Abstract

We develop a formulation of few-photon Fock-space waveguide transport that includes dissipation in the form of reservoir coupling. We develop the formalism for the case of a two-level atom and then show that our formalism leads to a simple rule that allows one to obtain the dissipative description of a system from the nondissipative case.

© 2013 Chinese Laser Press

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  1. I. R. Senitzky, “Dissipation in quantum mechanics. the harmonic oscillator,” Phys. Rev. 119, 670–679 (1960).
    [CrossRef]
  2. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations (Springer, 2003).
  3. J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
    [CrossRef]
  4. C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
    [CrossRef]
  5. E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
    [CrossRef]
  6. J.-T. Shen and S. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett. 95, 213001 (2005).
    [CrossRef]
  7. J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (2007).
    [CrossRef]
  8. E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
    [CrossRef]
  9. E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
    [CrossRef]
  10. S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
    [CrossRef]
  11. D. Roy, “Few-photon optical diode,” Phys. Rev. B 81, 155117 (2010).
    [CrossRef]
  12. D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency,” Phys. Rev. Lett. 106, 053601 (2011).
    [CrossRef]
  13. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
    [CrossRef]
  14. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
    [CrossRef]
  15. O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
    [CrossRef]
  16. P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems: interaction-induced radiation trapping,” Phys. Rev. Lett. 104, 023602 (2010).
    [CrossRef]
  17. T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (2011).
    [CrossRef]
  18. E. Rephaeli and S. Fan, “Few-photon single-atom cavity QED with input-output formalism in Fock space,” IEEE J. Sel. Top. Quantum Electron. 18, 1754–1762 (2012).
    [CrossRef]
  19. J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
    [CrossRef]
  20. 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]
  21. Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
    [CrossRef]
  22. J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).
  23. H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110, 113601 (2013).
    [CrossRef]
  24. B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
    [CrossRef]
  25. D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
    [CrossRef]
  26. 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 431, 162–167 (2004).
    [CrossRef]
  27. J.-T. Shen and S. 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]
  28. H. Zheng, D. J. Gauthier, and H. U. 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]

2013 (1)

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110, 113601 (2013).
[CrossRef]

2012 (4)

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

E. Rephaeli and S. Fan, “Few-photon single-atom cavity QED with input-output formalism in Fock space,” IEEE J. Sel. Top. Quantum Electron. 18, 1754–1762 (2012).
[CrossRef]

2011 (3)

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
[CrossRef]

T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (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, 053601 (2011).
[CrossRef]

2010 (5)

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

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

S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
[CrossRef]

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

H. Zheng, D. J. Gauthier, and H. U. 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]

2009 (1)

J.-T. Shen and S. 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 (2)

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]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

2007 (4)

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

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[CrossRef]

J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

2006 (1)

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef]

2005 (1)

J.-T. Shen and S. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett. 95, 213001 (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 431, 162–167 (2004).
[CrossRef]

1992 (1)

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef]

1985 (1)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

1960 (1)

I. R. Senitzky, “Dissipation in quantum mechanics. the harmonic oscillator,” Phys. Rev. 119, 670–679 (1960).
[CrossRef]

Abdumalikov, A. A.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Astafiev, O. V.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Auffèves, A.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Baranger, H. U.

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110, 113601 (2013).
[CrossRef]

H. Zheng, D. J. Gauthier, and H. U. 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]

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 431, 162–167 (2004).
[CrossRef]

Busch, K.

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

Carmichael, H. J.

H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations (Springer, 2003).

Castin, Y.

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef]

Chang, D. E.

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[CrossRef]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Collett, M. J.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

Dalibard, J.

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef]

Dayan, B.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Demler, E. A.

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[CrossRef]

Fan, S.

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

E. Rephaeli and S. Fan, “Few-photon single-atom cavity QED with input-output formalism in Fock space,” IEEE J. Sel. Top. Quantum Electron. 18, 1754–1762 (2012).
[CrossRef]

T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (2011).
[CrossRef]

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
[CrossRef]

S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
[CrossRef]

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

J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

J.-T. Shen and S. Fan, “Coherent single photon transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett. 95, 213001 (2005).
[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 431, 162–167 (2004).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

Gauthier, D. J.

H. Zheng, D. J. Gauthier, and H. U. 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]

Gérard, J. M.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[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 431, 162–167 (2004).
[CrossRef]

Gong, Z. R.

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]

Hemmer, P. R.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Huang, J.-F.

J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).

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 431, 162–167 (2004).
[CrossRef]

Kimble, H. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Kocabas, S. E.

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
[CrossRef]

S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
[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 431, 162–167 (2004).
[CrossRef]

Kwek, L. C.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Li, Y.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

Liu, Y.-x.

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, “Few-photon transport in low-dimensional systems: interaction-induced radiation trapping,” Phys. Rev. Lett. 104, 023602 (2010).
[CrossRef]

Lukin, M. D.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[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 431, 162–167 (2004).
[CrossRef]

Mølmer, K.

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef]

Mukherjee, A.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Nakamura, Y.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Nori, F.

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]

J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).

Ostby, E. P.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Park, H.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Parkins, A. S.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Pashkin, Y. A.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Poizat, J. P.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Povinelli, M. L.

J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

Rephaeli, E.

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

E. Rephaeli and S. Fan, “Few-photon single-atom cavity QED with input-output formalism in Fock space,” IEEE J. Sel. Top. Quantum Electron. 18, 1754–1762 (2012).
[CrossRef]

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
[CrossRef]

Roy, D.

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

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

Sandhu, S.

J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

Santos, M. F.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Schmitteckert, P.

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

Schoelkopf, R. 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 431, 162–167 (2004).
[CrossRef]

Schuster, D. I.

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 431, 162–167 (2004).
[CrossRef]

Senitzky, I. R.

I. R. Senitzky, “Dissipation in quantum mechanics. the harmonic oscillator,” Phys. Rev. 119, 670–679 (1960).
[CrossRef]

Shen, J.-T.

S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
[CrossRef]

J.-T. Shen and S. 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, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

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

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

Shi, T.

T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (2011).
[CrossRef]

J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).

Sorensen, A. S.

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[CrossRef]

Sun, C.

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).

Sun, C. P.

T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (2011).
[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]

Tsai, J. S.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Vahala, K. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Valente, D.

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Vuckovic, J.

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef]

Waks, E.

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef]

Wallraff, 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 431, 162–167 (2004).
[CrossRef]

Wang, Z.

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

Zagoskin, A. M.

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

Zhang, P.

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

Zheng, H.

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110, 113601 (2013).
[CrossRef]

H. Zheng, D. J. Gauthier, and H. U. 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, D.

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

Zhou, L.

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]

Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

E. Rephaeli and S. Fan, “Few-photon single-atom cavity QED with input-output formalism in Fock space,” IEEE J. Sel. Top. Quantum Electron. 18, 1754–1762 (2012).
[CrossRef]

Nat. Phys. (1)

D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
[CrossRef]

Nature (2)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature 450, 402–406 (2007).
[CrossRef]

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 431, 162–167 (2004).
[CrossRef]

New J. Phys. (1)

D. Valente, Y. Li, J. P. Poizat, J. M. Gérard, L. C. Kwek, M. F. Santos, and A. Auffèves, “Optimal irreversible stimulated emission,” New J. Phys. 14, 083029 (2012).
[CrossRef]

Phys. Rev. (1)

I. R. Senitzky, “Dissipation in quantum mechanics. the harmonic oscillator,” Phys. Rev. 119, 670–679 (1960).
[CrossRef]

Phys. Rev. A (8)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

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

E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Few-photon transport in a waveguide coupled to a pair of colocated two-level atoms,” Phys. Rev. A 84, 063832 (2011).
[CrossRef]

S. Fan, Ş. E. Kocabaş, and J.-T. Shen, “Input-output formalism for few-photon transport in one-dimensional nanophotonic waveguides coupled to a qubit,” Phys. Rev. A 82, 063821 (2010).
[CrossRef]

Z. Wang, Y. Li, D. Zhou, C. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A 86, 023824 (2012).
[CrossRef]

T. Shi, S. Fan, and C. P. Sun, “Two-photon transport in a waveguide coupled to a cavity in a two-level system,” Phys. Rev. A 84, 063803 (2011).
[CrossRef]

J.-T. Shen and S. 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]

H. Zheng, D. J. Gauthier, and H. U. 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]

Phys. Rev. B (2)

J.-T. Shen, M. L. Povinelli, S. Sandhu, and S. Fan, “Stopping single photons in one-dimensional circuit quantum electrodynamics systems,” Phys. Rev. B 75, 035320 (2007).
[CrossRef]

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

Phys. Rev. Lett. (9)

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

E. Rephaeli and S. Fan, “Stimulated emission from a single excited atom in a waveguide,” Phys. Rev. Lett. 108, 143602 (2012).
[CrossRef]

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96, 153601 (2006).
[CrossRef]

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

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef]

O. V. Astafiev, A. A. Abdumalikov, A. M. Zagoskin, Y. A. Pashkin, Y. Nakamura, and J. S. Tsai, “Ultimate on-chip quantum amplifier,” Phys. Rev. Lett. 104, 183603 (2010).
[CrossRef]

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

H. Zheng and H. U. Baranger, “Persistent quantum beats and long-distance entanglement from waveguide-mediated interactions,” Phys. Rev. Lett. 110, 113601 (2013).
[CrossRef]

Science (1)

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef]

Other (2)

J.-F. Huang, T. Shi, C. Sun, and F. Nori, “Controlling single-photon transport in waveguides with finite cross-section,” arXiv:1303.1981 (2013).

H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker–Planck Equations (Springer, 2003).

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Figures (1)

Fig. 1.
Fig. 1.

Schematic of sample system considered. A waveguide side coupled with rate κ to a two-level atom with transition frequency Ω . The atom is additionally coupled with rate γ to a reservoir. The initial state in the waveguide is either a one- or a two-photon Fock state, whereas the auxiliary waveguide is initially in the vacuum state.

Equations (26)

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H wvg + atom = d x ( i v g c R ( x ) d d x c R ( x ) + i v g c L ( x ) d d x c L ( x ) + κ δ ( x ) [ c R ( x ) σ + σ + c R ( x ) + c L ( x ) σ + σ + c L ( x ) ] ) + Ω 2 σ z .
H r = d x ( i v r b ( x ) d d x b ( x ) + γ δ ( x ) [ b ( x ) σ + σ + b ( x ) ] ) .
a ( x ) = a R ( x ) + a L ( x ) 2 ,
a o ( x ) = a R ( x ) a L ( x ) 2 ,
H e = d x ( i v g a ( x ) d d x a ( x ) i v r b ( x ) d d x b ( x ) + V δ ( x ) [ a ( x ) σ + σ + a ( x ) ] + V r δ ( x ) [ b ( x ) σ + σ + b ( x ) ] ) + 1 2 Ω σ z ,
H o = i v g d x a o ( x ) d d x a o ( x ) .
H e = d k ( k v g a k a k + k v r b k b k + κ 2 π [ a k σ + σ + a k ] + γ 2 π [ b k σ + σ + b k ] ) + 1 2 Ω σ z .
a in ( t ) = 1 2 π d k a k ( t 0 ) e i k ( t t 0 ) , a out ( t ) = 1 2 π d k a k ( t 1 ) e i k ( t t 1 ) ,
b in ( t ) = 1 2 π d k b k ( t 0 ) e i k ( t t 0 ) , b out ( t ) = 1 2 π d k b k ( t 1 ) e i k ( t t 1 ) ,
a out ( t ) = a in ( t ) i κ σ ( t ) ,
b out ( t ) = b in ( t ) i γ σ ( t ) ,
d σ ( t ) d t = i ( Ω i κ 2 i γ 2 ) σ ( t ) + i κ σ z ( t ) a in ( t ) + i γ σ z ( t ) b in ( t ) .
p | k + = 0 | a out ( p ) a in ( k ) | 0 = δ ( k p ) i κ 0 | σ ( p ) | k + ,
0 | σ ( p ) | k + = κ δ ( k p ) k Ω + i κ 2 + i γ 2 s k δ ( k p ) , 0 | σ ( p ) | k + r = γ δ ( k p ) k Ω + i κ 2 + i γ 2 δ ( k p ) s k ( r ) δ ( k p ) , p | k + = k Ω i ( κ 2 γ 2 ) k Ω + i ( κ 2 + γ 2 ) δ ( k p ) = t k δ ( k p ) , p | k + r = i κ γ δ ( k p ) k Ω + i ( κ 2 + γ 2 ) t k ( r ) δ ( k p ) .
p 1 , p 2 | k 1 + , k 2 + = 0 | a out ( p 2 ) a out ( p 1 ) a in ( k 1 ) a in ( k 2 ) | 0 .
I ^ 1 = d k | k + k + | + d k | k + r k + | r ,
p 1 , p 2 | k 1 + , k 2 + = d k p 1 | k + k + | a out ( p 2 ) a in ( k 1 ) a in ( k 2 ) | 0 + d k p 1 | k + r k + | r a out ( p 2 ) a in ( k 1 ) a in ( k 2 ) | 0 = t p 1 p 1 + | a out ( p 2 ) | k 1 + , k 2 + + t p 1 ( r ) p 1 + | r a out ( p 2 ) | k 1 + , k 2 + ,
= t p 1 [ δ ( k 1 p 1 ) δ ( k 2 p 2 ) + δ ( k 1 p 2 ) δ ( k 2 p 1 ) ] i κ t p 1 p 1 + | σ ( p 2 ) | k 1 + , k 2 + i κ t p 1 ( r ) p 1 + | r σ ( p 2 ) | k 1 + , k 2 + .
d d t p 1 | σ ( t ) | k 1 + , k 2 + = i ( Ω i κ 2 i γ 2 ) p 1 + | σ ( t ) | k 1 + , k 2 + + i κ p 1 + | σ z ( t ) a in ( t ) | k 1 + , k 2 + ,
d d t p 1 | r σ ( t ) | k 1 + , k 2 + = i ( Ω i κ 2 i γ 2 ) p 1 + | r σ ( t ) | k 1 + , k 2 + + i κ r p 1 + | σ z ( t ) a in ( t ) | k 1 + , k 2 + ,
p 1 + | σ z ( t ) a in ( t ) | k 1 + , k 2 + = e i k 2 t 2 π [ 1 π s p 1 * s k 2 e i ( p 1 k 2 ) t δ ( p 1 k 2 ) ] + e i k 1 t 2 π [ 1 π s p 1 * s k 1 e i ( p 1 k 1 ) t δ ( p 1 k 1 ) ] , p 1 + | r σ z ( t ) a in ( t ) | k 1 + , k 2 + = e i k 2 t 2 π 1 π s p 1 * ( r ) s k 2 e i ( p 1 k 2 ) t + e i k 1 t 2 π 1 π s p 1 * ( r ) s k 1 e i ( p 1 k 1 ) t .
p 1 + | r σ ( p 2 ) | k 1 + , k 2 + = 1 π s p 2 s p 1 * ( r ) [ s k 1 + s k 2 ] δ ( p 1 + p 2 k 1 k 2 ) ,
p 1 + | σ ( p 2 ) | k 1 + , k 2 + = s p 2 { [ δ ( p 2 k 1 ) δ ( p 1 k 2 ) + δ ( p 2 k 2 ) δ ( p 1 k 1 ) ] 1 π s p 1 * [ s k 1 + s k 2 ] δ ( p 1 + p 2 k 1 k 2 ) } .
p 1 , p 2 | k 1 + , k 2 + = t p 1 t p 2 [ δ ( p 2 k 1 ) δ ( p 1 k 2 ) + δ ( p 2 k 2 ) δ ( p 1 k 1 ) ] + i κ π s p 1 s p 2 [ s k 1 + s k 2 ] δ ( p 1 + p 2 k 1 k 2 ) .
H ad - hoc = d k ( k v g a k a k + κ 2 π [ a k σ + σ + a k ] ) + 1 2 ( Ω i γ 2 ) σ z .
p 1 , p 2 | k 1 + , k 2 + = t p 1 t p 2 [ δ ( p 2 k 1 ) δ ( p 1 k 2 ) + δ ( p 2 k 2 ) δ ( p 1 k 1 ) ] + i 1 π κ t p 1 s p 1 * s p 2 [ s k 1 + s k 2 ] δ ( p 1 + p 2 k 1 k 2 ) .

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