Abstract

We present experimental observations of a nonclassic and nonlocal interference effect with frequency-entangled photon pairs. We observed two-photon interference in a Hong–Ou–Mandel interferometer by monitoring the coincidence-counting rate as we varied the path-length difference or the relative time delay between two photons. The quantum-mechanical probabilities of joint detection by two detectors that respond to different frequency components exhibit differences that depend not only on the arrangement of the detector pairs but on the spectral filtering. The experimental results provide more understanding of two-photon entanglement and of the interference effects that arise from superposition of indistinguishable probability amplitudes.

© 2003 Optical Society of America

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  1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777-780 (1935).
    [CrossRef]
  2. J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics (Long Island City, N.Y.) 1, 195-200 (1964).
  3. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
    [CrossRef] [PubMed]
  4. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
    [CrossRef]
  5. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
    [CrossRef]
  6. T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
    [CrossRef]
  7. D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
    [CrossRef] [PubMed]
  8. W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
    [CrossRef]
  9. S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
    [CrossRef]
  10. A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
    [CrossRef]
  11. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
    [CrossRef] [PubMed]
  12. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274-S282 (1999).
    [CrossRef]
  13. A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288-S297 (1999).
    [CrossRef]
  14. D. M. Greenberg, M. A. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today 46(8), 22-29 (1993).
    [CrossRef]
  15. 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]
  16. Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54-57 (1988).
    [CrossRef] [PubMed]
  17. M. A. Horne, A. Shimony, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62, 2209-2212 (1989).
    [CrossRef] [PubMed]
  18. J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495-2498 (1990). In this experiment, two tillable glass plates were used to adjust the relative phases in a recombination of two color photons at the beam splitter.
    [CrossRef] [PubMed]
  19. J. G. Rarity and P. R. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Phys. Rev. A 41, 5139-5146 (1990).
    [CrossRef] [PubMed]
  20. K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).
  21. K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
    [CrossRef] [PubMed]
  22. N. Lu¨tkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
    [CrossRef]

2001 (1)

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

2000 (4)

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef]

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

1999 (4)

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
[CrossRef]

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274-S282 (1999).
[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288-S297 (1999).
[CrossRef]

N. Lu¨tkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

1998 (1)

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

1995 (1)

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

1993 (2)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

D. M. Greenberg, M. A. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today 46(8), 22-29 (1993).
[CrossRef]

1990 (2)

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495-2498 (1990). In this experiment, two tillable glass plates were used to adjust the relative phases in a recombination of two color photons at the beam splitter.
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Phys. Rev. A 41, 5139-5146 (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]

1988 (1)

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54-57 (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]

1964 (1)

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics (Long Island City, N.Y.) 1, 195-200 (1964).

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Abouraddy, A. F.

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

Bell, J. S.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics (Long Island City, N.Y.) 1, 195-200 (1964).

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Berglund, A. J.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
[CrossRef]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Brendel, J.

W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef]

Calsamiglia, J.

N. Lu¨tkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Gatti, A.

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
[CrossRef]

Gisin, N.

W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef]

Greenberg, D. M.

D. M. Greenberg, M. A. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today 46(8), 22-29 (1993).
[CrossRef]

Hardy, L.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[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. A.

D. M. Greenberg, M. A. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today 46(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]

Jannewein, T.

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Kimble, H. J.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Kolobov, M. I.

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
[CrossRef]

Kwiat, P. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

Lu¨tkenhaus, N.

N. Lu¨tkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Lugiato, L. A.

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled images,” Phys. Rev. Lett. 83, 1763-1766 (1999).
[CrossRef]

Mandel, L.

L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274-S282 (1999).
[CrossRef]

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54-57 (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.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

Michler, M.

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

Naik, D. S.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

Ou, Z. Y.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Z. Y. Ou and L. Mandel, “Observation of spatial quantum beating with separated photodetectors,” Phys. Rev. Lett. 61, 54-57 (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]

Pan, J. W.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

Pereira, S. F.

S. F. Pereira, Z. Y. Ou, and H. J. Kimble, “Quantum communication with correlated nonclassical states,” Phys. Rev. A 62, 042311 (2000).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Peterson, C. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Popescu, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 80, 1121-1125 (1998).
[CrossRef]

Rarity, J. G.

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495-2498 (1990). In this experiment, two tillable glass plates were used to adjust the relative phases in a recombination of two color photons at the beam splitter.
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Phys. Rev. A 41, 5139-5146 (1990).
[CrossRef] [PubMed]

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777-780 (1935).
[CrossRef]

Saleh, B. E. A.

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

Sergienko, A. V.

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

Shimony, A.

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

Simon, C.

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

Suominen, K. A.

N. Lu¨tkenhaus, J. Calsamiglia, and K. A. Suominen, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295–3300 (1999).
[CrossRef]

Tapster, P. R.

J. G. Rarity and P. R. Tapster, “Two-color photons and nonlocality in fourth-order interference,” Phys. Rev. A 41, 5139-5146 (1990).
[CrossRef] [PubMed]

J. G. Rarity and P. R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum,” Phys. Rev. Lett. 64, 2495-2498 (1990). In this experiment, two tillable glass plates were used to adjust the relative phases in a recombination of two color photons at the beam splitter.
[CrossRef] [PubMed]

Teich, M. C.

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

Tittle, W.

W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef]

Weihs, G.

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

Weinfurter, H.

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

White, A. G.

D. S. Naik, C. G. Peterson, A. G. White, A. J. Berglund, and P. G. Kwiat, “Entangled state quantum cryptography: eavesdropping on the Ekert protocol,” Phys. Rev. Lett. 84, 4733-4736 (2000).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895-1899 (1993).
[CrossRef] [PubMed]

Zbinden, H.

W. Tittle, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef]

Zeilinger, A.

T. Jannewein, C. Simon, G. Weihs, H. Weinfurter, and A. Zeilinger, “Quantum cryptography with entangled photons,” Phys. Rev. Lett. 84, 4729-4732 (2000).
[CrossRef]

A. Zeilinger, “Experiment and the foundations of quantum physics,” Rev. Mod. Phys. 71, S288-S297 (1999).
[CrossRef]

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656-4659 (1996).
[CrossRef] [PubMed]

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

D. M. Greenberg, M. A. Horne, and A. Zeilinger, “Multiparticle interferometry and the superposition principle,” Phys. Today 46(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]

Zeillinger, A.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeillinger, “Experimental quantum teleportation,” Nature 390, 575-579 (1997).
[CrossRef]

Zukowski, M.

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Appl. Phys. B (1)

K. Mattle, M. Michler, H. Weinfurter, A. Zeilinger, and M. Zukowski, “Non-classical statistics at multiport beam splitters,” Appl. Phys. B 60, S111-S117 (1995).

Nature (1)

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[CrossRef]

Phys. Rev. (1)

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[CrossRef]

Phys. Rev. A (3)

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[CrossRef]

Phys. Rev. Lett. (12)

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Phys. Today (1)

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[CrossRef]

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[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the experiment to observe quantum interference effects between two photons with nonoverlapping frequency components. The parametric downconverter (PDC) served as a nonlinear crystal in which spontaneous parametric downconversion was generated in a noncollinear frequency-nondegenerate configuration (ω0=ω1+ω2, where ω0, ω1, and ω2 represent the frequencies of pump, signal, and idler photons, respectively).

Fig. 2
Fig. 2

Schematic diagram of the experimental setup. The noncollinear frequency-nondegenerate type 1 phase-matched SPDC provides frequency-entangled photon pairs. Beam splitter BS1 introduces a path-length difference between ω1 and ω2. M1, M2, mirrors.

Fig. 3
Fig. 3

Coincidence counts as a function of beam splitter position or of the relative time delay between two photons: Filled circles represent experimental results with detector pairs (a) D1 and D2, (b) D1 and D2, and (c) D1 and D2 when there is an additional phase shift +π/2 between two amplitudes. Solid curves, theoretical results based on the probability of joint detection by the two detectors; and dotted curves, theoretical results when the two photons are at the same frequencies, which are a typical Hong–Ou–Mandel coincidence dip and peak.

Equations (8)

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T(ω1i)-T(ω2s)D1,D2
R(ω1s)-R(ω2i)D1,D2
T(ω1i)-R(ω2s)D1,D2,
R(ω1s)-T(ω2i)D1,D2.
|Ψω1,ω2=(1/2)(|ω1s|ω2i+eiθ|ω2s|ω1i),
PD1,D2(δτ)=PD1,D2(δτ)=1/4-1/4 exp(-1/2σ2δτ2)cos(ω1-ω2)δτ,
PD1,D2(δτ)=PD1,D2(δτ)=1/4+1/4 exp(-1/2σ2δτ2)cos(ω1-ω2)δτ,
PD1,D2(δτ)=1/4+1/4 exp(-1/2σ2δτ2)sin(ω1-ω2)δτ.

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