Abstract

We study the propagation of nonclassical light through arrays of coupled linear photonic waveguides and introduce some sets of refractive indices and coupling parameters that provide a closed-form propagator in terms of orthogonal polynomials. We present propagation examples of nonclassical states of light—single photon, coherent state, path-entangled state, and two-mode squeezed vacuum—impinging into two-waveguide couplers and a photonic lattice producing coherent transport.

© 2014 Optical Society of America

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  1. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
    [CrossRef]
  2. S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
    [CrossRef]
  3. G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
    [CrossRef]
  4. S. Longhi, “Rectification of light refraction in curved waveguide arrays,” Opt. Lett. 34, 458–460 (2009).
    [CrossRef]
  5. R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
    [CrossRef]
  6. A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
    [CrossRef]
  7. A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
    [CrossRef]
  8. A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
    [CrossRef]
  9. Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
    [CrossRef]
  10. G. S. Agarwal and K. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
    [CrossRef]
  11. S. Longhi, “Quantum simulation of decoherence in optical waveguide lattices,” Opt. Lett. 38, 4884–4887 (2013).
    [CrossRef]
  12. B. M. Rodríguez-Lara, “Exact dynamics of finite Glauber-Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
    [CrossRef]
  13. F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).
  14. B. M. Rodríguez-Lara and H. Moya-Cessa, “Photon transport in binary photonic lattices,” Phys. Scr. 87, 038116 (2013).
    [CrossRef]
  15. A. Zúñiga Segundo, B. M. Rodríguez-Lara, D. J. Fernández, and H. M. Moya-Cessa, “Jacobi photonic lattices and their SUSY partners,” Opt. Express 22, 987–994 (2014).
    [CrossRef]
  16. A. Luis and L. L. Sánchez Soto, “A quantum description of the beam splitter,” Quantum Semiclass. Opt. 7, 153–160 (1995).
    [CrossRef]
  17. 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]
  18. S. Prasad, M. O. Scully, and W. Martienssen, “A quantum description of the beam splitter,” Opt. Commun. 62, 139–145 (1987).
    [CrossRef]
  19. H. Fearn and R. Loudon, “Quantum theory of the lossless beam splitter,” Opt. Commun. 64, 485–490 (1987).
    [CrossRef]
  20. R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
    [CrossRef]
  21. U. Leonhardt, “Quantum statistics of a lossless beam splitter: su(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993).
    [CrossRef]
  22. G. S. Agarwal, “Engineering non-Gaussian entangled states with vortices by photon subtraction,” New J. Phys. 13, 073008 (2011).
    [CrossRef]
  23. M. Bellec, G. M. Nikolopoulos, and S. Tzortzakis, “Faithful communication Hamiltonian in photonic lattices,” Opt. Lett. 37, 4504–4506 (2012).
    [CrossRef]
  24. A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
    [CrossRef]

2014

2013

S. Longhi, “Quantum simulation of decoherence in optical waveguide lattices,” Opt. Lett. 38, 4884–4887 (2013).
[CrossRef]

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

B. M. Rodríguez-Lara and H. Moya-Cessa, “Photon transport in binary photonic lattices,” Phys. Scr. 87, 038116 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
[CrossRef]

2012

G. S. Agarwal and K. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[CrossRef]

M. Bellec, G. M. Nikolopoulos, and S. Tzortzakis, “Faithful communication Hamiltonian in photonic lattices,” Opt. Lett. 37, 4504–4506 (2012).
[CrossRef]

2011

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[CrossRef]

G. S. Agarwal, “Engineering non-Gaussian entangled states with vortices by photon subtraction,” New J. Phys. 13, 073008 (2011).
[CrossRef]

B. M. Rodríguez-Lara, “Exact dynamics of finite Glauber-Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
[CrossRef]

F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).

2010

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[CrossRef]

2009

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[CrossRef]

S. Longhi, “Rectification of light refraction in curved waveguide arrays,” Opt. Lett. 34, 458–460 (2009).
[CrossRef]

2008

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

1995

A. Luis and L. L. Sánchez Soto, “A quantum description of the beam splitter,” Quantum Semiclass. Opt. 7, 153–160 (1995).
[CrossRef]

1993

U. Leonhardt, “Quantum statistics of a lossless beam splitter: su(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993).
[CrossRef]

1989

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

1987

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]

S. Prasad, M. O. Scully, and W. Martienssen, “A quantum description of the beam splitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

H. Fearn and R. Loudon, “Quantum theory of the lossless beam splitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and K. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[CrossRef]

G. S. Agarwal, “Engineering non-Gaussian entangled states with vortices by photon subtraction,” New J. Phys. 13, 073008 (2011).
[CrossRef]

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

Aguilar-Loreto, O.

F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).

Bellec, M.

Bromberg, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[CrossRef]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Campos, R. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

Christodoulides, D.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

Christodoulides, D. N.

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
[CrossRef]

F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).

Coppa, A.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Eisfeld, A.

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

El-Ganainy, R.

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

Fearn, H.

H. Fearn and R. Loudon, “Quantum theory of the lossless beam splitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

Fernandez, T. T.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Fernández, D. J.

Foglietti, V.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Hong, C. K.

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]

Ismail, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Kay, A.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

Keil, R.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
[CrossRef]

Kwek, L.-C.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

Lahini, Y.

Y. Bromberg, Y. Lahini, and Y. Silberberg, “Bloch oscillations of path-entangled photons,” Phys. Rev. Lett. 105, 263604 (2010).
[CrossRef]

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Laporta, P.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Leonhardt, U.

U. Leonhardt, “Quantum statistics of a lossless beam splitter: su(2) symmetry in phase space,” Phys. Rev. A 48, 3265–3277 (1993).
[CrossRef]

Levy, M.

R. El-Ganainy, A. Eisfeld, M. Levy, and D. N. Christodoulides, “On-chip non-reciprocal optical devices based on quantum inspired photonic lattices,” Appl. Phys. Lett. 103, 161105 (2013).
[CrossRef]

Lobino, M.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Longhi, S.

S. Longhi, “Quantum simulation of decoherence in optical waveguide lattices,” Opt. Lett. 38, 4884–4887 (2013).
[CrossRef]

S. Longhi, “Classical simulation of relativistic quantum mechanics in periodic optical structures,” Appl. Phys. B 104, 453–468 (2011).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photonics Rev. 3, 243–261 (2009).
[CrossRef]

S. Longhi, “Rectification of light refraction in curved waveguide arrays,” Opt. Lett. 34, 458–460 (2009).
[CrossRef]

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Loudon, R.

H. Fearn and R. Loudon, “Quantum theory of the lossless beam splitter,” Opt. Commun. 64, 485–490 (1987).
[CrossRef]

Luis, A.

A. Luis and L. L. Sánchez Soto, “A quantum description of the beam splitter,” Quantum Semiclass. Opt. 7, 153–160 (1995).
[CrossRef]

Mandel, L.

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]

Martienssen, W.

S. Prasad, M. O. Scully, and W. Martienssen, “A quantum description of the beam splitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Matsuda, N.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Matthews, J. C. F.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Moya-Cessa, H.

B. M. Rodríguez-Lara and H. Moya-Cessa, “Photon transport in binary photonic lattices,” Phys. Scr. 87, 038116 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
[CrossRef]

F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).

Moya-Cessa, H. M.

Nikolopoulos, G. M.

Nolte, S.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

O’Brien, J. L.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Ornigotti, M.

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92, 011106 (2008).
[CrossRef]

Ou, Z. Y.

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]

Perez-Leija, A.

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, H. Moya-Cessa, A. Szameit, and D. N. Christodoulides, “Perfect transfer of path-entangled photons in Jx photonic lattices,” Phys. Rev. A 87, 022303 (2013).
[CrossRef]

F. Soto-Eguibar, O. Aguilar-Loreto, A. Perez-Leija, H. Moya-Cessa, and D. N. Christodoulides, “Finite photonic lattices: a solution using characteristic polynomials,” Rev. Mex. Fis. 57, 158–161 (2011).

Perk, J. H. H.

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

Peruzzo, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Politi, A.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Poulios, K.

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

Prasad, S.

S. Prasad, M. O. Scully, and W. Martienssen, “A quantum description of the beam splitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Qu, K.

G. S. Agarwal and K. Qu, “Spontaneous generation of photons in transmission of quantum fields in PT-symmetric optical systems,” Phys. Rev. A 85, 031802 (2012).
[CrossRef]

Rai, A.

A. Rai, G. S. Agarwal, and J. H. H. Perk, “Transport and quantum walk of nonclassical light in coupled waveguides,” Phys. Rev. A 78, 042304 (2008).
[CrossRef]

Rodríguez-Lara, B. M.

A. Zúñiga Segundo, B. M. Rodríguez-Lara, D. J. Fernández, and H. M. Moya-Cessa, “Jacobi photonic lattices and their SUSY partners,” Opt. Express 22, 987–994 (2014).
[CrossRef]

B. M. Rodríguez-Lara and H. Moya-Cessa, “Photon transport in binary photonic lattices,” Phys. Scr. 87, 038116 (2013).
[CrossRef]

A. Perez-Leija, R. Keil, A. Kay, H. Moya-Cessa, S. Nolte, L.-C. Kwek, B. M. Rodríguez-Lara, A. Szameit, and D. Christodoulides, “Coherent quantum transport in photonic lattices,” Phys. Rev. A 87, 012309 (2013).
[CrossRef]

B. M. Rodríguez-Lara, “Exact dynamics of finite Glauber-Fock photonic lattices,” Phys. Rev. A 84, 053845 (2011).
[CrossRef]

Saleh, B. E. A.

R. A. Campos, B. E. A. Saleh, and M. C. Teich, “Quantum-mechanical lossless beam splitter: su(2) symmetry and photon statistics,” Phys. Rev. A 40, 1371–1384 (1989).
[CrossRef]

Sánchez Soto, L. L.

A. Luis and L. L. Sánchez Soto, “A quantum description of the beam splitter,” Quantum Semiclass. Opt. 7, 153–160 (1995).
[CrossRef]

Scully, M. O.

S. Prasad, M. O. Scully, and W. Martienssen, “A quantum description of the beam splitter,” Opt. Commun. 62, 139–145 (1987).
[CrossRef]

Silberberg, Y.

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A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
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A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
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Science

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O’Brien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Propagation of the mean photon number at the first (solid black) and second (dashed blue) waveguides (first column); fidelities for finding the initial state back in the first (solid black) or transferred to the second (dashed blue) waveguide (second column); and two-point g1,1(2) (solid black), g1,2(2)=g2,1(2) (dashed blue), and g2,2(2) (dotted red) correlation functions (third column) for a single photon |ψ(0)=|1,0 (first row), a coherent state |ψ(0)=|α,0 with α=1 (second row), a two-mode entangled state |ψ(0)=(|1,0+|0,1)21/2 (third row), and a two-mode squeezed vacuum |ψ(0)=|r,0 with r=arcsinh21/2 (fourth row). The two-waveguide coupler is described by the parameter set Δ=0 and g=ω1.

Fig. 2.
Fig. 2.

Propagation of the mean photon number at the first (solid black), second (solid blue), third (dashed blue), and fourth (dashed black) waveguides (first column); fidelities for finding the initial state back in the first two (solid black) or transferred to the last two (dashed blue) waveguides (second column); and two-point g1,1(2) (solid black), g1,2(2)=g2,1(2) (dashed black), g1,3(2)=g3,1(2) (dotted black), g1,4(2)=g4,1(2) (dotted–dashed black), g2,2(2) (solid blue), g2,3(2)=g3,2(2) (dashed blue), g2,4(2)=g4,2(2) (dotted–dashed blue), g3,3(2) (solid red), g3,4(2)=g4,3(2) (dashed red), and g4,4(2) (solid green) correlation functions (third column) for a single photon in the first waveguide |ψ(0)=|1,0,0,0 (first row), a coherent state |ψ(0)=|α,0,0,0 with α=1 (second row), a two-mode entangled state |ψ(0)=(|1,0,0,0+|0,1,0,0)21/2 (third row), and a two-mode squeezed vacuum |ψ(0)=|r,0 with r=arcsinh21/2 (fourth row). The photonic lattice is described by the parameter set Δ=0 and gj=π(2zt)1j(Nj) with zt=1 and N=4.

Equations (12)

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H^=j=0N1ωjn^j+jk=0N2gj,k(a^ja^k+a^ja^k),
H^=j=0N1ωjn^j+j=0N2gj(a^ja^j+1+a^ja^j+1).
H^=j=0N1λjA^jA^j.
U^(z)=eizj=0N1λjA^jA^j.
n^j(z)=ψ(0)|U^(z)[V1A⃗]j[V1A⃗]jU^(z)|ψ(0),
gp,q(2)(z)=ψ(0)|U^(z)[V1A⃗]p[V1A⃗]p[V1A⃗]q[V1A⃗]qU^(z)|ψ(0),
F(z)=|ϕ|U^(z)|ψ(0)|,
H^=Δn^1+g(a^1a^2+a^2a^1),
=γ1A^1A^1+γ2A^2A^2,
n^1=ψ(0)|n^1(z)|ψ(0),n^2=ψ(0)|n^2(z)|ψ(0),
gp,q(2)=ψ(0)|n^p(z)n^q(z)|ψ(0),p,q=1,2,
H^=12j=1N1Jj(a^ja^j+1+a^ja^j+1),Jj=π2ztj(Nj)

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