Abstract

We present a consistent multimode theory that describes the coupling of single photons generated by collinear Type-I parametric down-conversion into single-mode optical fibers. We have calculated an analytic expression for the fiber diameter which maximizes the pair photon count rate. For a given focal length and wavelength, a lower limit of the fiber diameter for satisfactory coupling is obtained.

© 2004 Optical Society of America

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  1. D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
    [Crossref]
  2. Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
    [Crossref] [PubMed]
  3. C. K. Hong and L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
    [Crossref] [PubMed]
  4. 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]
  5. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
    [Crossref] [PubMed]
  6. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993).
    [Crossref] [PubMed]
  7. S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
    [Crossref]
  8. L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
    [Crossref] [PubMed]
  9. D. Bouwmeester, J-W Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
    [Crossref]
  10. J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
    [Crossref]
  11. D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
    [Crossref]
  12. A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
    [Crossref] [PubMed]
  13. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
    [Crossref] [PubMed]
  14. 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]
  15. S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, “Coupling efficiencies in single photon on-demand sources,” ArXiv:quant-ph/0311099 (2003).
  16. F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
    [Crossref]
  17. E. R. Pike and S. Sarkar, The Quantum Theory of Radiation, Oxford University Press (1995).
  18. R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum semiclass. Opt. 1, 588–597 (1999).
    [Crossref]
  19. A. Yariv, Optical Electronics in Modern Communications (5th Edition, Oxford Series in Electrical and Computer Engineering).
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), chaps. 7 and 8.
  21. Q. Cao and S. Chi, “Approximate Analytical Description for Fundamental-Mode Fields of Graded-Index Fibers: Beyond the Gaussian Approximation,” J. Lightwave Technol. 19, 54- (2001).
    [Crossref]
  22. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  23. A. L. Migdall, D. Branning, and S. Castelleto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A,  66, 053805-1–053805-4 (2002).
    [Crossref]

2003 (1)

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

2002 (1)

A. L. Migdall, D. Branning, and S. Castelleto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A,  66, 053805-1–053805-4 (2002).
[Crossref]

2001 (3)

Q. Cao and S. Chi, “Approximate Analytical Description for Fundamental-Mode Fields of Graded-Index Fibers: Beyond the Gaussian Approximation,” J. Lightwave Technol. 19, 54- (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

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]

2000 (1)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
[Crossref] [PubMed]

1999 (2)

R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum semiclass. Opt. 1, 588–597 (1999).
[Crossref]

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

1998 (2)

J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

1997 (1)

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

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

1994 (1)

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref] [PubMed]

1993 (1)

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

1992 (1)

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
[Crossref] [PubMed]

1990 (1)

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[Crossref] [PubMed]

1988 (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]

1985 (1)

C. K. Hong and L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref] [PubMed]

1970 (1)

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Andrews, R.

R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum semiclass. Opt. 1, 588–597 (1999).
[Crossref]

Bennett, C. H.

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

Bouwmeester, D.

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

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

Bovino, F. A.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Branning, D.

A. L. Migdall, D. Branning, and S. Castelleto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A,  66, 053805-1–053805-4 (2002).
[Crossref]

Brassard, G.

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

Braunstein, S. L.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[Crossref]

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
[Crossref] [PubMed]

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

Cao, Q.

Q. Cao and S. Chi, “Approximate Analytical Description for Fundamental-Mode Fields of Graded-Index Fibers: Beyond the Gaussian Approximation,” J. Lightwave Technol. 19, 54- (2001).
[Crossref]

Castagnoli, G.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Castelleto, S.

A. L. Migdall, D. Branning, and S. Castelleto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A,  66, 053805-1–053805-4 (2002).
[Crossref]

Castelletto, S.

S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, “Coupling efficiencies in single photon on-demand sources,” ArXiv:quant-ph/0311099 (2003).

Chi, S.

Q. Cao and S. Chi, “Approximate Analytical Description for Fundamental-Mode Fields of Graded-Index Fibers: Beyond the Gaussian Approximation,” J. Lightwave Technol. 19, 54- (2001).
[Crossref]

Colla, A. M.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Crepeau, C.

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

Daniell, M.

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

Degiovanni, I. P.

S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, “Coupling efficiencies in single photon on-demand sources,” ArXiv:quant-ph/0311099 (2003).

Eibl, M.

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

Ekert, A. K.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
[Crossref] [PubMed]

Gisin, N.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
[Crossref] [PubMed]

Giuseppe, G. D.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), chaps. 7 and 8.

Hong, C. K.

C. K. Hong and L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref] [PubMed]

Jozsa, R.

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

Kimble, H. J.

S. L. Braunstein and H. J. Kimble, “Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).
[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. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Mandel, L.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[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]

C. K. Hong and L. Mandel, “Theory of parametric frequency down-conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[Crossref] [PubMed]

Mattle, K.

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

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Migdall, A.

S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, “Coupling efficiencies in single photon on-demand sources,” ArXiv:quant-ph/0311099 (2003).

Migdall, A. L.

A. L. Migdall, D. Branning, and S. Castelleto, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A,  66, 053805-1–053805-4 (2002).
[Crossref]

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]

Ou, Z. Y.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[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]

Palma, G. M.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
[Crossref] [PubMed]

Pan, J-W

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

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

Peres, A.

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

Pike, E. R.

R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum semiclass. Opt. 1, 588–597 (1999).
[Crossref]

E. R. Pike and S. Sarkar, The Quantum Theory of Radiation, Oxford University Press (1995).

Rarity, J. G.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
[Crossref] [PubMed]

Sarkar, S.

E. R. Pike and S. Sarkar, The Quantum Theory of Radiation, Oxford University Press (1995).

Sarkar, Sarben

R. Andrews, E. R. Pike, and Sarben Sarkar, “Photon correlations and interference in type-I optical parametric down-conversion,” J. Opt. B: Quantum semiclass. Opt. 1, 588–597 (1999).
[Crossref]

Sergienko, A. V.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Shih, Y. H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Tapster, P. R.

A. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on two-photon interferometry,” Phys. Rev. Lett. 69 (9), 1293–1295 (1992).
[Crossref] [PubMed]

Tittel, W.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
[Crossref] [PubMed]

Vaidman, L.

L. Vaidman, “Teleportation of quantum states,” Phys. Rev. A 49, 1473–1476 (1994).
[Crossref] [PubMed]

Varisco, P.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. D. Giuseppe, and A. V. Sergienko, “Effective fiber coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Wang, L. J.

Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, “Experiment on nonclassical fourth-order interference,” Phys. Rev. A 42, 2957–2965 (1990).
[Crossref] [PubMed]

Ware, M.

S. Castelletto, I. P. Degiovanni, M. Ware, and A. Migdall, “Coupling efficiencies in single photon on-demand sources,” ArXiv:quant-ph/0311099 (2003).

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of simultaneity in parametric production of optical photon pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
[Crossref]

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]

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

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

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Wootters, W. K.

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

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (5th Edition, Oxford Series in Electrical and Computer Engineering).

Zbinden, H.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Quantum cryptography using entangled photons in energy-time Bell states,” Phys. Rev. Lett. 84 (20), 4737–4740, 2000.
[Crossref] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[Crossref] [PubMed]

D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345–1349 (1999).
[Crossref]

J-W Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping : Entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998).
[Crossref]

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

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Zou, X. Y.

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Figures (1)

Fig. 1.
Fig. 1.

Schematic of the experimental setup to determine pair photon coupling in fibers

Equations (18)

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A ( 2 ) = E H + ( r 1 , t 1 ) E H + ( r 2 , t 2 )
d 3 r 3 d 3 k 1 d 3 k 2 U k 1 λ 1 * ( r 3 ) U k 2 λ 2 * ( r 3 ) U k 0 λ 0 ( r 3 ) f p ( r 3 ) ( ω k 0 2 ε 0 ) 1 2 ( ω k 1 2 ε 0 ) 1 2 ( ω k 2 2 ε 0 ) 1 2
× α k 0 , 0 E I ( + ) ( r 2 , t 2 ) E I ( + ) ( r 1 , t 1 ) ω k 0 , k 1 , k 2 δ ( ω k 1 ω k 2 ω k 0 )
E + ( r , t ) = i λ λ d 3 k d 3 k ( ω k 2 ε 0 ) 1 2 ε k λ β k λ , k λ U k λ f ( r ) e i ω t a k λ
β k λ k λ = d x d y U k λ in ( x , y ) U k λ f * ( x , y )
d 3 k 1 d 3 k 2 f ˜ p ( k 1 t + k 2 t ) sin c ( Δ k 1 z k 2 z d 2 ) β k 1 λ 1 β k 2 λ 2 U f ( r 1 ) U f ( r 2 )
× ( ω k 1 2 ε 0 ) 1 2 ( ω k 2 2 ε 0 ) 1 2 e i ω k 1 t 1 e i ω k 2 t 2 δ ( ω k 0 ω k 1 ω k 2 )
f ( r t ) exp ( x 2 + y 2 w p )
f ˜ p ( k 1 t + k 2 t ) exp ( 1 4 w p 2 v 2 ( ω k 1 ω k 2 ) 2 sin 2 θ * )
U k λ in ( x , y ) = 1 i k d e i k ( d + d ) e i k 2 d ( x 2 + y 2 ) 0 2 π 0 R r d θ d r ( e i ( k 2 d k 2 f ) r 2 e i k ( x cos θ d + y sin θ d ) r )
U f ( x , y ) = 1 w 0 π exp ( x 2 + y 2 2 w 0 2 )
β k λ w 0 2 d 2 + i k w 0 4 d k d w 0 ( d 2 + k 2 w 0 4 ) ( 1 e ( A k + i B k ) R 2 ) ( A k + i B k )
A k = k 2 w 0 2 2 ( d 2 + k 2 w 0 4 )
B k = ( 1 2 d 1 2 f ) k k 3 w 0 4 2 d ( d 2 + k 2 w 0 4 )
A ( 2 ) e i τ x x 2 Δ 2 ( 1 e ( a + b x ) ) 2 d x
a = ( k * 2 w 0 2 2 f 2 i k * 3 w 0 4 2 f 3 ) R 2
b = ( k * w 0 2 n g c f 2 i 3 2 n g k * 2 w 0 4 2 c f 3 ) R 2
C ( 1 4 e y + 6 e 2 y 4 e 3 y + e 4 y )

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