Abstract

Control of spatial quantum correlations in bi-photons is one of the fundamental principles of Quantum Imaging. Up to now, experiments have been restricted to controlling the state of a single bi-photon, by using linear optical elements. In this work we demonstrate experimental control of quantum correlations in a four-photon state comprised of two pairs of photons. Our scheme is based on a high-efficiency parametric down-conversion source coupled to a double slit by a variable linear optical setup, in order to obtain spatially encoded qubits. Both entangled and separable pairs have been obtained, by altering experimental parameters. We show how the correlations influence both the interference and diffraction on the double slit.

© 2011 Optical Society of America

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2010 (2)

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

T. Vértesi, S. Pironio, and N. Brunner, “Closing the Detection Loophole in Bell Experiments Using Qudits,” Phys. Rev. Lett. 104, 060401 (2010).
[CrossRef] [PubMed]

2009 (3)

M. Ostermeyer, D. Puhlmann, and D. Korn, “Quantum diffraction of biphotons at a blazed grating,” J. Opt. Soc. Am. B 26, 2347–2356 (2009).
[CrossRef]

W. Peeters, and J. Renema, “andM. V. Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

2008 (1)

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

2007 (1)

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

2006 (1)

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

2005 (2)

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

2004 (3)

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

2002 (2)

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

2001 (3)

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

2000 (1)

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

1999 (1)

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

1998 (2)

W. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

C. Monken, P. 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 (1)

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

1994 (1)

P. H. Souto 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]

1993 (1)

G. Jaeger, M. Horne, and A. Shimony, “Complementarity of one-particle and two-particle interference,” Phys. Rev. A 48, 1023–1027 (1993).
[CrossRef] [PubMed]

1989 (1)

M. A. Horne, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62, 2209–2212 (1989).
[CrossRef] [PubMed]

Abouraddy, A.

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Acín, A.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Barbosa, G. A.

P. H. Souto 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]

Berchera, I. R.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Brida, G.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Brunner, N.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the Detection Loophole in Bell Experiments Using Qudits,” Phys. Rev. Lett. 104, 060401 (2010).
[CrossRef] [PubMed]

Caspani, L.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Collins, D.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

da Silva, J. C. M.

P. H. Souto 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]

Davidovich, L.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

Dougakiuchi, T.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Fiorentino, M.

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

Fonseca, E.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

Fonseca, E. J. S.

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

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

Gatti, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Genovese, M.

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Gisin, N.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Gómez, J. A.

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Hofmann, H. F.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Horne, M.

G. Jaeger, M. Horne, and A. Shimony, “Complementarity of one-particle and two-particle interference,” Phys. Rev. A 48, 1023–1027 (1993).
[CrossRef] [PubMed]

Horne, M. A.

M. A. Horne, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62, 2209–2212 (1989).
[CrossRef] [PubMed]

Iinuma, M.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Jaeger, G.

G. Jaeger, M. Horne, and A. Shimony, “Complementarity of one-particle and two-particle interference,” Phys. Rev. A 48, 1023–1027 (1993).
[CrossRef] [PubMed]

Kadoya, Y.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Kasai, K.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Klyshko, D.

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Korn, D.

Kuklewicz, C.

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

Lima, G.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

Linden, N.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Massar, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Meda, A.

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

Messin, G.

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

Monken, C.

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

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

Monken, C. H.

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

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

Nasr, M.

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

Neves, L.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

Nussenzveig, P.

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

Ostermeyer, M.

Pádua, S.

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

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

C. Monken, P. 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. 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]

Paulini, Z.

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

Peeters, W.

W. Peeters, and J. Renema, “andM. V. Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

Pironio, S.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the Detection Loophole in Bell Experiments Using Qudits,” Phys. Rev. Lett. 104, 060401 (2010).
[CrossRef] [PubMed]

Pittman, T.

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Popescu, S.

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

Puhlmann, D.

Renema, J.

W. Peeters, and J. Renema, “andM. V. Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

Ribeiro, P.

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

Rubin, M.

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Saavedra, C.

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

Saleh, B.

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Santos, I.

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

Sergienko, A.

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Shapiro, J.

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

Shih, Y.

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Shimony, A.

G. Jaeger, M. Horne, and A. Shimony, “Complementarity of one-particle and two-particle interference,” Phys. Rev. A 48, 1023–1027 (1993).
[CrossRef] [PubMed]

Souto Ribeiro, P. H.

P. H. Souto 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]

Strekalov, D.

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

Taguchi, G.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Teich, M.

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Terra Cunha, M. O.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Thew, R. T.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Vértesi, T.

T. Vértesi, S. Pironio, and N. Brunner, “Closing the Detection Loophole in Bell Experiments Using Qudits,” Phys. Rev. Lett. 104, 060401 (2010).
[CrossRef] [PubMed]

Walborn, S. P.

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Wong, F.

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

Wootters, W.

W. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

Yoshimoto, N.

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

Zbinden, H.

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

Zeilinger, A.

M. A. Horne, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62, 2209–2212 (1989).
[CrossRef] [PubMed]

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

Nat. Photonics (1)

G. Brida, M. Genovese, and I. R. Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4, 227–230 (2010).
[CrossRef]

Phys. Rev. A (15)

S. P. Walborn, M. O. Terra Cunha, S. Pádua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

B. Saleh, A. Abouraddy, A. Sergienko, and M. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

I. Santos, L. Neves, G. Lima, C. H. Monken, and S. Pádua, “Generation and detection of magnified images via illumination by entangled photon pairs,” Phys. Rev. A 72, 033802 (2005).
[CrossRef]

G. Jaeger, M. Horne, and A. Shimony, “Complementarity of one-particle and two-particle interference,” Phys. Rev. A 48, 1023–1027 (1993).
[CrossRef] [PubMed]

P. H. Souto 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]

T. Pittman, D. Strekalov, D. Klyshko, M. Rubin, A. Sergienko, and Y. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef] [PubMed]

E. J. S. Fonseca, Z. Paulini, P. Nussenzveig, C. H. Monken, and S. Pádua, “Nonlocal de Broglie wavelength of a two-particle system,” Phys. Rev. A 63, 043819 (2001).
[CrossRef]

G. Lima, L. Neves, I. Santos, J. A. Gómez, C. Saavedra, and S. Pádua, “Propagation of spatially entangled qudits through free space,” Phys. Rev. A 73, 032340 (2006).
[CrossRef]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[CrossRef]

L. Neves, G. Lima, E. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys. Rev. A 76, 032314 (2007).
[CrossRef]

G. Taguchi, T. Dougakiuchi, N. Yoshimoto, K. Kasai, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Measurement and control of spatial qubits generated by passing photons through double slits,” Phys. Rev. A 78, 012307 (2008).
[CrossRef]

W. Peeters, and J. Renema, “andM. V. Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

C. Kuklewicz, M. Fiorentino, G. Messin, F. Wong, and J. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO4 parametric down-converter,” Phys. Rev. A 69, 13807 (2004).
[CrossRef]

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

A. Abouraddy, M. Nasr, B. Saleh, A. Sergienko, and M. Teich, “Demonstration of the complementarity of oneand two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

Phys. Rev. Lett. (9)

D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, “Bell inequalities for arbitrarily high-dimensional systems,” Phys. Rev. Lett. 88, 040404 (2002).
[CrossRef] [PubMed]

R. T. Thew, A. Acín, H. Zbinden, and N. Gisin, “Bell-type test of energy-time entangled qutrits,” Phys. Rev. Lett. 93, 010503 (2004).
[CrossRef]

T. Vértesi, S. Pironio, and N. Brunner, “Closing the Detection Loophole in Bell Experiments Using Qudits,” Phys. Rev. Lett. 104, 060401 (2010).
[CrossRef] [PubMed]

W. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

L. Neves, G. Lima, J. A. Gómez, C. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

A. Abouraddy, B. Saleh, A. Sergienko, and M. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
[CrossRef] [PubMed]

M. A. Horne, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62, 2209–2212 (1989).
[CrossRef] [PubMed]

G. Brida, L. Caspani, A. Gatti, M. Genovese, A. Meda, and I. R. Berchera, “Measurement of Sub-Shot-Noise Spatial Correlations without Background Subtraction,” Phys. Rev. Lett. 102, 213602 (2009).
[CrossRef] [PubMed]

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

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[CrossRef]

. F. Wong, M. A. Albota, F. Koenig, C. E. Kuklewicz, E. J. Mason, G. Messin, and J. H. Shapiro, “High-flux entanglement sources using periodically-poled nonlinear crystals,” Nonlinear Optics: Materials, Fundamentals and Applications (2002), paper FC8 (1).

Z.-Y. J. Ou, Multi-Photon Quantum Interference (Springer, 2007), 1st ed.

A. Cabello, and M. Terra Cunha, “Proposal of a two-qutrit contextuality test free of the finite precision and compatibility loopholes,” arXiv:1009.2330v1 [quant-ph] (2010).

O. Cosme, A. Delgado, G. Lima, C. H. Monken, and S. Pádua, “Controlling the transverse correlation in QPM parametric down-conversion,” arXiv:0906.4734v1 [quant-ph].

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company Publishers, 2004), 3rd ed.

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

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for control of transverse correlations over the double slit (DS). Coupling is done so that either the position (a) or momentum (b) degree of freedom of the bi-photons is mapped onto the double slit plane [26]. The first uses a cylindrical lens (CL) of f1 = 5 cm and a spherical lens (SL2) of f2 = 20 cm to project a magnified image of the crystal center, while the latter uses only the f2 = 20 cm lens to project the Fourier transform of the same plane onto the plane of the double slit. The slits are 80 μm wide and have a separation 2d = 240 μm. SL1 is the f = 31 cm spherical lens that focuses the pump beam on the PPKTP crystal and DM is a dichroic mirror that reflects the 413 nm beam while allowing the 826 nm down-converted photons to pass.

Fig. 2
Fig. 2

A schematic view of the detection apparatus, showing how the incoming photons are divided into two branches by a PBS. On each branch the photons are further divided by a BS. This allows us to make coincidence detection between two detectors on the same branch or between detectors on different branches. Detections on the same branch originate only from double-pair events, while the raw different branch detections are a sum of contributions from single-pair and double-pair events. In this figure, the focal plane of FL corresponds to the detection plane, upon which all four detectors are free to move parallel to the plane of the table and perpendicular to the direction of beam propagation after passing through the beamsplitters. DS is the double-slit.

Fig. 5
Fig. 5

Normalized two-photon measured and simulated broad scan coincidence maps for a four-photon spatial state presenting a high degree of spatial correlation in each bi-photon. The upper row, from (a) to (c), includes the measured coincidences on the H branch (D2D4), the calculated uncorrelated pattern corresponding to the product of the single counts (D2*D4), weighted by the repetition rate of the pump, and the SBC simulation, using equations 14 and 16. The lower row, from (d) to (f), corresponds respectively to the coincidences between the H and V branches (D2D3) and to the same map corrected by subtracting the uncorrelated contribution (D2D3-D2*D3), as well as a simulated DBC map, using equations 13 and 16. The simulation parameters used are, as before, α a exp = 176 ° and φ a exp = 170 °. For a measurement time of 25 s per point, the maximum in map (a) corresponds to 483 counts and in map (d) to 1598 counts.

Fig. 3
Fig. 3

Normalized two-photon measured and simulated coincidence maps for a four-photon path state presenting a high degree of spatial correlation in each bi-photon. The upper row, from (a) to (c), includes the measured coincidences on the H branch (D2D4), the calculated uncorrelated pattern corresponding to the product of the single counts (D2*D4), weighted by the repetition rate of the pump, and the SBC simulation, generated with equation 14. The lower row, from (d) to (f), corresponds respectively to the coincidences between the H and V branches (D2D3) and to the same map corrected by subtracting the uncorrelated contribution (D2D3-D2*D3), as well as a simulated DBC map, generated with equation 13. The simulation parameters used are α a exp = 176 ° and φ a exp = 170 °, corresponding to �� ≈ 0.997±0.003. For a measurement time of 25 s per point, the maximum in map (a) corresponds to 549 coincidence counts and in map (d) to 1630 coincidence counts. The measured maps were obtained at the Fourier plane of Fig. 2, after the photon pairs cross the double-slit.

Fig. 4
Fig. 4

Normalized two-photon measured and simulated coincidence maps for a four-photon path state of negligible spatial correlation. The upper row, from (a) to (c), includes the measured coincidences on the H branch (D2D4), the calculated uncorrelated pattern corresponding to the product of the single counts (D2*D4), weighted by the repetition rate of the pump, and the SBC simulation, generated with equation 14. The lower row, from (d) to (f), corresponds respectively to the coincidences between the H and V branches (D2D3) and to the same map corrected by subtracting the uncorrelated contribution (D2D3-D2*D3), as well as a simulated DBC map, generated with equation 13. The simulation parameters used are α b exp = 86 ° and φ b exp = 5 °, corresponding to �� ≈ 0.11±0.03. For a measurement time of 25 s per point, the maximum in map (a) corresponds to 122 counts and in map (d) to 247 counts. The measured maps were obtained at the Fourier plane of Fig. 2, after the photon pairs cross the double-slit.

Fig. 6
Fig. 6

Normalized two-photon measured and simulated broad scan coincidence maps for a four-photon path state of negligible spatial correlation. The upper row, from (a) to (c), includes the measured coincidences on the H branch (D2D4), the calculated uncorrelated pattern corresponding to the product of the single counts (D2*D4), weighted by the repetition rate of the pump, and the SBC simulation, using equations 14 and 16. The lower row, from (d) to (f), corresponds respectively to the coincidences between the H and V branches (D2D3) and to the same map corrected by subtracting the uncorrelated contribution (D2D3-D2*D3), as well as a simulated DBC map, using equations 13 and 16. The simulation parameters used are, as before, α b exp = 86 ° and φ b exp = 5 °. For a measurement time of 25 s per point, the maximum in map (a) corresponds to 75 coincidence counts and in map (d) to 117 coincidence counts.

Equations (16)

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

| Ψ H , V = cos ( α / 2 ) | ψ + + e i φ sin ( α / 2 ) | ϕ +
| ψ + = 1 2 ( | 01 A , B + | 10 A , B )
| ϕ + = 1 2 ( | 00 A , B + | 11 A , B )
| Ψ = M ( | vac + η | Ψ H , V + η 2 2 | Ψ H , V I | Ψ H , V I I )
| Ψ H , V 1 | Ψ H , V 2 = ( cos ( α / 2 ) | ψ + + e i φ sin ( α / 2 ) | ϕ + ) 2
𝒞 = 1 ( cos ( φ ) sin ( α ) ) 2
𝒫 = 1 4 ( 1 + ( cos ( φ ) sin ( α ) ) 2 ) 2 .
𝒫 = 1 4 ( 2 𝒞 2 ) 2 .
Φ ˜ ( q 1 , q 2 ) = E ˜ p ( q 1 + q 2 ) ξ ˜ ( q 1 q 2 ) ,
ξ ˜ sinc ( ϕ 0 + L ( q 1 q 2 ) 2 ( 8 n eff ω S P D C / c ) )
p = exp ( i φ ) tan ( α / 2 ) = A ( d , d ) A ( d , d ) ,
P ( x 1 , x 2 ) ( H , V ) | E H + ( x 1 ) E V + ( x 2 ) | Ψ H , V | 2 ,
P ( x 1 , x 2 ) ( H , V ) 1 + cos 2 ( α / 2 ) cos ( β ( x 1 x 2 ) ) + | sin ( α ) | cos ( φ ) [ cos ( β ( x 1 ) ) + cos ( β ( x 2 ) ) ] + sin 2 ( α / 2 ) cos ( β ( x 1 + x 2 ) ) .
P ( x 1 , x 2 ) { ( H , H ) ; ( V , V ) } 1 + ( sin ( α ) cos ( φ ) ) 2 cos ( x 1 ) cos ( x 2 ) + sin ( α ) cos ( φ ) ( cos ( x 1 ) + cos ( x 2 ) ) .
P ( x 1 , x 2 ) { ( H , H ) ; ( V , V ) } vac | E + ( x 1 ) ρ ( I , j ) E ( x 1 ) | vac × vac | E + ( x 2 ) ρ ( I I , j ) E ( x 2 ) | vac ,
sinc 2 ( a ± x ± ) x 1 = ± x 2 A ( ξ 1 , ξ 2 ) T ( ξ 1 , ξ 2 ) exp [ i k f F F ( ξ 1 x 1 + ξ 2 x 2 ) ] d x 1 d x 2 ,

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