Abstract

Understanding transport properties in quantum nanophotonics plays a central role in designing few-photon devices, yet it suffers from a longstanding extensive computational burden. In this work, we propose a statistically driven model with a tremendously eased computational burden, which is based on the deep understanding of the few-photon spontaneous emission process. By utilizing phenomenological, statistically driven inter-photon offset parameters, the proposed model expedites the transport calculation with a three-order-of-magnitude enhancement of speed in contrast to conventional numerical approaches. We showcase the two-photon transport computation benchmarked by the rigorous analytical approach. Our work provides an efficient tool for designing few-photon nano-devices, and it significantly deepens the understanding of correlated quantum many-body physics.

© 2020 Optical Society of America

Full Article  |  PDF Article
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Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems

Yuecheng Shen, Zihao Chen, Yu He, Zhaohui Li, and Jung-Tsung Shen
J. Opt. Soc. Am. B 35(3) 607-616 (2018)

Dissipation in few-photon waveguide transport [Invited]

Eden Rephaeli and Shanhui Fan
Photon. Res. 1(3) 110-114 (2013)

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  1. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
    [Crossref]
  2. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [Crossref]
  3. O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
    [Crossref]
  4. J. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. 98, 153003 (2007).
    [Crossref]
  5. H. Zheng, D. Gauthier, and H. Baranger, “Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system,” Phys. Rev. A 82, 063816 (2010).
    [Crossref]
  6. T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
    [Crossref]
  7. Y. Shen and J. Shen, “Photonic-Fock-state scattering in a waveguide-QED system and their correlation functions,” Phys. Rev. A 92, 033803 (2015).
    [Crossref]
  8. S. Xu and S. Fan, “Input-output formalism for few-photon transport: a systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
    [Crossref]
  9. Z. Chen, Y. Zhou, and J. Shen, “Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system,” Opt. Lett. 41, 3313–3316 (2016).
    [Crossref]
  10. M. Manzoni, D. Chang, and J. Douglas, “Simulating quantum light propagation through atomic ensembles using matrix product states,” Nat. Commun. 8, 1743 (2017).
    [Crossref]
  11. C. Gonzalez-Ballestero, E. Moreno, and F. Garcia-Vidal, “Generation, manipulation, and detection of two-qubit entanglement in waveguide QED,” Phys. Rev. A 89, 042328 (2014).
    [Crossref]
  12. Q. Li, L. Zhou, and C. Sun, “Waveguide quantum electrodynamics: controllable channel from quantum interference,” Phys. Rev. A 89, 063810 (2014).
    [Crossref]
  13. G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
    [Crossref]
  14. M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
    [Crossref]
  15. I. Mirza and J. Schotland, “Multiqubit entanglement in bidirectional-chiral-waveguide QED,” Phys. Rev. A 94, 012302 (2016).
    [Crossref]
  16. Y. Zhou, Z. Chen, and J. Shen, “Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide,” Phys. Rev. A 95, 043832 (2017).
    [Crossref]
  17. Z. Liao, M. Al-Amri, and M. Zubairy, “Measurement of deep-subwavelength emitter separation in a waveguide-QED system,” Opt. Express 25, 31997–32009 (2017).
    [Crossref]
  18. X. Zhang and H. Baranger, “Heralded Bell state of dissipative qubits using classical light in a waveguide,” Phys. Rev. Lett. 122, 140502 (2019).
    [Crossref]
  19. G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
    [Crossref]
  20. M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
    [Crossref]
  21. D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
    [Crossref]
  22. J. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. 30, 2001–2003 (2005).
    [Crossref]
  23. Z. Chen, Y. Zhou, and J. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
    [Crossref]
  24. Y. Shen, Z. Chen, Y. He, Z. Li, and J. Shen, “Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems,” J. Opt. Soc. Am. B 35, 607–616 (2018).
    [Crossref]
  25. Z. Chen, Y. Zhou, and J. Shen, “Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems,” Opt. Lett. 42, 887–890 (2017).
    [Crossref]
  26. Z. Chen, Y. Zhou, and J. Shen, “Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems,” Phys. Rev. A 98, 053830 (2018).
    [Crossref]

2019 (3)

X. Zhang and H. Baranger, “Heralded Bell state of dissipative qubits using classical light in a waveguide,” Phys. Rev. Lett. 122, 140502 (2019).
[Crossref]

G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
[Crossref]

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

2018 (3)

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Y. Shen, Z. Chen, Y. He, Z. Li, and J. Shen, “Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems,” J. Opt. Soc. Am. B 35, 607–616 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems,” Phys. Rev. A 98, 053830 (2018).
[Crossref]

2017 (5)

Z. Chen, Y. Zhou, and J. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems,” Opt. Lett. 42, 887–890 (2017).
[Crossref]

Y. Zhou, Z. Chen, and J. Shen, “Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide,” Phys. Rev. A 95, 043832 (2017).
[Crossref]

Z. Liao, M. Al-Amri, and M. Zubairy, “Measurement of deep-subwavelength emitter separation in a waveguide-QED system,” Opt. Express 25, 31997–32009 (2017).
[Crossref]

M. Manzoni, D. Chang, and J. Douglas, “Simulating quantum light propagation through atomic ensembles using matrix product states,” Nat. Commun. 8, 1743 (2017).
[Crossref]

2016 (4)

G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
[Crossref]

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

I. Mirza and J. Schotland, “Multiqubit entanglement in bidirectional-chiral-waveguide QED,” Phys. Rev. A 94, 012302 (2016).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system,” Opt. Lett. 41, 3313–3316 (2016).
[Crossref]

2015 (3)

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Y. Shen and J. Shen, “Photonic-Fock-state scattering in a waveguide-QED system and their correlation functions,” Phys. Rev. A 92, 033803 (2015).
[Crossref]

S. Xu and S. Fan, “Input-output formalism for few-photon transport: a systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

2014 (2)

C. Gonzalez-Ballestero, E. Moreno, and F. Garcia-Vidal, “Generation, manipulation, and detection of two-qubit entanglement in waveguide QED,” Phys. Rev. A 89, 042328 (2014).
[Crossref]

Q. Li, L. Zhou, and C. Sun, “Waveguide quantum electrodynamics: controllable channel from quantum interference,” Phys. Rev. A 89, 063810 (2014).
[Crossref]

2010 (2)

H. Zheng, D. Gauthier, and H. Baranger, “Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system,” Phys. Rev. A 82, 063816 (2010).
[Crossref]

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

2007 (1)

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

2005 (1)

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[Crossref]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

Abdumalikov, A.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Ahmed, S.

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

Al-Amri, M.

Astafiev, O.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Baranger, H.

X. Zhang and H. Baranger, “Heralded Bell state of dissipative qubits using classical light in a waveguide,” Phys. Rev. Lett. 122, 140502 (2019).
[Crossref]

H. Zheng, D. Gauthier, and H. Baranger, “Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system,” Phys. Rev. A 82, 063816 (2010).
[Crossref]

Busch, K.

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

Calajó, G.

G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
[Crossref]

Chang, D.

M. Manzoni, D. Chang, and J. Douglas, “Simulating quantum light propagation through atomic ensembles using matrix product states,” Nat. Commun. 8, 1743 (2017).
[Crossref]

G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
[Crossref]

Chang, D. E.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Chen, Z.

Y. Shen, Z. Chen, Y. He, Z. Li, and J. Shen, “Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems,” J. Opt. Soc. Am. B 35, 607–616 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems,” Phys. Rev. A 98, 053830 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems,” Opt. Lett. 42, 887–890 (2017).
[Crossref]

Y. Zhou, Z. Chen, and J. Shen, “Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide,” Phys. Rev. A 95, 043832 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system,” Opt. Lett. 41, 3313–3316 (2016).
[Crossref]

Cheng, M.

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Ciccarello, F.

G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
[Crossref]

Cirac, J. I.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Deng, F.

G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
[Crossref]

Douglas, J.

M. Manzoni, D. Chang, and J. Douglas, “Simulating quantum light propagation through atomic ensembles using matrix product states,” Nat. Commun. 8, 1743 (2017).
[Crossref]

Fan, S.

S. Xu and S. Fan, “Input-output formalism for few-photon transport: a systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

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

Garcia-Vidal, F.

C. Gonzalez-Ballestero, E. Moreno, and F. Garcia-Vidal, “Generation, manipulation, and detection of two-qubit entanglement in waveguide QED,” Phys. Rev. A 89, 042328 (2014).
[Crossref]

Gauthier, D.

H. Zheng, D. Gauthier, and H. Baranger, “Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system,” Phys. Rev. A 82, 063816 (2010).
[Crossref]

Gonzalez-Ballestero, C.

C. Gonzalez-Ballestero, E. Moreno, and F. Garcia-Vidal, “Generation, manipulation, and detection of two-qubit entanglement in waveguide QED,” Phys. Rev. A 89, 042328 (2014).
[Crossref]

He, Y.

Huang, X.

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Inomata, K.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Kwek, L.

G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
[Crossref]

Lakshmi, A.

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

Li, Q.

Q. Li, L. Zhou, and C. Sun, “Waveguide quantum electrodynamics: controllable channel from quantum interference,” Phys. Rev. A 89, 063810 (2014).
[Crossref]

Li, Z.

Liao, Z.

Long, G.

G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
[Crossref]

Ma, X.

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Manzoni, M.

M. Manzoni, D. Chang, and J. Douglas, “Simulating quantum light propagation through atomic ensembles using matrix product states,” Nat. Commun. 8, 1743 (2017).
[Crossref]

Mirza, I.

I. Mirza and J. Schotland, “Multiqubit entanglement in bidirectional-chiral-waveguide QED,” Phys. Rev. A 94, 012302 (2016).
[Crossref]

Moreno, E.

C. Gonzalez-Ballestero, E. Moreno, and F. Garcia-Vidal, “Generation, manipulation, and detection of two-qubit entanglement in waveguide QED,” Phys. Rev. A 89, 042328 (2014).
[Crossref]

Nakamura, Y.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Panigrahi, P.

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

Parit, M.

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

Pashkin, Y.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Rabl, P.

G. Calajó, F. Ciccarello, D. Chang, and P. Rabl, “Atom-field dressed states in slow-light waveguide QED,” Phys. Rev. A 93, 033833 (2016).
[Crossref]

Schmitteckert, P.

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

Schneider, M.

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

Schotland, J.

I. Mirza and J. Schotland, “Multiqubit entanglement in bidirectional-chiral-waveguide QED,” Phys. Rev. A 94, 012302 (2016).
[Crossref]

Shen, J.

Y. Shen, Z. Chen, Y. He, Z. Li, and J. Shen, “Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems,” J. Opt. Soc. Am. B 35, 607–616 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems,” Phys. Rev. A 98, 053830 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems,” Opt. Lett. 42, 887–890 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
[Crossref]

Y. Zhou, Z. Chen, and J. Shen, “Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide,” Phys. Rev. A 95, 043832 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system,” Opt. Lett. 41, 3313–3316 (2016).
[Crossref]

Y. Shen and J. Shen, “Photonic-Fock-state scattering in a waveguide-QED system and their correlation functions,” Phys. Rev. A 92, 033803 (2015).
[Crossref]

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

Shen, Y.

Y. Shen, Z. Chen, Y. He, Z. Li, and J. Shen, “Exact approach for spatiotemporal dynamics of spontaneous emissions in waveguide quantum electrodynamic systems,” J. Opt. Soc. Am. B 35, 607–616 (2018).
[Crossref]

Y. Shen and J. Shen, “Photonic-Fock-state scattering in a waveguide-QED system and their correlation functions,” Phys. Rev. A 92, 033803 (2015).
[Crossref]

Shi, T.

T. Shi, D. E. Chang, and J. I. Cirac, “Multiphoton-scattering theory and generalized master equations,” Phys. Rev. A 92, 053834 (2015).
[Crossref]

Singh, S.

M. Parit, S. Ahmed, S. Singh, A. Lakshmi, and P. Panigrahi, “Correlated photons of desired characteristics from a dipole coupled three-atom system,” OSA Contin. 2, 2293–2307 (2019).
[Crossref]

Song, G.

G. Song, L. Kwek, F. Deng, and G. Long, “Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal,” Phys. Rev. A 99, 043830 (2019).
[Crossref]

Sproll, T.

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

Stawiarski, C.

M. Schneider, T. Sproll, C. Stawiarski, P. Schmitteckert, and K. Busch, “Green’s-function formalism for waveguide QED applications,” Phys. Rev. A 93, 013828 (2016).
[Crossref]

Sun, C.

Q. Li, L. Zhou, and C. Sun, “Waveguide quantum electrodynamics: controllable channel from quantum interference,” Phys. Rev. A 89, 063810 (2014).
[Crossref]

Tsai, J.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Xu, J.

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Xu, S.

S. Xu and S. Fan, “Input-output formalism for few-photon transport: a systematic treatment beyond two photons,” Phys. Rev. A 91, 043845 (2015).
[Crossref]

Yamamoto, T.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Yang, D.

D. Yang, M. Cheng, X. Ma, J. Xu, C. Zhu, and X. Huang, “Phase-modulated single-photon router,” Phys. Rev. A 98, 063809 (2018).
[Crossref]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[Crossref]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[Crossref]

Zagoskin, A.

O. Astafiev, A. Zagoskin, A. Abdumalikov, Y. Pashkin, T. Yamamoto, K. Inomata, Y. Nakamura, and J. Tsai, “Resonance fluorescence of a single artificial atom,” Science 327, 840–843 (2010).
[Crossref]

Zhang, X.

X. Zhang and H. Baranger, “Heralded Bell state of dissipative qubits using classical light in a waveguide,” Phys. Rev. Lett. 122, 140502 (2019).
[Crossref]

Zheng, H.

H. Zheng, D. Gauthier, and H. Baranger, “Waveguide QED: many-body bound-state effects in coherent and Fock-state scattering from a two-level system,” Phys. Rev. A 82, 063816 (2010).
[Crossref]

Zhou, L.

Q. Li, L. Zhou, and C. Sun, “Waveguide quantum electrodynamics: controllable channel from quantum interference,” Phys. Rev. A 89, 063810 (2014).
[Crossref]

Zhou, Y.

Z. Chen, Y. Zhou, and J. Shen, “Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems,” Phys. Rev. A 98, 053830 (2018).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems,” Opt. Lett. 42, 887–890 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
[Crossref]

Y. Zhou, Z. Chen, and J. Shen, “Single-photon superradiant emission rate scaling for atoms trapped in a photonic waveguide,” Phys. Rev. A 95, 043832 (2017).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematics of the system of interest. $\omega$ is the frequency of the incident photon, and ${\omega_a}$ is the resonant frequency of the two-level atom. (b) Single-photon transmission and reflection spectra of the system. $g$ is the coupling strength between the atom and the waveguide. (c) Two-photon transmission of the system for incident photons with different pulse widths. The blue solid line describes the probability of finding both photons being transmitted, while the red dashed line represents the square of the single-photon transmission. (d) The probability density function of a typical two-photon state (${{\rm\sigma}_x}=15\;{\rm v}/{\rm g}$) after interacting with the two-level atom.
Fig. 2.
Fig. 2. (a) Transport properties of the waveguide QED system for two-photon input states with variable pulse width ${\sigma_x}$. The values predicted using our model (solid lines) were in agreement with the ones computed using the S-matrix approach. (b) Relative errors between the values obtained using our model and S matrix.
Fig. 3.
Fig. 3. (a) Probability density function in the fourth quadrant. The white dashed line represents the function of ${x_2}=-{x_1}$. (b) Comparison of the values computed using our model and the S matrix. Relative errors are plotted using the blue dashed line.
Fig. 4.
Fig. 4. Comparison of the transport properties under various dissipations computed using our modified model (solid lines) and the S matrix (round circles). ${P_{{\rm TT}}}(\gamma)$, ${P_{{\rm RR}}}(\gamma)$, and ${P_{{\rm TR}}}(\gamma)$ are represented using blue, black, and red, respectively. (a) ${{\rm\sigma}_x}=15\;{\rm v}/{\rm g}$. (b) ${{\rm\sigma}_x}=10\;{\rm v}/{\rm g}$.

Tables (1)

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Table 1. Performance Comparison of Different Methods to Compute Transport Propertiesa

Equations (13)

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t ( ω ) = ( ω ω a ) ( ω ω a ) + i g ,
r ( ω ) = i g ( ω ω a ) + i g ,
φ T ( x ) = F 1 [ t ( ω ) F [ φ i n ( x ) ] ] ,
φ R ( x ) = F 1 [ r ( ω ) F [ φ i n ( x ) ] ] ,
P T = + | φ T ( x ) | 2 d x ,
P R = + | φ R ( x ) | 2 d x .
P T T = 0 l 1 + + | φ i n ( x 1 , x 2 ) | 2 × δ ( | x 1 x 2 | l ) d l d x 1 d x 2 .
P R R = l 2 + + + | φ i n ( x 1 , x 2 ) | 2 × δ ( | x 1 x 2 | l ) d l d x 1 d x 2 .
P T R = l 1 l 2 + + | φ i n ( x 1 , x 2 ) | 2 × δ ( | x 1 x 2 | l ) d l d x 1 d x 2 ,
P T T ( γ ) = g 4 ( γ + g ) 4 P T T ( γ = 0 ) .
P R R ( γ ) = g 4 ( γ + g ) 4 P R R ( γ = 0 ) .
P T R ( γ ) = P R ( γ ) P T R ( γ = 0 ) + 2 P R ( γ ) P T ( γ ) P R R ( γ = 0 ) .
P T R ( γ ) = g 2 ( γ + g ) 2 P T R ( γ = 0 ) + 2 g 2 γ 2 ( γ + g ) 2 P R R ( γ = 0 ) .

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