Crossref]

Huang, J.-F.

J.-Q. Liao, J.-F. Huang, Y.-X. Liu, L.-M. Kuang, and C. P. Sun, “Quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator array,” Phys. Rev. A 80(1), 014301 (2009).
[Crossref]

Huang, K.

Q. Zhou, K. Huang, H. Pan, E. Wu, and H. Zeng, “Ultrasensitive mid-infrared up-conversion imaging at few-photon level,” Appl. Phys. Lett. 102(24), 241110 (2013).
[Crossref]

Huang, R.-S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

Ian, H.

Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A 78(5), 053806 (2008).
[Crossref]

Irvine, W. T. M.

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

W. T. M. Irvine, K. Hennessy, and D. Bouwmeester, “Strong Coupling between Single Photons in Semiconductor Microcavities,” Phys. Rev. Lett. 96(5), 057405 (2006).
[Crossref]

Jin, Z.

S. L. Su, E. J Liang, S. Zhang, J. J. Wen, L. L. Sun, Z. Jin, and A. D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93(1), 012306 (2016).
[Crossref]

Joannopoulos, J. D.

Johansson, G.

I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, “Demonstration of a Single-Photon Router in the Microwave Regime,” Phys. Rev. Lett. 107(7), 073601 (2011).
[Crossref]

M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, “Tuning the field in a microwave resonator faster than the photon lifetime,” Appl. Phys. Lett. 92(20), 203501 (2008).
[Crossref]

Johnson, S. G.

Jung, H.

X. Guo, C.-L. Zou, C. Schuck, H. Jung, R. Cheng, and H. X. Tang, “Parametric down-conversion photon-pair source on a nanophotonic chip,” Light: Sci. Appl. 6(5), e16249 (2017).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117(12), 123902 (2016).
[Crossref]

Kocabas, S. E.

E. Rephaeli, S. E. Kocabas, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A 84(6), 063832 (2011).
[Crossref]

Kuang, L.-M.

J.-Q. Liao, J.-F. Huang, Y.-X. Liu, L.-M. Kuang, and C. P. Sun, “Quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator array,” Phys. Rev. A 80(1), 014301 (2009).
[Crossref]

Kumar, S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

Kuo, P. S.

P. S. Kuo, J. Bravo-Abad, and G. S. Solomon, “Second-harmonic generation using-quasi-phasematching in a GaAs whispering-gallery-mode microcavity,” Nat. Commun. 5(1), 3109 (2014).
[Crossref]

L.Su, S.

S. L.Su, Y. Gao, E. J. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95(2), 022319 (2017).
[Crossref]

Law, C. K.

T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A 80(3), 033823 (2009).
[Crossref]

T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A 78(6), 063832 (2008).
[Crossref]

Li, J.

K. Wang, J. Li, R. Gao, and Z. Qi, “LiNbO3 waveguide Based Fourier Transform Spectrometer with Algorithmic Enhancement of Spectral Resolution,” in Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), OSA Techncail Digest (online) (Optical Society of America, 2018), paper JTu6D.1.

Li, Y.

Z. H. Wang, C. P. Sun, and Y. Li, “Microwave degenerate parametric down-conversion with a single cyclic three-level system in a circuit-QED setup,” Phys. Rev. A 91(4), 043801 (2015).
[Crossref]

Liang, E. J

S. L. Su, E. J Liang, S. Zhang, J. J. Wen, L. L. Sun, Z. Jin, and A. D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93(1), 012306 (2016).
[Crossref]

Liang, E. J.

S. L.Su, Y. Gao, E. J. Liang, and S. Zhang, “Fast Rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95(2), 022319 (2017).
[Crossref]

S. L. Su, Y. Z. Tian, H. Z. Shen, H. P. Zang, E. J. Liang, and S. Zhang, “Applications of the modified Rydberg antiblockade regime with simultaneous driving,” Phys. Rev. A 96(4), 042335 (2017).
[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(4), 042304 (2010).
[Crossref]

Liao, J.-Q.

J.-Q. Liao, J.-F. Huang, Y.-X. Liu, L.-M. Kuang, and C. P. Sun, “Quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator array,” Phys. Rev. A 80(1), 014301 (2009).
[Crossref]

Liu, H. D.

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(4), 042304 (2010).
[Crossref]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78(6), 063827 (2008).
[Crossref]

Liu, Y.-X.

J.-Q. Liao, J.-F. Huang, Y.-X. Liu, L.-M. Kuang, and C. P. Sun, “Quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator array,” Phys. Rev. A 80(1), 014301 (2009).
[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(10), 100501 (2008).
[Crossref]

Loncar, M.

Longo, P.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83(6), 063828 (2011).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett. 104(2), 023602 (2010).
[Crossref]

Lukin, M. D.

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97(5), 053002 (2006).
[Crossref]

Luo, X. Y.

Y. H. Zhou, H. Z. Shen, X. Y. Luo, Y. Wang, F. Gao, and C. Y. Xin, “Tunable three-wave-mixing-induced transparency,” Phys. Rev. A 96(6), 063815 (2017).
[Crossref]

Luo, Y.-Q.

M.-T. Cheng, X.-S. Ma, M.-T. Ding, Y.-Q. Luo, and G.-X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal coupling to a nanocavity containing a two-level system,” Phys. Rev. A 85(5), 053840 (2012).
[Crossref]

Ma, X.-S.

M.-T. Cheng, X.-S. Ma, M.-T. Ding, Y.-Q. Luo, and G.-X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal coupling to a nanocavity containing a two-level system,” Phys. Rev. A 85(5), 053840 (2012).
[Crossref]

Majer, J.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431(7005), 162–167 (2004).
[Crossref]

Majumdar, A.

A. Majumdar and D. Gerace, “Single-photon blockade in doubly resonant nanocavities with second-order nonlinearity,” Phys. Rev. B 87(23), 235319 (2013).
[Crossref]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature (London) 425(6961), 944–947 (2003).
[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(4), 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(10), 100501 (2008).
[Crossref]

L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A 78(6), 063827 (2008).
[Crossref]

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savelev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80(4), 1201–1213 (2008).
[Crossref]

Oblak, D.

N. Sinclair, D. Oblak, C. W. Thiel, R. L. Cone, and W. Tittel, “Properties of a Rare-Earth-Ion-Doped Waveguide at Sub-Kelvin Temperatures for Quantum Signal Processing,” Phys. Rev. Lett. 118(10), 100504 (2017).
[Crossref]

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H. Z. Shen, C. Shang, Y. H. Zhou, and X. X. Yi, “Unconventional single-photon blockade in non-Markovian systems,” Phys. Rev. A 98(2), 023856 (2018).
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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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S. L. Su, E. J Liang, S. Zhang, J. J. Wen, L. L. Sun, Z. Jin, and A. D. Zhu, “One-step implementation of the Rydberg-Rydberg-interaction gate,” Phys. Rev. A 93(1), 012306 (2016).
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Zhu, S.-Q.

Zou, C.-L.

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Optica (1)

Phys. Rev. A (24)

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Other (1)

K. Wang, J. Li, R. Gao, and Z. Qi, “LiNbO3 waveguide Based Fourier Transform Spectrometer with Algorithmic Enhancement of Spectral Resolution,” in Advanced Photonics 2018 (BGPP, IPR, NP, NOMA, Sensors, Networks, SPPCom, SOF), OSA Techncail Digest (online) (Optical Society of America, 2018), paper JTu6D.1.

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Figures (5)

Fig. 1.
Fig. 1. Schematic illustration of the coherent transport of a single photon in a coupled-resonator waveguide, where one resonator of the waveguide coupling to an additional resonator via $\chi ^{(2)}$ nonlinearity.
Fig. 2.
Fig. 2. Transmission rate $T$ as a function of $k$ and $g$ for different $\omega _a$ and $\omega _b$ . (a) $\omega _a=3$ and $\omega _b=1.5$ . (b) $\omega _a=3$ and $\omega _b=1$ . (c) $\omega _a=6$ and $\omega _b=2$ . All the parameters are rescaled by the hopping energy $\xi$ in this paper.
Fig. 3.
Fig. 3. (a) $T$ as a function of $\Delta _a$ and $\Delta _b$ with $g=1$ . (b) $T$ as a function of $g$ and $\Delta$ . (c) $T$ as a function of $\Delta$ with $g=0.4$ . In both (b) and (c), $\Delta =\Delta _a=\Delta _b$ , $\Delta _a=E_k-\omega _a$ and $\Delta _a=E_k-2\omega _b$ .
Fig. 4.
Fig. 4. The comparison of the transmission rate of the second-order nonlinearity system with the two-level system, where the solid line denotes the second-order nonlinearity system and the dotted line denotes the two-level system. (a) $g=0.3$ , $J=0.3$ . (b) $g=1$ , $J=1$ . In both (a) and (b), the parameters are $\omega _a=6$ and $\omega _b=3$ for second-order nonlinear system, and $\omega _a=6$ and $\omega _b=6$ for the two-level system.
Fig. 5.
Fig. 5. $T$ as a function of $k$ with $g=1$ for different $\omega _a$ , $\omega _b$ and $\omega _c$ .

Equations (24)

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H = H a + H b + H i ,
H a = ω a j a j a j ξ j ( a j a j + 1 + a j + 1 a j ) , H b = ω b b 0 b 0 , H i = g ( a 0 b 0 2 + b 0 2 a 0 ) ,
| E k = j u k ( j ) a j | 0 a | 0 b + u b | 0 a | 2 b ,
( E k ω a ) u k ( j ) 2 g u b δ j , 0 = ξ [ u k ( j 1 ) + u k ( j + 1 ) ] , ( E k 2 ω b ) u b = 2 g u k ( 0 ) .
( E k ω a + V g ) u k ( j ) = ξ [ u k ( j 1 ) + u k ( j + 1 ) ] ,
V g = 2 g 2 δ j , 0 E k 2 ω b .
u k ( j ) = { e i k j + r e i k j , j < 0 , t e i k j , j > 0 ,
E k = ω a 2 ξ cos k ,
t = 2 i ξ ( E k 2 ω b ) sin k 2 g 2 + 2 i ξ ( E k 2 ω b ) sin k , r = 2 g 2 2 g 2 + 2 i ξ ( E k 2 ω b ) sin k .
k = n π , k = arccos ( ω a 2 ω b 2 ξ ) .
t = 2 i ξ Δ b 1 ( Δ a 2 ξ ) 2 2 g 2 + 2 i ξ Δ b 1 ( Δ a 2 ξ ) 2 ,
H = H a + ω b σ + σ + J ( a 0 σ + σ + a 0 ) ,
t = 2 i ξ ( E k ω b ) sin k J 2 + 2 i ξ ( E k ω b ) sin k .
V J = J 2 δ j , 0 E k ω b .
H = H a + H b + H i ,
H b = ω b b 0 b 0 + ω c c 0 c 0 , H i = g ( a 0 b 0 c 0 + c 0 b 0 a 0 ) ,
| E k = j u k ( j ) a j | 0 a | 0 b | 0 c + u b | 0 a | 1 b | 1 c ,
( E k ω a ) u k ( j ) g u b δ j , 0 = ξ [ u k ( j 1 ) + u k ( j + 1 ) ] , ( E k ω b ω c ) u b = g u k ( 0 ) δ j , 0 .
t = 2 i ξ sin k ( E k ω b ω c ) g 2 + 2 i ξ ( E k ω b ω c ) sin k .
k = n π , k = arccos ( ω a ω b ω c 2 ξ ) ,
a k = 1 N j a j e i k j , a j = 1 N k a k e i k j .
ω a j a j a j ξ j ( a j + 1 a j + a j a j + 1 ) , = j { ω a 1 N k a k e i k j 1 N k a k e i k j ξ [ 1 N k a k e i k ( j + 1 ) 1 N k a k e i k j + 1 N k a k e i k j 1 N k a k e i k ( j + 1 ) ] } = j ω a 1 N k k a k a k e i ( k k ) j ξ j [ 1 N k k a k a k e i ( k k ) j e i k + 1 N k k a k a k e i ( k k ) j e i k ] .
1 N j e i ( k k ) j = δ k , k ,
ω a k k a k a k δ k , k ξ ( k k a k a k δ k , k e i k + k k a k a k δ k , k e i k ) = ω a k a k a k ξ ( k a k a k e i k + k a k a k e i k ) = ( ω a 2 ξ cos k ) k a k a k .

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