Abstract

We report the results of two experiments performed with two-photon light, produced via collinear degenerate optical spontaneous parametric downconversion (SPDC), in which both second-order (one-photon) and fourth-order (two-photon) interferograms are recorded in a Mach–Zehnder interferometer (MZI). In the first experiment, high-visibility fringes are obtained for both the second- and fourth-order interferograms. In the second experiment, the MZI is modified by the removal of a mirror from one of its arms; this leaves the fourth-order interferogram unchanged, but extinguishes the second-order interferogram. A theoretical model that takes into consideration both the temporal and spatial degrees-of-freedom of the two-photon state successfully explains the results. While the temporal interference in the MZI is independent of the spatial coherence of the source, that of the modified MZI is not.

© 2008 Optical Society of America

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  1. M. A. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Phys. Rev. Lett. 62, 2209-2212 (1989).
    [CrossRef] [PubMed]
  2. D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
    [CrossRef]
  3. M. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Nature (London) 347, 429-430 (1990).
    [CrossRef]
  4. G. Jaeger, M. A. Horne, and A. Shimony, "Complementarity of one-particle and two-particle interference," Phys. Rev. A 48, 1023-1027 (1993).
    [CrossRef] [PubMed]
  5. G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
    [CrossRef] [PubMed]
  9. J. D. Franson, "Two-photon interferometry over large distances," Phys. Rev. A 44, 4552-4555 (1991).
    [CrossRef] [PubMed]
  10. J. G. Rarity and P. R. Tapster, "Fourth-order interference effects at large distances," Phys. Rev. A 45, 2052-2056 (1992).
    [CrossRef] [PubMed]
  11. D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
    [CrossRef] [PubMed]
  12. J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
    [CrossRef] [PubMed]
  13. A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
    [CrossRef]
  14. C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
    [CrossRef] [PubMed]
  15. 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]
  16. A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
    [CrossRef]
  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. 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]
  19. M. P. van Exter, P. S. K. Lee, S. Doesburg, and J. P. Woerdman, "Mode counting in high-dimensional orbital angular momentum entanglement," Opt. Express 15, 6431-6438 (2007).
    [CrossRef] [PubMed]
  20. S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
    [CrossRef]
  21. A. Zeilinger, "Quantum entanglement: A fundamental concept finding its applications," Phys. Scr. T76, 203-209 (1998).
    [CrossRef]
  22. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
    [CrossRef]
  23. 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]

2007 (3)

A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
[CrossRef]

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]

M. P. van Exter, P. S. K. Lee, S. Doesburg, and J. P. Woerdman, "Mode counting in high-dimensional orbital angular momentum entanglement," Opt. Express 15, 6431-6438 (2007).
[CrossRef] [PubMed]

2005 (1)

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

2003 (2)

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]

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]

2002 (1)

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
[CrossRef] [PubMed]

2001 (1)

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[CrossRef]

2000 (1)

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]

1998 (1)

A. Zeilinger, "Quantum entanglement: A fundamental concept finding its applications," Phys. Scr. T76, 203-209 (1998).
[CrossRef]

1996 (1)

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

1995 (1)

G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
[CrossRef] [PubMed]

1993 (3)

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
[CrossRef]

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

1992 (2)

J. G. Rarity and P. R. Tapster, "Fourth-order interference effects at large distances," Phys. Rev. A 45, 2052-2056 (1992).
[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]

1991 (1)

J. D. Franson, "Two-photon interferometry over large distances," Phys. Rev. A 44, 4552-4555 (1991).
[CrossRef] [PubMed]

1990 (2)

M. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Nature (London) 347, 429-430 (1990).
[CrossRef]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

1989 (1)

M. A. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Phys. Rev. Lett. 62, 2209-2212 (1989).
[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]

1967 (1)

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
[CrossRef]

Abouraddy, A. F.

A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
[CrossRef]

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, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[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]

Barreiro, J. T.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Byer, R. L.

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
[CrossRef]

Campos, R. A.

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

de Oliveira, A. N.

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]

Doesburg, S.

Fattal, D.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
[CrossRef] [PubMed]

Franson, J. D.

J. D. Franson, "Two-photon interferometry over large distances," Phys. Rev. A 44, 4552-4555 (1991).
[CrossRef] [PubMed]

Greenberger, D. M.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
[CrossRef]

Harris, S. E.

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
[CrossRef]

Hong, C. K.

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

Horne, M.

M. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Nature (London) 347, 429-430 (1990).
[CrossRef]

Horne, M. A.

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

D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
[CrossRef]

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

Jaeger, G.

G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
[CrossRef] [PubMed]

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

Jakeman, E.

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

Kwiat, P. G.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

Langford, N. K.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Larchuk, T.

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

Larchuk, T. S.

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

Lee, P. S. K.

Mandel, L.

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

Monken, C. H.

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]

Nasr, M. B.

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[CrossRef]

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]

Oshman, M. K.

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
[CrossRef]

Ou, Z. Y.

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

Pádua, S.

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]

Peters, N. A.

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Pittman, T. B.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

Rarity, J. G.

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, "Fourth-order interference effects at large distances," Phys. Rev. A 45, 2052-2056 (1992).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

Saleh, B. E. A.

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, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[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]

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
[CrossRef] [PubMed]

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
[CrossRef] [PubMed]

Santori, C.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
[CrossRef] [PubMed]

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]

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.

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[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]

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

Shih, Y. H.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

Shimony, A.

G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
[CrossRef] [PubMed]

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

M. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Nature (London) 347, 429-430 (1990).
[CrossRef]

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

Solomon, G. S.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
[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]

Strekalov, D. V.

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
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Tapster, P. R.

T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
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J. G. Rarity and P. R. Tapster, "Fourth-order interference effects at large distances," Phys. Rev. A 45, 2052-2056 (1992).
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J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
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Teich, M. C.

A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
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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).
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A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
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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).
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T. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
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J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
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G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
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Vuckovic, J.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
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Walborn, S. P.

S. P. Walborn, A. N. de Oliveira, S. Pádua, and C. H. Monken, "Multimode Hong-Ou-Mandel interference," Phys. Rev. Lett. 90, 143601 (2003).
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Yamamoto, Y.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
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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).
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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, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
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A. Zeilinger, "Quantum entanglement: A fundamental concept finding its applications," Phys. Scr. T76, 203-209 (1998).
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D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
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Nature (London) (2)

M. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Nature (London) 347, 429-430 (1990).
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C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device," Nature (London) 419, 594-597 (2002).
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Opt. Express (1)

Phys. Rev. A (9)

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).
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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]

A. F. Abouraddy, T. Yarnall, B. E. A. Saleh, and M. C. Teich, "Violation of Bells inequality with continuous spatial variables," Phys. Rev. A 75, 052114 (2007).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of the complementarity of one- and two-photon interference," Phys. Rev. A 63, 063803 (2001).
[CrossRef]

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

G. Jaeger, A. Shimony, and L. Vaidman, "Two interferometric complementarities," Phys. Rev. A 51, 54-67 (1995).
[CrossRef] [PubMed]

J. D. Franson, "Two-photon interferometry over large distances," Phys. Rev. A 44, 4552-4555 (1991).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, "Fourth-order interference effects at large distances," Phys. Rev. A 45, 2052-2056 (1992).
[CrossRef] [PubMed]

D. V. Strekalov, T. B. Pittman, A. V. Sergienko, Y. H. Shih, and P. G. Kwiat, "Postselection-free energy-time entanglement," Phys. Rev. A 54, R1-R4 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (9)

J. G. Rarity, P. R. Tapster, E. Jakeman, T. Larchuk, R. A. Campos, M. C. Teich, and B. E. A. Saleh, "Two-photon interference in a Mach-Zehnder interferometer," Phys. Rev. Lett. 65, 1348-1351 (1990).
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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).
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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. S. Larchuk, R. A. Campos, J. G. Rarity, P. R. Tapster, E. Jakeman, B. E. A. Saleh, and M. C. Teich, "Interfering entangled photons of different colors," Phys. Rev. Lett. 70, 1603-1606 (1993).
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J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, "Generation of hyperentangled photon pairs," Phys. Rev. Lett. 95, 260501 (2005).
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M. A. Horne, A. Shimony, and A. Zeilinger, "Two-particle interferometry," Phys. Rev. Lett. 62, 2209-2212 (1989).
[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]

M. Segev, R. Solomon, and A. Yariv, "Manifestation of Berry??s phase in image-bearing optical beams," Phys. Rev. Lett. 69, 590-592 (1992).
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S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of tunable optical parametric fluorescence," Phys. Rev. Lett. 18, 732-735 (1967).
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Phys. Scr. (1)

A. Zeilinger, "Quantum entanglement: A fundamental concept finding its applications," Phys. Scr. T76, 203-209 (1998).
[CrossRef]

Phys. Today (1)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle interferometry and the superposition principle," Phys. Today 8, 22-29 (1993).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Conceptual layout for two Mach-Zehnder interferometer experiments. The upper diagram illustrates the traditional MZI while the lower diagram illustrates a modified version (MZIM) in which a spatial flip (SF) has been inserted into one arm. Both are followed by detectors that record the coincidence rate at the two output ports, G (2)(τ), as well as the singles rate, I(τ).

Fig. 2.
Fig. 2.

(a) Schematic of the Mach-Zehnder experimental arrangements for studying second-and fourth-order temporal interference. NLC: nonlinear crystal; PBS: polarizing beam splitter; F: interference filter; D: detector; ⊗: coincidence circuit. The upper shaded region highlights one arm of the traditional Mach–Zehnder interferometer (MZI), which comprises three mirrors, while the lower shaded region highlights one arm of the modified Mach–Zehnder interferometer (MZIM), which comprises two mirrors. (b) Singles and coincidence interferograms for the MZI experiment. (c) Singles and coincidence interferograms for the MZIM experiment. The coincidence interferograms are similar while the singles interferograms are distinctly different. The insets show data in the vicinity of τ=0 for each of the four plots; coincidence interferograms oscillate at the pump period, with a frequency twice that of the singles interferograms.

Equations (6)

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

ψ = dxdx d Ω d Ω ϕ ( x , x ) ψ ( Ω , Ω ) 1 x , ω p 2 + Ω , 1 x , ω p 2 + Ω ,
ρ = dxdx d Ω d Ω ρ x ( x , x ) ρ Ω ( Ω , Ω ) 1 x , ω p 2 + Ω 1 x , ω p 2 + Ω ,
G ( 2 ) ( τ ) = 1 1 2 cos ω p τ 1 2 d Ω ψ ( Ω ) 2 cos 2 Ω τ ,
I t ( τ ) = 1 cos ω p 2 τ d Ω ψ ( Ω ) 2 cos Ω τ ,
I t ( τ ) = 1 α cos ( ω p 2 τ φ ) d Ω ψ ( Ω ) 2 cos Ω τ ,
α = α e i φ = d x ρ x ( x , x ) .

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