Abstract

We study the high-dimensional orbital angular momentum (OAM) entanglement contained in the spatial profiles of two quantum-correlated photons. For this purpose, we use a multi-mode two-photon interferometer with an image rotator in one of the interferometer arms. By measuring the two-photon visibility as a function of the image rotation angle we measure the azimuthal Schmidt number, i.e., we count the number of OAM modes involved in the entanglement; in our setup this number is tunable from 1 to 8.

© 2007 Optical Society of America

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  1. Z.Y. Ou and L. Mandel, "Violation of Bell’s inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988).
    [CrossRef] [PubMed]
  2. P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
    [CrossRef] [PubMed]
  3. C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
    [CrossRef]
  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. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
    [CrossRef] [PubMed]
  6. N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
    [CrossRef] [PubMed]
  7. S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
    [CrossRef] [PubMed]
  8. D.P. Caetano and P.H. Souto Ribeiro, "Generation of spatial antibunching with free-propagating twin beams," Phys. Rev. A 68, 043806 (2003).
    [CrossRef]
  9. S.P. Walborn, A.N. de Oliveira, S. P’adua, and C.H. Monken, "Multimode Hong-Ou-Mandel interference," Phys. Rev. Lett. 90, 143601 (2003).
    [CrossRef] [PubMed]
  10. W.A.T. Nogueira, S.P. Walborn, S. P’adua, and C.H. Monken, "Generation of a two-photon singlet beam," Phys. Rev. Lett. 92, 043602 (2004).
    [CrossRef] [PubMed]
  11. L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
    [CrossRef] [PubMed]
  12. H. Bechmann-Pasquinucci and A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 3313-3316 (2000).
    [CrossRef] [PubMed]
  13. J.P. Torres, A. Alexandrescu, and L. Torner, "Quantum spiral bandwidth of entangled two-photon states," Phys. Rev. A 68, 050301(R) (2003).
    [CrossRef]
  14. L. Torner, J.P. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-881 (2005).
    [CrossRef] [PubMed]
  15. C.K. Law and J.H. Eberly, "Analysis and interpretation of high transverse entanglement in optical parametric down conversion," Phys. Rev. Lett. 92, 127903 (2004).
    [CrossRef] [PubMed]
  16. M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
    [CrossRef] [PubMed]
  17. H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
    [CrossRef]
  18. H. Sasada and M. Okamoto, "Tranverse-mode beam splitter of a light beam and its application to cryptography," Phys. Rev. A 68, 012323 (2003).
    [CrossRef]
  19. C.K. Hong, Z.Y. Ou and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
    [CrossRef] [PubMed]
  20. B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
    [CrossRef]
  21. 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]
  22. R. Bhandari and J. Samuel, "Observation of topological phase by use of a laser interferometer," Phys. Rev. Lett. 60, 1211-1213 (1988).
    [CrossRef] [PubMed]
  23. W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, "Orbital angular momentum analysis of high-dimensional entanglement," submitted toPhys. Rev. A.
  24. C.H. Monken, P.H. Souto Ribeiro, and S. Padua, "Transfer of angular spectrum and image formation in spontaneous parametric down-conversion," Phys. Rev. A 57, 3123-3126 (1998).
    [CrossRef]
  25. R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
    [CrossRef]
  26. A. Ekert and P.L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415- 423 (1995).
    [CrossRef]
  27. M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
    [CrossRef]

2006 (1)

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

2005 (3)

L. Torner, J.P. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-881 (2005).
[CrossRef] [PubMed]

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

2004 (4)

C.K. Law and J.H. Eberly, "Analysis and interpretation of high transverse entanglement in optical parametric down conversion," Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

W.A.T. Nogueira, S.P. Walborn, S. P’adua, and C.H. Monken, "Generation of a two-photon singlet beam," Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (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]

2003 (4)

D.P. Caetano and P.H. Souto Ribeiro, "Generation of spatial antibunching with free-propagating twin beams," Phys. Rev. A 68, 043806 (2003).
[CrossRef]

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

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[CrossRef]

H. Sasada and M. Okamoto, "Tranverse-mode beam splitter of a light beam and its application to 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 (2)

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

2000 (2)

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

H. Bechmann-Pasquinucci and A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 3313-3316 (2000).
[CrossRef] [PubMed]

1998 (1)

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

1995 (2)

A. Ekert and P.L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415- 423 (1995).
[CrossRef]

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

1994 (1)

R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
[CrossRef]

1992 (1)

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
[CrossRef] [PubMed]

1988 (2)

Z.Y. Ou and L. Mandel, "Violation of Bell’s inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988).
[CrossRef] [PubMed]

R. Bhandari and J. Samuel, "Observation of topological phase by use of a laser interferometer," Phys. Rev. Lett. 60, 1211-1213 (1988).
[CrossRef] [PubMed]

1987 (1)

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

’t Hooft, G.W.

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Abouraddy, A.F.

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Aguirre Gomez, J.G.

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Aiello, A.

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Alexandrescu, A.

J.P. Torres, A. Alexandrescu, and L. Torner, "Quantum spiral bandwidth of entangled two-photon states," Phys. Rev. A 68, 050301(R) (2003).
[CrossRef]

Barnett, S.M.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[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]

Bartlett, S.D.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Bechmann-Pasquinucci, H.

H. Bechmann-Pasquinucci and A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 3313-3316 (2000).
[CrossRef] [PubMed]

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]

Bhandari, R.

R. Bhandari and J. Samuel, "Observation of topological phase by use of a laser interferometer," Phys. Rev. Lett. 60, 1211-1213 (1988).
[CrossRef] [PubMed]

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]

Caetano, D.P.

D.P. Caetano and P.H. Souto Ribeiro, "Generation of spatial antibunching with free-propagating twin beams," Phys. Rev. A 68, 043806 (2003).
[CrossRef]

Carrasco, S.

Courtial, J.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[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]

Dalton, R.B.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

de Oliveira, A.N.

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

Eberly, J.H.

C.K. Law and J.H. Eberly, "Analysis and interpretation of high transverse entanglement in optical parametric down conversion," Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
[CrossRef]

Ekert, A.

A. Ekert and P.L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415- 423 (1995).
[CrossRef]

Eliel, E.R.

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Franke-Arnold, S.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[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]

Gilchrist, A.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Grobe, R.

R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
[CrossRef]

Harvey, M.D.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Hong, C.K.

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

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]

Knight, P.L.

A. Ekert and P.L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415- 423 (1995).
[CrossRef]

Kurtsiefer, C.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Kwiat, P.G.

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Langford, N.K.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Law, C.K.

C.K. Law and J.H. Eberly, "Analysis and interpretation of high transverse entanglement in optical parametric down conversion," Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

Leach, J.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[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]

Lima, G.

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Ma, X.

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Mandel, L.

Z.Y. Ou and L. Mandel, "Violation of Bell’s inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988).
[CrossRef] [PubMed]

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

Mattle, K.

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Monken, C.H.

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

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

Neves, L.

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Nienhuis, G.

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Nogueira, W.A.T.

W.A.T. Nogueira, S.P. Walborn, S. P’adua, and C.H. Monken, "Generation of a two-photon singlet beam," Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

O’Brien, J.L.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Oberparleiter, M.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Oemrawsingh, S.S.R.

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Okamoto, M.

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

Ou, Z.Y.

Z.Y. Ou and L. Mandel, "Violation of Bell’s inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988).
[CrossRef] [PubMed]

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

Padgett, M.J.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[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]

Padua, S.

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

Peeters, W.H.

W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, "Orbital angular momentum analysis of high-dimensional entanglement," submitted toPhys. Rev. A.

Peres, A.

H. Bechmann-Pasquinucci and A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 3313-3316 (2000).
[CrossRef] [PubMed]

Pryde, G.J.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Rzazewski, K.

R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
[CrossRef]

Saavedra, C.

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

Saleh, B.E.A.

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Samuel, J.

R. Bhandari and J. Samuel, "Observation of topological phase by use of a laser interferometer," Phys. Rev. Lett. 60, 1211-1213 (1988).
[CrossRef] [PubMed]

Sasada, H.

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

Segev, M.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
[CrossRef] [PubMed]

Sergienko, A.V.

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Shih, Y.

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Solomon, R.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
[CrossRef] [PubMed]

Souto Ribeiro, P.H.

D.P. Caetano and P.H. Souto Ribeiro, "Generation of spatial antibunching with free-propagating twin beams," Phys. Rev. A 68, 043806 (2003).
[CrossRef]

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

Teich, M.C.

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Torner, L.

L. Torner, J.P. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-881 (2005).
[CrossRef] [PubMed]

J.P. Torres, A. Alexandrescu, and L. Torner, "Quantum spiral bandwidth of entangled two-photon states," Phys. Rev. A 68, 050301(R) (2003).
[CrossRef]

Torres, J.P.

L. Torner, J.P. Torres, and S. Carrasco, "Digital spiral imaging," Opt. Express 13, 873-881 (2005).
[CrossRef] [PubMed]

J.P. Torres, A. Alexandrescu, and L. Torner, "Quantum spiral bandwidth of entangled two-photon states," Phys. Rev. A 68, 050301(R) (2003).
[CrossRef]

van Exter, M.P.

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, "Orbital angular momentum analysis of high-dimensional entanglement," submitted toPhys. Rev. A.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Verstegen, E.J.K.

W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, "Orbital angular momentum analysis of high-dimensional entanglement," submitted toPhys. Rev. A.

Voigt, D.

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Walborn, S.P.

W.A.T. Nogueira, S.P. Walborn, S. P’adua, and C.H. Monken, "Generation of a two-photon singlet beam," Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

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

Wei, H.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Weinfurter, H.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
[CrossRef]

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

White, A.G.

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

Woerdman, J.P.

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

Xue, X.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[CrossRef]

Yao, E.

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[CrossRef]

Yariv, A.

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

Am. J. Phys. (1)

A. Ekert and P.L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415- 423 (1995).
[CrossRef]

J. Phys. B (1)

R. Grobe, K. Rzazewski, and J.H. Eberly, "Measure of electron-electron correlation in atomic physics," J. Phys. B 27, L503-L508 (1994).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entangelement of the orbital angular momentum states of photons," Nature 412, 313-316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

H. Wei, X. Xue, J. Leach, M.J. Padgett, S.M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, "Simplified measurement of the orbital angular momentum of single photons," Opt. Commun. 223, 117-122 (2003).
[CrossRef]

Opt. Express (1)

Phys. Rev. A (6)

M.P. van Exter, A. Aiello, S.S.R. Oemrawsingh, G. Nienhuis, and J.P. Woerdman, "Effect of spatial filtering on the Schmidt decomposition of entangled photons," Phys. Rev. A 74, 012309 (2006).
[CrossRef]

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

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

B.E.A. Saleh, A.F. Abouraddy, A.V. Sergienko, and M.C. Teich, "Duality between partial coherence and partial entanglement," Phys. Rev. A 62, 043816 (2000).
[CrossRef]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, "High-efficiency entangled photon pair collection in type-II parametric fluorescence," Phys. Rev. A 64, 023802 (2001).
[CrossRef]

D.P. Caetano and P.H. Souto Ribeiro, "Generation of spatial antibunching with free-propagating twin beams," Phys. Rev. A 68, 043806 (2003).
[CrossRef]

Phys. Rev. A. (1)

W.H. Peeters, E.J.K. Verstegen, and M.P. van Exter, "Orbital angular momentum analysis of high-dimensional entanglement," submitted toPhys. Rev. A.

Phys. Rev. Lett. (14)

S.P. Walborn, A.N. de Oliveira, S. P’adua, 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. P’adua, and C.H. Monken, "Generation of a two-photon singlet beam," Phys. Rev. Lett. 92, 043602 (2004).
[CrossRef] [PubMed]

L. Neves, G. Lima, J.G. Aguirre Gomez, C.H. Monken, C. Saavedra, and S. P’adua, "Generation of entangled states of qudits using twin photons," Phys. Rev. Lett. 94, 100501 (2005).
[CrossRef] [PubMed]

H. Bechmann-Pasquinucci and A. Peres, "Quantum cryptography with 3-state systems," Phys. Rev. Lett. 85, 3313-3316 (2000).
[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]

Z.Y. Ou and L. Mandel, "Violation of Bell’s inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988).
[CrossRef] [PubMed]

P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, and Y. Shih, "New high-intensity source of polarization-entangled photon pairs," Phys. Rev. Lett. 75, 4337-4341 (1995).
[CrossRef] [PubMed]

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]

R. Bhandari and J. Samuel, "Observation of topological phase by use of a laser interferometer," Phys. Rev. Lett. 60, 1211-1213 (1988).
[CrossRef] [PubMed]

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

N.K. Langford, R.B. Dalton, M.D. Harvey, J.L. O’Brien, G.J. Pryde, A. Gilchrist, S.D. Bartlett, and A.G. White, "Measuring entangled qutrits and their use for quantum bit commitment, " Phys. Rev. Lett. 93, 053601 (2004).
[CrossRef] [PubMed]

S.S.R. Oemrawsingh, X. Ma, D. Voigt, A. Aiello, E.R. Eliel, G.W. ’t Hooft, and J.P. Woerdman, "Experimental demonstration of fractional orbital angular momentum entanglement of two photons," Phys. Rev. Lett. 95, 240501 (2005).
[CrossRef] [PubMed]

C.K. Law and J.H. Eberly, "Analysis and interpretation of high transverse entanglement in optical parametric down conversion," Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry’s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
[CrossRef] [PubMed]

Other (1)

J.P. Torres, A. Alexandrescu, and L. Torner, "Quantum spiral bandwidth of entangled two-photon states," Phys. Rev. A 68, 050301(R) (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Schematic view of the experimental setup, representing a two-photon interferometer with an image rotator R(θ), comprising four out-of-plane mirrors, in one arm.

Fig. 2.
Fig. 2.

Two-photon coincidence rate versus the time delay Δt between the two interferometer arms, measured at a fixed rotation angle of θ = -30° behind a 1 mm aperture (dots) and a 10 mm aperture (squares). The coincidence rate measured for the 1 mm aperture has been multiplied by the area ratio (≈ 100x) for a direct comparison with the other geometry.

Fig. 3.
Fig. 3.

Two-photon visibility versus the aperture diameter 2a, measured at a fixed rotation angle of θ = -30°. The solid curve represents a fit. The two encircled data points correspond to the interference patterns shown in Fig. (2).

Fig. 4.
Fig. 4.

Two-photon visibility measured as a function of the rotation angle θ behind different aperture geometries (specified by the azimuthal Schmidt number Kaz ) and behind single-mode fibers (Kaz = 1). The three dashed lines have been calculated from Eq. (1)

Equations (6)

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

V ( a sin θ ) = ( 1 exp ( ξ ) ) ξ ,
V ( θ ) = l P l cos ( 2 ) ,
V ( θ ) = 1 1 + ( K 2 D 1 ) sin 2 θ ,
Ψ = i λ i | u i | v i ,
| Ψ in = l p λ l , p e l , p | l , p | l , p ,
| Ψ ( θ ) det = l p λ l , p e l , p ( e i ( + 1 2 Δωτ ) e i ( + 1 2 Δωτ ) ) l , p l , p ,

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