Abstract

The Hong-Ou-Mandel effect is studied in the context of two-photon transport in a one-dimensional waveguide with a single scatterer. We numerically investigate the scattering problem within a time-dependent, wave-function-based framework. Depending on the realization of the scatterer and its properties, we calculate the joint probability of finding both photons on either side of the waveguide after scattering. We specifically point out how Hong-Ou-Mandel interferometry techniques could be exploited to identify effective photon–photon interactions which are mediated by the scatterer. The Hong-Ou-Mandel dip is discussed in detail for the case of a single two-level atom embedded in the waveguide, and dissipation and dephasing are taken into account by means of a quantum jump approach.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  28. M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
    [CrossRef]
  29. A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
    [CrossRef]
  30. D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
    [CrossRef]
  31. M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
    [CrossRef]
  32. J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “Reconfigurable quantum metamaterials,” Opt. Express 19, 11018–11033 (2011).
    [CrossRef] [PubMed]
  33. M. T. C. Wong and C. K. Law, “Two-polariton bound states in the Jaynes-Cummings-Hubbard model,” Phys. Rev. A 83, 055802 (2011).
    [CrossRef]
  34. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).
    [CrossRef]
  35. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
    [CrossRef] [PubMed]
  36. R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
    [CrossRef] [PubMed]

2012 (1)

2011 (4)

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

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

M. T. C. Wong and C. K. Law, “Two-polariton bound states in the Jaynes-Cummings-Hubbard model,” Phys. Rev. A 83, 055802 (2011).
[CrossRef]

J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “Reconfigurable quantum metamaterials,” Opt. Express 19, 11018–11033 (2011).
[CrossRef] [PubMed]

2010 (2)

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] [PubMed]

E. Rephaeli, J. T. Shen, and S. Fan, “Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries,” Phys. Rev. A 82, 033804 (2010).
[CrossRef]

2009 (8)

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]

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

D. Witthaut and A.S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. 12, 043052 (2009).
[CrossRef]

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

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

2008 (1)

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] [PubMed]

2007 (7)

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

D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

H. Takesue, “1.5 μm band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. 90, 204101 (2007).
[CrossRef]

J. Niegemann, L. Tkeshelashvili, and K. Busch, “Higher-order time-domain simulations of Maxwell’s equations using Krylov-subspace methods,” J. Comput. Theor. Nanosci. 4, 627–634 (2007).

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (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, 153003 (2007).
[CrossRef] [PubMed]

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

2006 (3)

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

2005 (3)

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

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[CrossRef] [PubMed]

Y. L. Lim and A. Beige, “Generalized Hong-Ou-Mandel experiments with bosons and fermions,” New J. Phys. 7, 155 (2005).
[CrossRef]

1999 (1)

1998 (1)

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998)
[CrossRef]

1993 (1)

1992 (1)

Y. Saad, “Analysis of some Krylov subspace approximations to the matrix exponential operator,” SIAM Journal on Numerical Analysis 29, 209–228 (1992).
[CrossRef]

1987 (2)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, and L. Mandel, “Relation between input and output states for a beam splitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Angelakis, D.

D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Beige, A.

Y. L. Lim and A. Beige, “Generalized Hong-Ou-Mandel experiments with bosons and fermions,” New J. Phys. 7, 155 (2005).
[CrossRef]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Bose, S.

D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

Brandao, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

Busch, K.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83, 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, 023602 (2010).
[CrossRef] [PubMed]

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

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

J. Niegemann, L. Tkeshelashvili, and K. Busch, “Higher-order time-domain simulations of Maxwell’s equations using Krylov-subspace methods,” J. Comput. Theor. Nanosci. 4, 627–634 (2007).

Castin, Y.

Chang, D. E.

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

Cole, J.

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

Cole, J. H.

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

Dalibard, J.

Demler, E. A.

D. E. Chang, A. S. Sørensen, 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, J. T. Shen, and S. Fan, “Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries,” Phys. Rev. A 82, 033804 (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 multi-particle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (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, 153003 (2007).
[CrossRef] [PubMed]

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

Fazio, R.

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

Freymann, G. v.

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Frustaglia, D.

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

Gerry, C. G.

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, 2005).

Giovannetti, V.

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

Gong, X. Y.

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] [PubMed]

Greentree, A.

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

Greentree, A. D.

J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “Reconfigurable quantum metamaterials,” Opt. Express 19, 11018–11033 (2011).
[CrossRef] [PubMed]

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

Hartmann, M. J.

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Hill, C. D.

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

Hollenberg, L.

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

Hollenberg, L. C. L.

J. Q. Quach, C.-H. Su, A. M. Martin, A. D. Greentree, and L. C. L. Hollenberg, “Reconfigurable quantum metamaterials,” Opt. Express 19, 11018–11033 (2011).
[CrossRef] [PubMed]

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, and L. Mandel, “Relation between input and output states for a beam splitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Huang, J.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Knight, P. L.

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998)
[CrossRef]

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, 2005).

Laing, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Law, C. K.

M. T. C. Wong and C. K. Law, “Two-polariton bound states in the Jaynes-Cummings-Hubbard model,” Phys. Rev. A 83, 055802 (2011).
[CrossRef]

Lee, R. K.

Li, T.

Lim, Y. L.

Y. L. Lim and A. Beige, “Generalized Hong-Ou-Mandel experiments with bosons and fermions,” New J. Phys. 7, 155 (2005).
[CrossRef]

Linden, S.

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Liu, H.

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] [PubMed]

Longo, P.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83, 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, 023602 (2010).
[CrossRef] [PubMed]

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

Lukin, M. D.

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

Makin, M. I.

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, and L. Mandel, “Relation between input and output states for a beam splitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Martin, A. M.

Mingaleev, S. F.

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Mølmer, K.

Mu, S. Y.

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Niegemann, J.

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

J. Niegemann, L. Tkeshelashvili, and K. Busch, “Higher-order time-domain simulations of Maxwell’s equations using Krylov-subspace methods,” J. Comput. Theor. Nanosci. 4, 627–634 (2007).

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

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] [PubMed]

O’Brien, J. L.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

Z. Y. Ou, C. K. Hong, and L. Mandel, “Relation between input and output states for a beam splitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Pausauskie, P.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Peruzzo, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Plenio, M. B.

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998)
[CrossRef]

Politi, A.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Pototschnig, M.

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

Quach, J. Q.

Raymer, M. G.

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[CrossRef] [PubMed]

Rephaeli, E.

E. Rephaeli, J. T. Shen, and S. Fan, “Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries,” Phys. Rev. A 82, 033804 (2010).
[CrossRef]

Rudolph, T.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Saad, Y.

Y. Saad, “Analysis of some Krylov subspace approximations to the matrix exponential operator,” SIAM Journal on Numerical Analysis 29, 209–228 (1992).
[CrossRef]

Santos, M.

D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

Scherer, A.

Schmitteckert, P.

P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A 83, 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, 023602 (2010).
[CrossRef] [PubMed]

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

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Shen, J. T.

E. Rephaeli, J. T. Shen, and S. Fan, “Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries,” Phys. Rev. A 82, 033804 (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 multi-particle transport in one dimension through a quantum impurity,” Phys. Rev. A 76, 062709 (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, 153003 (2007).
[CrossRef] [PubMed]

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

Shi, T.

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

Sørensen, A. S.

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

Sørensen, A.S.

D. Witthaut and A.S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. 12, 043052 (2009).
[CrossRef]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Su, C.-H.

Sun, C. P.

T. Shi and C. P. Sun, “Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled resonator arrays,” Phys. Rev. B 79, 205111 (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, 100501 (2008).
[CrossRef] [PubMed]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Taddei, F.

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

Tahan, C.

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

Takesue, H.

H. Takesue, “1.5 μm band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. 90, 204101 (2007).
[CrossRef]

Tkeshelashvili, L.

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

J. Niegemann, L. Tkeshelashvili, and K. Busch, “Higher-order time-domain simulations of Maxwell’s equations using Krylov-subspace methods,” J. Comput. Theor. Nanosci. 4, 627–634 (2007).

Walmsley, I. A.

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[CrossRef] [PubMed]

Wang, S. M.

Wegener, M.

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Witthaut, D.

D. Witthaut and A.S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. 12, 043052 (2009).
[CrossRef]

Wong, M. T. C.

M. T. C. Wong and C. K. Law, “Two-polariton bound states in the Jaynes-Cummings-Hubbard model,” Phys. Rev. A 83, 055802 (2011).
[CrossRef]

Xu, P.

Xu, Y.

Yan, R.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Yang, P.

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Yariv, A.

Zhang, X.

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] [PubMed]

Zhu, C.

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

Zhu, S. N.

Appl. Phys. Lett. (1)

H. Takesue, “1.5 μm band Hong-Ou-Mandel experiment using photon pairs generated in two independent dispersion shifted fibers,” Appl. Phys. Lett. 90, 204101 (2007).
[CrossRef]

IEEE Trans. Ant. Propagat. (1)

M. Pototschnig, J. Niegemann, L. Tkeshelashvili, and K. Busch, “Time-domain simulation of the nonlinear Maxwell equations using operator-exponential techniques,” IEEE Trans. Ant. Propagat. 57, 475–483 (2009).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

J. Niegemann, L. Tkeshelashvili, and K. Busch, “Higher-order time-domain simulations of Maxwell’s equations using Krylov-subspace methods,” J. Comput. Theor. Nanosci. 4, 627–634 (2007).

J. Opt. A: Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[CrossRef] [PubMed]

Nat. Phys. (3)

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

M. J. Hartmann, F. G. S. L. Brandao, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. 2, 849–855 (2006).
[CrossRef]

A. Greentree, C. Tahan, J. Cole, and L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. 2, 856–861 (2006).
[CrossRef]

Nature (1)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef] [PubMed]

New J. Phys. (2)

Y. L. Lim and A. Beige, “Generalized Hong-Ou-Mandel experiments with bosons and fermions,” New J. Phys. 7, 155 (2005).
[CrossRef]

D. Witthaut and A.S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. 12, 043052 (2009).
[CrossRef]

Opt. Commun. (1)

Z. Y. Ou, C. K. Hong, and L. Mandel, “Relation between input and output states for a beam splitter,” Opt. Commun. 63, 118–122 (1987).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rep. (1)

K. Busch, G. v. Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Phys. Rev. A (7)

D. Angelakis, M. Santos, and S. Bose, “Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays,” Phys. Rev. A 76, 31805 (2007).
[CrossRef]

M. I. Makin, J. H. Cole, C. D. Hill, A. D. Greentree, and L. C. L. Hollenberg, “Time evolution of the one-dimensional Jaynes-Cummings-Hubbard Hamiltonian,” Phys. Rev. A 80, 043842 (2009).
[CrossRef]

M. T. C. Wong and C. K. Law, “Two-polariton bound states in the Jaynes-Cummings-Hubbard model,” Phys. Rev. A 83, 055802 (2011).
[CrossRef]

E. Rephaeli, J. T. Shen, and S. Fan, “Full inversion of a two-level atom with a single-photon pulse in one-dimensional geometries,” Phys. Rev. A 82, 033804 (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]

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

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

Phys. Rev. B (2)

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

V. Giovannetti, D. Frustaglia, F. Taddei, and R. Fazio, “Electronic Hong-Ou-Mandel interferometer for multimode entanglement detection,” Phys. Rev. B 74, 115315 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

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, 153003 (2007).
[CrossRef] [PubMed]

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

R. Yan, P. Pausauskie, J. Huang, and P. Yang, “Direct photonic-plasmonic coupling and routing in single nanowires,” Proc. Natl. Acad. Sci. USA 106, 21045–21050 (2009).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

M. B. Plenio and P. L. Knight, “The quantum-jump approach to dissipative dynamics in quantum optics,” Rev. Mod. Phys. 70, 101–144 (1998)
[CrossRef]

Science (1)

I. A. Walmsley and M. G. Raymer, “Toward quantum-information processing with photons,” Science 307, 1733–1734 (2005).
[CrossRef] [PubMed]

SIAM Journal on Numerical Analysis (1)

Y. Saad, “Analysis of some Krylov subspace approximations to the matrix exponential operator,” SIAM Journal on Numerical Analysis 29, 209–228 (1992).
[CrossRef]

Other (1)

C. G. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University Press, 2005).

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Figures (8)

Fig. 1
Fig. 1

Schematic sketch of a beam splitter as a four-port device and its analogy to a scattering problem.

Fig. 2
Fig. 2

Schematic sketch of a local on-site potential (left panel) and a two-level atom (right panel) in a tight-binding waveguide.

Fig. 3
Fig. 3

Schematic sketch of the two-excitation initial state.

Fig. 4
Fig. 4

Hong-Ou-Mandel dip for a system where a local scattering potential is coupled to a photonic tight-binding waveguide. The latter consists of N = 199 sites and the local scatterer in form of an on-site potential is coupled to site x0 = 100. The strength of the potential is g = 2 |J||sin(k0a)|, which is the condition for a balanced beam splitter (cf. Eqs. (9) and (12)). We operate at a carrier wavenumber of k 0 = π 2 a.

Fig. 5
Fig. 5

Hong-Ou-Mandel dip for a system where a two-level system is coupled to a photonic tight-binding waveguide. For a central carrier wave number of k 0 = 3 π 4 a, the beam splitter condition reads V = 2 | J | | 2 J Ω |. Note that by varying the atomic transition energy relative to the cosine band, the atom-photon coupling strength V changes as well due to the beam splitter constraint. The combinations of transition energy and coupling strength used are Ω = 0: V = 2 J, Ω = 0.4J: V = 1.198J, Ω = 0.6J: V = 1.073J, Ω = 0.8J: V = 0.932J, Ω = 1.0J: V = 0.765J, Ω = 1.2J: V = 0.550J.

Fig. 6
Fig. 6

Hong-Ou-Mandel dip for the same system as investigated in Fig. 5 but for Ω = J and different strengths of the anharmonicity U (see text for details). For U = 0, the fading of the Hong-Ou-Mandel dip is solely due to beam splitter imperfections at the single-photon level. The fading depends non-monotonically on the anharmonicity (see text for explanation). The single-photon limit (Δ → ±∞) is independent of the actual value of the anharmonicity. In the inset, we display the the depth of the Hong-Ou-Mandel dip as a function of the anharmonicity U (the gray line is just a guide to the eye).

Fig. 7
Fig. 7

Left panel: Hong-Ou-Mandel dip for the same parameters as in Fig. 5 with Ω = J but the two-level system experiences losses of T1-type. Even though losses of T1-type lead to irreversible photon loss, the single-photon limit is independent of the value of T1 because of the normalization of Eq. (20). The black dashed curve represents the lossless case in which T1 = ∞. We used 500 samples in the simulation for the stochastic time evolution. Right panel: Influence of pure dephasing of T2-type on the Hong-Ou-Mandel dip. Moderate dephasing times affect the depth of the Hong-Ou-Mandel dip but leave the single-photon limit practically unchanged. Very short dephasing times change the single-particle transport characteristics and, therefore, the single-photon limit in the Hong-Ou-Mandel dip. The black dashed curve represents the lossless case in which T2 = ∞. We used 2000 samples in the simulation for the stochastic time evolution.

Fig. 8
Fig. 8

Single-particle transmittance T through a two-level system which is subjected to pure dephasing of T2-type. For strong dephasing, i.e., T2-times comparable to the temporal overlap of the wavepacket at the position of the atom, the transmission is, for parameters we chose here, enhanced. We used k 0 = 3 π 4 a, s = 12a, and xc = 50 as parameters for the initial wave packet and 1000 samples in the simulation for the stochastic time evolution. The transmittance is defined in line with Ref. [8]. The solid line is just a guide to the eye.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

( a 2 a 3 ) = S ^ ( a 0 a 1 ) ,
S ^ = ( t r r t )
| in = a 0 a 1 | 0 ,
| out = 1 2 ( a 2 + i a 3 ) ( i a 2 + a 3 ) | 0 = i 2 ( a 2 a 2 + a 3 a 3 ) | 0 .
a k S ^ a k = r k a k + t k a k
φ x = { e i k x + r k e i k x x < x 0 t k e i k x x x 0
0 = ( h ¯ ω E ) φ x J ( φ x + 1 + φ x 1 ) + δ x x 0 G ( E ) φ x 0
r k = e 2 i k J 2 ( h ¯ ω E + G ( E ) J e i k ) ( h ¯ ω E J e i k ) J 2 ( h ¯ ω E + G ( E ) J e i k ) ( h ¯ ω E J e i k ) .
H pot = g a 0 a 0
G ( E ) = g .
r k = g g 2 i J sin ( k a ) .
g = ± 2 | J | | sin ( k a ) | .
H TLS = Ω 2 σ z + V ( a 0 σ + a 0 σ + ) .
G ( E ) = V 2 E Ω
r k = V 2 2 i J sin ( k a ) ( Ω 2 J cos ( k a ) ) V 2 .
V = ± | 2 J sin ( k a ) ( 2 J cos ( k a ) Ω ) | .
| Ψ ( t ) = e i h ¯ H t | Ψ ( 0 ) ,
| Ψ ( 0 ) = x 1 x 2 Φ x 1 x 2 a x 1 a x 2 | 0 ,
Φ x 1 x 2 ( φ x 1 k 0 ( 1 ) x c ( 1 ) s ( 1 ) φ x 2 k 0 ( 2 ) x c ( 2 ) s ( 2 ) + φ x 2 k 0 ( 1 ) x c ( 1 ) s ( 1 ) φ x 1 k 0 ( 2 ) x c ( 2 ) s ( 2 ) ) ,
P LR = x y a y a x a x a y x , y a y a x a x a y ,

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