Abstract

The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to “retrieve” a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.

© 2011 OSA

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  1. S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
    [CrossRef]
  2. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [CrossRef] [PubMed]
  3. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
    [CrossRef] [PubMed]
  4. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
    [CrossRef] [PubMed]
  5. C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
    [CrossRef]
  6. E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
    [CrossRef]
  7. W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
    [CrossRef] [PubMed]
  8. A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
    [CrossRef] [PubMed]
  9. P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
    [CrossRef] [PubMed]
  10. G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
    [CrossRef] [PubMed]
  11. D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74–85 (1988).
    [CrossRef]
  12. A. V. Belinskii and D. N. Klyshko, “Two-photon optics: diffraction, holography, and transformation of two-dimensional signals,” J. Exp. Theor. Phys. 78, 259–262 (1994).
  13. P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
    [CrossRef] [PubMed]
  14. H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
    [CrossRef]
  15. A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
    [CrossRef]
  16. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
    [CrossRef] [PubMed]
  17. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
    [CrossRef]
  18. S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
    [CrossRef]
  19. S. P. Walborn and C. H. Monken, “Transverse spatial entanglement in parametric down-conversion,” Phys. Rev. A 76, 062305 (2007).
    [CrossRef]
  20. S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
    [CrossRef] [PubMed]
  21. S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
    [CrossRef]
  22. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  23. B. E. A. Saleh and M. C. Teich, Fundamental Photonics (Wiley, 1991).
    [CrossRef]
  24. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  25. P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
    [CrossRef] [PubMed]
  26. S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
    [CrossRef]
  27. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [CrossRef] [PubMed]
  28. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef] [PubMed]

2010 (1)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

2007 (3)

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

S. P. Walborn and C. H. Monken, “Transverse spatial entanglement in parametric down-conversion,” Phys. Rev. A 76, 062305 (2007).
[CrossRef]

2005 (3)

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
[CrossRef]

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
[CrossRef]

2004 (3)

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[CrossRef] [PubMed]

2003 (3)

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

2002 (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

2001 (1)

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

1999 (1)

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[CrossRef]

1998 (1)

C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
[CrossRef]

1996 (2)

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef] [PubMed]

P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef] [PubMed]

1995 (3)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

1994 (2)

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

A. V. Belinskii and D. N. Klyshko, “Two-photon optics: diffraction, holography, and transformation of two-dimensional signals,” J. Exp. Theor. Phys. 78, 259–262 (1994).

1988 (1)

D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74–85 (1988).
[CrossRef]

Abouraddy, A. F.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

Barbosa, G. A.

P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef] [PubMed]

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Barnett, S. M.

Belinskii, A. V.

A. V. Belinskii and D. N. Klyshko, “Two-photon optics: diffraction, holography, and transformation of two-dimensional signals,” J. Exp. Theor. Phys. 78, 259–262 (1994).

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Boyd, R. W.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Courtial, J.

da Silva, J. C. M.

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

de Oliveira, A. N.

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

Fonseca, E.

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[CrossRef]

Franke-Arnold, S.

Gibson, G.

Howell, J. C.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

A. V. Belinskii and D. N. Klyshko, “Two-photon optics: diffraction, holography, and transformation of two-dimensional signals,” J. Exp. Theor. Phys. 78, 259–262 (1994).

D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74–85 (1988).
[CrossRef]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Machado da Silva, J. C.

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

Monken, C.

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[CrossRef]

Monken, C. H.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

S. P. Walborn and C. H. Monken, “Transverse spatial entanglement in parametric down-conversion,” Phys. Rev. A 76, 062305 (2007).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
[CrossRef]

S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
[CrossRef]

Nogueira, W. A. T.

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

Okamoto, M.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Padgett, M. J.

Pádua, S.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[CrossRef]

C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
[CrossRef]

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Pas’ko, V.

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Ribeiro, P. H. S.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

Ribeiro, P. S.

C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
[CrossRef]

Saleh, B. E. A.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

B. E. A. Saleh and M. C. Teich, Fundamental Photonics (Wiley, 1991).
[CrossRef]

Sasada, H.

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

Sergienko, A. V.

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

Souto Ribeiro, P. H.

P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

Stone, P. R.

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

Teich, M. C.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

B. E. A. Saleh and M. C. Teich, Fundamental Photonics (Wiley, 1991).
[CrossRef]

Vasnetsov, M.

Walborn, S. P.

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

S. P. Walborn and C. H. Monken, “Transverse spatial entanglement in parametric down-conversion,” Phys. Rev. A 76, 062305 (2007).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
[CrossRef]

S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
[CrossRef]

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Yarnall, T.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

Europhys. Lett. (1)

S. P. Walborn, W. A. T. Nogueira, S. Pádua, and C. H. Monken, “Optical Bell-state analysis in the coincidence basis,” Europhys. Lett. 62, 161–167 (2003).
[CrossRef]

J. Exp. Theor. Phys. (1)

A. V. Belinskii and D. N. Klyshko, “Two-photon optics: diffraction, holography, and transformation of two-dimensional signals,” J. Exp. Theor. Phys. 78, 259–262 (1994).

J. Opt. B: Quantum Semiclassical Opt. (1)

A. N. de Oliveira, S. P. Walborn, and C. H. Monken, “Implementation of the Deutsch algorithm using polarization and transverse modes,” J. Opt. B: Quantum Semiclassical Opt. 7, 288–292 (2005).
[CrossRef]

Mod. Phys. Lett. B (1)

S. P. Walborn, W. A. T. Nogueira, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interferometry,” Mod. Phys. Lett. B 19, 1–19 (2005).
[CrossRef]

Opt. Express (1)

Phys. Rep. (1)

S. P. Walborn, C. H. Monken, S. Pádua, and P. H. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[CrossRef]

Phys. Rev. A (8)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995).
[CrossRef] [PubMed]

S. P. Walborn, S. Pádua, and C. H. Monken, “Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion,” Phys. Rev. A 71, 053812 (2005).
[CrossRef]

S. P. Walborn and C. H. Monken, “Transverse spatial entanglement in parametric down-conversion,” Phys. Rev. A 76, 062305 (2007).
[CrossRef]

P. H. Souto Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef] [PubMed]

H. Sasada and M. Okamoto, “Transverse-mode beam splitter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68, 012323 (2003).
[CrossRef]

P. H. S. Ribeiro, S. Pádua, J. C. M. da Silva, and G. A. Barbosa, “Controlling the degree of visibility of young’s fringes with photon coincidence measurements,” Phys. Rev. A 49, 4176–4179 (1994).
[CrossRef] [PubMed]

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, S. Pádua, J. C. Machado da Silva, and G. A. Barbosa, “Control of Young’s fringes visibility by stimulated down-conversion,” Phys. Rev. A 51, 1631–1633 (1995).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

C. H. Monken, P. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A. 57, 3123–3126 (1998).
[CrossRef]

Phys. Rev. Lett. (9)

E. Fonseca, C. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868–2871 (1999).
[CrossRef]

W. A. T. Nogueira, S. P. Walborn, S. Pádua, and C. H. Monken, “Experimental observation of spatial antibunching of photons,” Phys. Rev. Lett. 86, 4009–4012 (2001).
[CrossRef] [PubMed]

A. F. Abouraddy, P. R. Stone, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-photon imaging of a pure phase object,” Phys. Rev. Lett. 93, 213903 (2004).
[CrossRef] [PubMed]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
[CrossRef] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon ghost interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[CrossRef] [PubMed]

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, “Multimode Hong-Ou-Mandel interference,” Phys. Rev. Lett. 90, 143601 (2003).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bell’s inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

D. N. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74–85 (1988).
[CrossRef]

Other (3)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

B. E. A. Saleh and M. C. Teich, Fundamental Photonics (Wiley, 1991).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

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Figures (4)

Fig. 1
Fig. 1

Interference experiment considered here. The orthogonally polarized photons created by type-II SPDC are separated by a polarizing beam splitter (PBS). One photon is subject to an AMZ interferometer. The photons are registered by detectors D 1 and D 2 with square detection apertures of width 2a 1 and 2a 2, respectively. Here ϕ is an adjustable phase.

Fig. 2
Fig. 2

Visibility as a function of a 2/w for a Gaussian pump beam of width w p = 1 / 2 . The solid lines correspond to the fourth-order visibility for various values of a 1/w. The dark blue dashed line is the second-order visibility.

Fig. 3
Fig. 3

Visibility as a function of a 2/w for a Hermite-Gaussian pump beam HG01 of width w p = 1 / 2 . The solid lines correspond to the fourth-order visibility for various values of a 1/w. The dark blue dashed line is the second-order visibility.

Fig. 4
Fig. 4

The coincidence counts (P 1 + P 2) are composed of two out of phase contributions, P 1 and P 2. The visibility depends on the difference in overall weights.

Equations (29)

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a 2 ( q ) = 1 2 { a i n ( q x , q y ) e i ϕ a i n ( q x , q y ) }
P ( r 1 , r 2 ) = | Ψ ( r 1 , r 2 ) | 2 ,
Ψ ( r 1 , r 2 ) = vac | E 2 ( + ) ( r 2 ) E 1 ( + ) ( r 1 ) | ψ ,
E l ( + ) ( r ) e i k z d q a l ( q ) e i q ρ ,
Ψ d ( r 1 , r 2 ) = 1 2 { Ψ ( ρ 1 , ρ 2 ) + e i ϕ Ψ ( ρ 1 , ρ 2 ) } ,
P d ( r 1 , r 2 ) = P ( ρ 1 , ρ 2 ) + P ( ρ 2 , ρ 2 ) + Ψ * ( ρ 1 , ρ 2 ) Ψ ( ρ 1 , ρ 2 ) e i ϕ + Ψ * ( ρ 1 , ρ 2 ) Ψ ( ρ 1 , ρ 2 ) e i ϕ ,
Ψ ( ρ 1 , ρ 2 ) U ( ρ 1 + ρ 2 2 ) .
P d ( r 1 , r 2 ) = P d ( x 1 , x 2 ) P d ( y 1 , y 2 )
P d ( y 1 , y 2 ) | U y ( y 1 + y 2 2 ) | 2 + | U y ( y 1 y 2 2 ) | 2 + 2 U y ( y 1 + y 2 2 ) U y ( y 1 y 2 2 ) cos [ ϕ + ξ ( y 1 , y 2 ) ] ,
C ( a 1 , a 2 ) A 1 ( y 1 ) A 2 ( y 2 ) P d ( y 1 , y 2 ) d y 1 d y 2 ,
C ( a 1 , a 2 ) A 1 ( y 1 ) A 2 ( y 2 ) { e | y 1 + y 2 | 2 / w 2 + e | y 1 y 2 | 2 / w 2 + 2 e y 1 2 / w 2 e y 2 2 / w 2 cos ϕ } d y 1 d y 2 ,
C ( a 1 , a 2 ) I g ( a 1 + a 2 ) + w 2 π erf ( a 1 w ) erf ( a 2 w ) cos ϕ ,
I g ( a 1 , a 2 ) = 2 min ( a 1 , a 2 ) w π erf ( | a 1 a 2 | w ) + ( a 1 + a 2 ) w π erf ( a 1 + a 2 w ) ( a 1 + a 2 ) w π erf ( | a 1 a 2 | w ) w 2 [ e | a 1 a 2 | 2 / w 2 e ( a 1 + a 2 ) 2 / w 2 ] .
V ( a 1 , a 2 ) = | C max ( a 1 , a 2 ) C min ( a 1 , a 2 ) C max ( a 1 , a 2 ) + C min ( a 1 , a 2 ) | .
V ( a 1 , a 2 ) = { w π erf ( a 1 w ) erf ( a 2 w ) } [ I g ( a 1 , a 2 ) ] 1 .
C 2 ( a 2 ) 2 π w 2 [ a 2 w + π 2 erf ( a 2 w ) cos ϕ ] .
V 2 ( a 2 ) = π 2 w a 2 erf ( a 2 w ) .
HG 01 ( x , y ) y e ( x 2 + y 2 ) / w p 2 .
C ( a 1 , a 2 ) A 1 ( y 1 ) A 2 ( y 2 ) d y 1 d y 2 { 2 ( y 1 2 y 2 2 ) e y 1 2 / w 2 e y 2 2 / w 2 cos ϕ + ( y 1 + y 2 ) 2 e | y 1 + y 2 | 2 / w 2 + ( y 1 y 2 ) 2 e | y 1 y 2 | 2 / w 2 } ,
C ( a 1 , a 2 ) π w 3 { I h g ( a 1 + a 2 ) + cos ϕ a 2 e a 2 2 / w 2 erf ( a 1 w ) cos ϕ a 1 e a 1 2 / w 2 erf ( a 2 w ) } ,
I h g ( a 1 , a 2 ) = π w 3 { ( a 1 + a 2 2 min ( a 1 , a 2 ) ) [ | a 1 a 2 | π w e | a 1 a 2 | 2 / w 2 1 2 erf ( | a 1 a 2 | w ) ] + ( a 1 + a 2 ) 1 2 erf ( a 1 + a 2 w ) ( a 1 + a 2 ) a 1 + a 2 π w e ( a 1 + a 2 ) 2 / w 2 } .
V ( a 1 , a 2 ) = | a 2 e a 2 2 / w 2 erf ( a 1 w ) a 1 e a 1 2 / w 2 erf ( a 2 w ) | { I h g ( a 1 , a 2 ) } 1
C 2 ( a 2 ) π w 4 a 2 ( 1 + e a 2 2 / w 2 cos ϕ ) .
V 2 ( a 2 ) = e a 2 2 / w 2 .
| ψ = 1 2 ( | E O 12 + | O E 12 ) ,
| E O 12 = j even , k odd C j k | H G j 1 | H G k 2 ,
V h g = | C O E ( a 1 , a 2 ) C E O ( a 1 , a 2 ) C O E ( a 1 , a 2 ) + C E O ( a 1 , a 2 ) |
| ψ = α | E E 12 + β | O O 12 ,
V g = | C E E ( a 1 , a 2 ) C O O ( a 1 , a 2 ) C E E ( a 1 , a 2 ) + C O O ( a 1 , a 2 ) |

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