Abstract

A theoretical investigation of the performance of single-mode coupled spontaneous parametric downconversion sources is proposed, which only requires very few assumptions of practical interest: quasi-degenerate collinear generation and narrow bandwidth obtained through spectral filtering. Other assumptions, such as pump-beam spatial and temporal envelopes, target single-mode profile and size, and nonlinear susceptibility distribution, are only taken into account in the final step of the computation, thus making the theory general and flexible. Figures of merit for performance include absolute coupled brightness and conditional coupling efficiency. Their optimization is investigated using functions that only depend on dimensionless parameters, so that the results provide the best experimental configuration for a whole range of design choices (e.g., crystal length, pump power, etc.). A particular application of the theory is validated by an experimental optimization obtained under compatible assumptions. A comparison with other works and proposals for numerically implementing the theory under less stringent assumptions is also provided.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quantum Inf. Comput. 1, 3–56 (2001).
  2. S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
    [CrossRef]
  3. N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
    [CrossRef]
  4. N. Gisin and R. T. Thew, “Quantum communication technology,” Electron. Lett. 46, 965–U20 (2010).
    [CrossRef]
  5. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
    [CrossRef]
  6. J. H. Shapiro, “Architectures for long-distance quantum teleportation,” New J. Phys. 4, 47 (2002).
    [CrossRef]
  7. C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
    [CrossRef]
  8. F. Wong, J. Shapiro, and T. Kim, “Efficient generation of polarization-entangled photons in a nonlinear crystal,” Laser Phys. 16, 1517–1524 (2006).
    [CrossRef]
  9. 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]
  10. T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
    [CrossRef]
  11. J. Altepeter, E. Jeffrey, and P. Kwiat, “Phase-compensated ultra-bright source of entangled photons,” Opt. Express 13, 8951–8959 (2005).
    [CrossRef]
  12. B. Shi and A. Tomita, “Highly efficient generation of pulsed photon pairs with bulk periodically poled potassium titanyl phosphate,” J. Opt. Soc. Am. B 21, 2081–2084 (2004).
    [CrossRef]
  13. H. Guillet de Chatellus, A. Sergienko, B. Saleh, M. Teich, and G. Di Giuseppe, “Non-collinear and non-degenerate polarization-entangled photon generation via concurrent type-I parametric downconversion in ppln,” Opt. Express 14, 10060–10072 (2006).
    [CrossRef]
  14. M. Fiorentino, C. Kuklewicz, and F. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
    [CrossRef]
  15. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
    [CrossRef]
  16. O. Kuzucu and F. N. C. Wong, “Pulsed sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
    [CrossRef]
  17. S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
    [CrossRef]
  18. J. L. Smirr, R. Frey, E. Diamanti, R. Alléaume, and I. Zaquine, “Intrinsic limitations to the quality of pulsed spontaneous parametric downconversion sources for quantum information applications,” J. Opt. Soc. Am. B 28, 832–841 (2011).
    [CrossRef]
  19. A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
    [CrossRef]
  20. C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
    [CrossRef]
  21. T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
    [CrossRef]
  22. E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
    [CrossRef]
  23. C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
    [CrossRef]
  24. W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
    [CrossRef]
  25. C. K. Hong and L. Mandel, “Theory of parametric frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
    [CrossRef]
  26. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
    [CrossRef]
  27. L. Mandel, “Quantum effects in one-photon and two-photon interference,” Rev. Mod. Phys. 71, S274–S282 (1999).
    [CrossRef]
  28. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
    [CrossRef]
  29. T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
    [CrossRef]
  30. T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
    [CrossRef]
  31. A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
    [CrossRef]
  32. 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]
  33. 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]
  34. S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
    [CrossRef]
  35. S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
    [CrossRef]
  36. D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72, 062301 (2005).
    [CrossRef]
  37. A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
    [CrossRef]
  38. M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: geometry and absolute brightness,” Phys. Rev. A 79, 043835 (2009).
    [CrossRef]
  39. R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010).
    [CrossRef]
  40. R. Boyd, Nonlinear Optics (Academic, 2008).
  41. A. Yariv, Quantum Electronics (Wiley, 1989).
  42. M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
    [CrossRef]
  43. M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009).
    [CrossRef]
  44. J. Garrison and R. Chiao, Quantum Optics (Oxford University, 2008).
  45. J. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569(2009).
    [CrossRef]
  46. The natural phase matching bandwidth has no influence on the results that follow if it is much larger than the pump linewidth.
  47. J. L. Smirr, S. Guilbaud, J. Ghalbouni, R. Frey, E. Diamanti, R. Alléaume, and I. Zaquine, “Simple performance evaluation of pulsed spontaneous parametric down-conversion sources for quantum communications,” Opt. Express 19, 616–627 (2011).
    [CrossRef]
  48. J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
    [CrossRef]
  49. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [CrossRef]
  50. Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
    [CrossRef]
  51. J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.
  52. J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
    [CrossRef]
  53. L. Mandel, “Configuration-space photon number operators in quantum optics,” Phys. Rev. 144, 1071–1077 (1966).
    [CrossRef]
  54. A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

2012 (1)

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

2011 (4)

J. L. Smirr, S. Guilbaud, J. Ghalbouni, R. Frey, E. Diamanti, R. Alléaume, and I. Zaquine, “Simple performance evaluation of pulsed spontaneous parametric down-conversion sources for quantum communications,” Opt. Express 19, 616–627 (2011).
[CrossRef]

J. L. Smirr, R. Frey, E. Diamanti, R. Alléaume, and I. Zaquine, “Intrinsic limitations to the quality of pulsed spontaneous parametric downconversion sources for quantum information applications,” J. Opt. Soc. Am. B 28, 832–841 (2011).
[CrossRef]

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

2010 (6)

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
[CrossRef]

N. Gisin and R. T. Thew, “Quantum communication technology,” Electron. Lett. 46, 965–U20 (2010).
[CrossRef]

R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010).
[CrossRef]

Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
[CrossRef]

2009 (4)

M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: geometry and absolute brightness,” Phys. Rev. A 79, 043835 (2009).
[CrossRef]

M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009).
[CrossRef]

J. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569(2009).
[CrossRef]

A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

2008 (2)

O. Kuzucu and F. N. C. Wong, “Pulsed sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[CrossRef]

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[CrossRef]

2007 (5)

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
[CrossRef]

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

2006 (2)

2005 (4)

M. Fiorentino, C. Kuklewicz, and F. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[CrossRef]

J. Altepeter, E. Jeffrey, and P. Kwiat, “Phase-compensated ultra-bright source of entangled photons,” Opt. Express 13, 8951–8959 (2005).
[CrossRef]

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72, 062301 (2005).
[CrossRef]

2004 (3)

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

B. Shi and A. Tomita, “Highly efficient generation of pulsed photon pairs with bulk periodically poled potassium titanyl phosphate,” J. Opt. Soc. Am. B 21, 2081–2084 (2004).
[CrossRef]

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[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)

J. H. Shapiro, “Architectures for long-distance quantum teleportation,” New J. Phys. 4, 47 (2002).
[CrossRef]

2001 (2)

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quantum Inf. Comput. 1, 3–56 (2001).

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]

1999 (1)

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

1997 (1)

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[CrossRef]

1996 (1)

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

1995 (1)

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]

1994 (2)

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[CrossRef]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

1991 (2)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
[CrossRef]

1987 (1)

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

1985 (1)

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

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

1966 (1)

L. Mandel, “Configuration-space photon number operators in quantum optics,” Phys. Rev. 144, 1071–1077 (1966).
[CrossRef]

1961 (1)

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Afzelius, M.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

Alléaume, R.

Altepeter, J.

Appel, J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Bennink, R. S.

R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010).
[CrossRef]

Berntsen, J.

J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
[CrossRef]

Bonarota, M.

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[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]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, 2008).

Brukner, C.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Bussières, F.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[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]

Castelletto, S.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

Chanelière, T.

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

Chiao, R.

J. Garrison and R. Chiao, Quantum Optics (Oxford University, 2008).

Clarkson, W. A.

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.

Clausen, C.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[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]

de Chatellus, H. Guillet

de la Giroday, A. Boyer

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

de Riedmatten, H.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

Degiovanni, I.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

Degiovanni, I. P.

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

Dewhurst, S. J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Di Giuseppe, G.

Diamanti, E.

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

Espelid, T. O.

J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
[CrossRef]

Fedrizzi, A.

Fiorentino, M.

M. Fiorentino, C. Kuklewicz, and F. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[CrossRef]

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

Forbes, A.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Frey, R.

Furno, G.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

Galvez, E. J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Garrison, J.

J. Garrison and R. Chiao, Quantum Optics (Oxford University, 2008).

Genz, A.

J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
[CrossRef]

George, M.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Ghalbouni, J.

Ghatak, A.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

Ghosh, R.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

Giovannini, D.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Gisin, N.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

N. Gisin and R. T. Thew, “Quantum communication technology,” Electron. Lett. 46, 965–U20 (2010).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

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]

Godbout, N.

S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
[CrossRef]

Gouët, J.-L. L.

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

Gröblacher, S.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Guilbaud, S.

Hayes, J. R.

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.

Hentschel, M.

Herbst, T.

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]

Hu, C. Y.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Hübel, H.

Jeffrey, E.

Jelezko, F.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Jennewein, T.

Jeronimo-Moreno, Y.

Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
[CrossRef]

Jin, J.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Joobeur, A.

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[CrossRef]

Kaltenbaek, R.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Keller, T. E.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[CrossRef]

Kim, H.

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

Kim, J.

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

Kim, J. W.

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.

Kim, T.

F. Wong, J. Shapiro, and T. Kim, “Efficient generation of polarization-entangled photons in a nonlinear crystal,” Laser Phys. 16, 1517–1524 (2006).
[CrossRef]

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Klyshko, D. N.

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

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

Kröll, S.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Kuklewicz, C.

Kuklewicz, C. E.

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

Kurtsiefer, C.

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[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]

Kuzucu, O.

O. Kuzucu and F. N. C. Wong, “Pulsed sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[CrossRef]

Kwiat, P.

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]

Lacroix, S.

S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
[CrossRef]

Lamas-Linares, A.

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[CrossRef]

Ling, A.

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[CrossRef]

Ljunggren, D.

D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72, 062301 (2005).
[CrossRef]

Louisell, W. H.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Lvovsky, A.

A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

Mackenzie, J. I.

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.

Mandel, L.

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

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

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

L. Mandel, “Configuration-space photon number operators in quantum optics,” Phys. Rev. 144, 1071–1077 (1966).
[CrossRef]

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]

McLaren, M. G.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Messin, G.

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

Migdall, A.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

Mitchell, M. W.

M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: geometry and absolute brightness,” Phys. Rev. A 79, 043835 (2009).
[CrossRef]

Müller, J. H.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Noh, T. G.

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

Nunn, J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[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]

Oblak, D.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Padgett, M. J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Paterek, T.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Pittman, T. B.

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

Polzik, E. S.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Poppe, A.

Rarity, J. G.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Ricken, R.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Rodriguez-Benavides, S.

Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
[CrossRef]

Romero, J.

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

Rosenfeld, W.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Rubin, M. H.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[CrossRef]

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

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

Ruggiero, J.

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

Saglamyurek, E.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Saleh, B.

Saleh, B. E. A.

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[CrossRef]

Sanders, B.

A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

Sangouard, N.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

Schettini, V.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

Sergienko, A.

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]

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

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

Shapiro, J.

J. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569(2009).
[CrossRef]

F. Wong, J. Shapiro, and T. Kim, “Efficient generation of polarization-entangled photons in a nonlinear crystal,” Laser Phys. 16, 1517–1524 (2006).
[CrossRef]

Shapiro, J. H.

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

J. H. Shapiro, “Architectures for long-distance quantum teleportation,” New J. Phys. 4, 47 (2002).
[CrossRef]

Shi, B.

Shields, A. J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

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]

Shih, Y. H.

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

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

Siegman, A. E.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Simon, C.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

Sinclair, N.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Sköld, N.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Slater, J.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Smirr, J. L.

Sohler, W.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

Stevenson, R. M.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Strekalov, D. V.

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

Teich, M.

Teich, M. C.

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[CrossRef]

Tengner, M.

D. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72, 062301 (2005).
[CrossRef]

Thew, R.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

Thew, R. T.

N. Gisin and R. T. Thew, “Quantum communication technology,” Electron. Lett. 46, 965–U20 (2010).
[CrossRef]

Thyagarajan, K.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

Tittel, W.

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quantum Inf. Comput. 1, 3–56 (2001).

Tomita, A.

U’Ren, A. B.

Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
[CrossRef]

Usmani, I.

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

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]

Virally, S.

S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
[CrossRef]

Walmsley, I. A.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Ware, M.

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

Weber, M. C.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Weihs, G.

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quantum Inf. Comput. 1, 3–56 (2001).

Weinfurter, H.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[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]

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]

Wong, F.

F. Wong, J. Shapiro, and T. Kim, “Efficient generation of polarization-entangled photons in a nonlinear crystal,” Laser Phys. 16, 1517–1524 (2006).
[CrossRef]

M. Fiorentino, C. Kuklewicz, and F. Wong, “Source of polarization entanglement in a single periodically poled KTiOPO4 crystal with overlapping emission cones,” Opt. Express 13, 127–135 (2005).
[CrossRef]

Wong, F. N. C.

O. Kuzucu and F. N. C. Wong, “Pulsed sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[CrossRef]

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

Wrachtrup, J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Yariv, A.

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, 1989).

Young, R. J.

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

Zaquine, I.

Zbinden, H.

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[CrossRef]

Ždotukowski, M.

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

Zeilinger, A.

M. Hentschel, H. Hübel, A. Poppe, and A. Zeilinger, “Three-color Sagnac source of polarization-entangled photon pairs,” Opt. Express 17, 23153–23159 (2009).
[CrossRef]

A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15, 15377–15386 (2007).
[CrossRef]

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[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]

Zyung, T.

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

ACM Trans. Math. Softw. (1)

J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Trans. Math. Softw. 17, 437–451 (1991).
[CrossRef]

Appl. Phys. Lett. (1)

T. G. Noh, H. Kim, T. Zyung, and J. Kim, “Efficient source of high purity polarization-entangled photon pairs in the 1550 nm telecommunication band,” Appl. Phys. Lett. 90, 011116 (2007).
[CrossRef]

Electron. Lett. (1)

N. Gisin and R. T. Thew, “Quantum communication technology,” Electron. Lett. 46, 965–U20 (2010).
[CrossRef]

Eur. Phys. J. D (1)

C. Simon, M. Afzelius, J. Appel, A. Boyer de la Giroday, S. J. Dewhurst, N. Gisin, C. Y. Hu, F. Jelezko, S. Kröll, J. H. Müller, J. Nunn, E. S. Polzik, J. G. Rarity, H. De Riedmatten, W. Rosenfeld, A. J. Shields, N. Sköld, R. M. Stevenson, R. Thew, I. A. Walmsley, M. C. Weber, H. Weinfurter, J. Wrachtrup, and R. J. Young, “Quantum memories,” Eur. Phys. J. D 58, 1–22 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron. 15, 1547–1569(2009).
[CrossRef]

IEEE Trans. Instr. Meas. (1)

S. Castelletto, I. Degiovanni, G. Furno, V. Schettini, A. Migdall, and M. Ware, “Two-photon mode preparation and matching efficiency: definition, measurement, and optimization,” IEEE Trans. Instr. Meas. 54, 890–893 (2005).
[CrossRef]

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused Gaussian light beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

J. Opt. (1)

J. Romero, D. Giovannini, M. G. McLaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Phys. (2)

F. Wong, J. Shapiro, and T. Kim, “Efficient generation of polarization-entangled photons in a nonlinear crystal,” Laser Phys. 16, 1517–1524 (2006).
[CrossRef]

Y. Jeronimo-Moreno, S. Rodriguez-Benavides, and A. B. U’Ren, “Theory of cavity-enhanced spontaneous parametric downconversion,” Laser Phys. 20, 1221–1233 (2010).
[CrossRef]

Nat. Photonics (2)

A. Lvovsky, B. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

N. Gisin and R. Thew, “Quantum communication,” Nat. Photonics 1, 165–171 (2007).
[CrossRef]

Nature (3)

E. Saglamyurek, N. Sinclair, J. Jin, J. Slater, D. Oblak, F. Bussières, M. George, R. Ricken, W. Sohler, and W. Tittel, “Broadband waveguide quantum memory for entangled photons,” Nature 469, 512 (2011).
[CrossRef]

C. Clausen, I. Usmani, F. Bussières, N. Sangouard, M. Afzelius, H. de Riedmatten, and N. Gisin, “Quantum storage of photonic entanglement in a crystal,” Nature 469, 508 (2011).
[CrossRef]

S. Gröblacher, T. Paterek, R. Kaltenbaek, C. Brukner, M. Ždotukowski, M. Aspelmeyer, and A. Zeilinger, “An experimental test of non-local realism,” Nature 446, 871–875 (2007).
[CrossRef]

New J. Phys. (3)

J. H. Shapiro, “Architectures for long-distance quantum teleportation,” New J. Phys. 4, 47 (2002).
[CrossRef]

T. Chanelière, J. Ruggiero, M. Bonarota, M. Afzelius, and J.-L. L. Gouët, “Efficient light storage in a crystal using an atomic frequency comb,” New J. Phys. 12, 023025 (2010).
[CrossRef]

S. Castelletto, I. P. Degiovanni, A. Migdall, and M. Ware, “On the measurement of two-photon single-mode coupling efficiency in parametric down-conversion photon sources,” New J. Phys. 6, 87 (2004).
[CrossRef]

Opt. Commun. (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]

Opt. Express (6)

Phys. Rev. (2)

L. Mandel, “Configuration-space photon number operators in quantum optics,” Phys. Rev. 144, 1071–1077 (1966).
[CrossRef]

W. H. Louisell, A. Yariv, and A. E. Siegman, “Quantum fluctuations and noise in parametric processes,” Phys. Rev. 124, 1646–1654 (1961).
[CrossRef]

Phys. Rev. A (13)

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

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[CrossRef]

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[CrossRef]

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

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatio-temporal coherence properties of entangled light beams generated by parametric down-conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[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. Ljunggren and M. Tengner, “Optimal focusing for maximal collection of entangled narrow-band photon pairs into single-mode fibers,” Phys. Rev. A 72, 062301 (2005).
[CrossRef]

A. Ling, A. Lamas-Linares, and C. Kurtsiefer, “Absolute emission rates of spontaneous parametric down-conversion into single transverse gaussian modes,” Phys. Rev. A 77, 043834 (2008).
[CrossRef]

M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: geometry and absolute brightness,” Phys. Rev. A 79, 043835 (2009).
[CrossRef]

R. S. Bennink, “Optimal collinear gaussian beams for spontaneous parametric down-conversion,” Phys. Rev. A 81, 053805 (2010).
[CrossRef]

O. Kuzucu and F. N. C. Wong, “Pulsed sagnac source of narrow-band polarization-entangled photons,” Phys. Rev. A 77, 032314 (2008).
[CrossRef]

S. Virally, S. Lacroix, and N. Godbout, “Limits of heralded single-photon sources based on parametric photon-pair generation,” Phys. Rev. A 81, 013808 (2010).
[CrossRef]

M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A 69, 041801 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, “Quantum repeaters with photon pair sources and multi-mode memories,” Phys. Rev. Lett. 98, 190503 (2007).
[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]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).
[CrossRef]

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[CrossRef]

Quantum Inf. Comput. (1)

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quantum Inf. Comput. 1, 3–56 (2001).

Rev. Mod. Phys. (1)

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

Other (6)

R. Boyd, Nonlinear Optics (Academic, 2008).

A. Yariv, Quantum Electronics (Wiley, 1989).

J. Garrison and R. Chiao, Quantum Optics (Oxford University, 2008).

J. W. Kim, J. I. Mackenzie, J. R. Hayes, and W. A. Clarkson, “High-power fibre-laser-pumped Er:YAG laser with ‘top-hat’ output beam,” in Proceedings of 2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference (CLEO EUROPE/EQEC), Munich, Germany, 2011.

A. Ghatak and K. Thyagarajan, Introduction to Fiber Optics (Cambridge University, 1998).

The natural phase matching bandwidth has no influence on the results that follow if it is much larger than the pump linewidth.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

General configuration considered in the theoretical framework: a nonlinear crystal is pumped by a beam of arbitrary temporal and spatial profiles. The photon pairs produced through SPDC are spectrally filtered and coupled to a single spatial mode, before being split toward channels A and B .

Fig. 2.
Fig. 2.

Effect of the relative Gaussian pump linewidth δ on the spectral transmission factor Ω 2 / Δ ω F for Gaussian spectral filters.

Fig. 3.
Fig. 3.

Optimization of the spatial filtering factor K 2 / ( k p 0 L ) with respect to the normalized target mode waist α and the longitudinal phase mismatch φ 0 for three values of the focusing parameter ξ : ξ = 0.1 (a), ξ = 1 (b), and ξ = 10 (c).

Fig. 4.
Fig. 4.

Maximal value of the spatial filtering factor K 2 / ( k p 0 L ) (a) and associated optimal values of the normalized target mode waist α (b) and the longitudinal phase mismatch φ 0 (c), for various values of the focusing parameter ξ .

Fig. 5.
Fig. 5.

Pair coupling efficiency Γ 2 = P 2 / ψ 0 | ψ 0 (a) compared to the pair production probability (b) for various values of the focusing parameter ξ . P 0 is evaluated for the longitudinal phase mismatch φ 0 that maximizes Γ 2 .

Fig. 6.
Fig. 6.

Optimization of the conditional coupling efficiency Γ 2 | 1 with respect to the normalized target mode waist α and the longitudinal phase mismatch φ 0 for three values of the focusing parameter ξ : (a)  ξ = 0.1 , (b)  ξ = 1 , and (c)  ξ = 10 .

Fig. 7.
Fig. 7.

Experimental setup: a pulsed pump laser at wavelength 782 nm is focused in a PPLN crystal with a lens L p of focal length f p . Downconverted photons at 1564 nm are coupled into a single-mode fiber through an optical system composed of lenses L c and L i of respective focal lengths f c and f i . Spectral filtering is performed via a DWDM add-drop filter of bandwidth 75 GHz, and photons are split with 50% efficiency toward detectors A and B using a balanced fibered coupler.

Fig. 8.
Fig. 8.

(a) Measured conditional coupling efficiency Γ 2 | 1 plotted for four focal lengths f p = 150 , 100, 75, 50 mm, as a function of the focusing parameter ξ = 0.44 , 0.76, 1.05, 2.70. (b) Corresponding experimental (circles) and calculated (solid curve) values of the normalized target mode waist α for each value of Γ 2 | 1 .

Fig. 9.
Fig. 9.

Conditional coupling efficiency Γ 2 | 1 : experimental values normalized to the measured maximum (represented with their error bars) and theoretical values (solid curve), plotted as a function of the normalized target mode waist α , for two different focusing parameters: ξ = 0.76 (a) and ξ = 2.7 (b). The corresponding raw data are given in Appendix B.

Tables (1)

Tables Icon

Table 1. Raw Single Counts ( N A , N B ) and Coincidences ( N C ) Per Second, Net Single-Count Probabilities ( P A , P B ), and True Coincidence Probability P A B a

Equations (69)

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

E ^ s , i ( + ) ( r , t ) = s , i ε⃗ s , i a ^ s , i A ( s , i ) e i ( k s , i · r ω s , i t ) ,
A ( ) = i ω 2 ϵ 0 V n 2 ( k ) .
H ^ ( t ) = ϵ 0 d 3 r E p ( + ) ( r , t ) χ ¯ ¯ ( 2 ) ( r ) E ^ s ( ) ( r , t ) E ^ i ( ) ( r , t ) + H.c. ,
E p ( + ) ( ρ , z , t ) = ε⃗ x C p T p ( t z v p ) S p ( ρ , z ) e i ( k p 0 z ω p 0 t ) .
| ψ ( t ) = 1 i t d t H ^ ( t ) | 0 .
ε⃗ x χ ¯ ¯ ( 2 ) ( r ) ε⃗ s ε⃗ i = χ ( s , i ) · R ( r ) .
| ψ = ϵ 0 i s , i χ ( s , i ) A ( s ) A ( i ) d 3 r e i ( k s + k i ) · r × R ( r ) Ĕ p ( + ) ( r , ω s + ω i ) a ^ s a ^ i | 0 .
| ψ = s , i γ 0 ( s , i ) a ^ s a ^ i | 0 ,
γ 0 ( s , i ) = ϵ 0 i χ ( s , i ) A ( s ) A ( i ) × * Ĕ p ( + ) ( k s + k i , ω s + ω i ) ,
p ( κ , z ) = p ( κ , 0 ) e i | κ | 2 2 k p 0 z ,
Ĕ p ( + ) ( κ , k z , ω ) = C p p ( ω ω p 0 ) p ( κ , 0 ) × 2 π δ ( k z k p 0 ω ω p 0 v p + | κ | 2 2 k p 0 ) .
R ( z ) = rect ( z / L ) × m R m e i 2 π m z L ,
( k z ) = m R m sinc ( k z + 2 π m / L ) .
γ 0 m ( s , i ) = ϵ 0 i R m χ ( s , i ) A ( s ) A ( i ) × C p p ( ω s + ω i ω p 0 ) p ( κ s + κ i , 0 ) × L sinc ( Δ K m ( k s + k i , ω s + ω i ) L 2 ) ,
Δ K m ( k , ω ) = k z k p 0 ω ω p 0 v p + | κ | 2 2 k p 0 + m 2 π L .
| ψ 0 = s , i γ 0 ( s , i ) γ T ( 2 ) ( s , i ) a ^ s a ^ i | 0 ignored one and zero-photon terms ,
γ T ( 2 ) ( s , i ) = F ( ω s ω s 0 , κ s ) F ( ω i ω i 0 , κ i ) ,
| ψ 2 = s , i γ 0 ( s , i ) γ T ( 2 ) ( s , i ) γ S ( 2 ) ( s , i ) o ^ ω s o ^ ω i | 0 ignored one and zero-photon terms ,
γ S ( 2 ) ( s , i ) = 1 S Ŏ ω s , 0 * ( κ s , z 0 ) Ŏ ω i , 0 * ( κ i , z 0 ) × e i ( k z , s + k z , i ) z 0 ,
k z s = k s 0 + ω s ω s 0 v s 1 2 | κ s | 2 | k s | ,
Δ K ( κ s , κ i ) Δ k 0 + | κ s + κ i | 2 2 k p 0 ( 1 δ ω ω p 0 ) n p n s | κ s | 2 k p 0 ( 1 + δ ω ω p 0 ) n p n i | κ i | 2 k p 0 ,
P 2 = ψ 2 | ψ 2 .
P 2 = | C | 2 Ω 2 K 2 ,
C = i e i ( n s ω s 0 + n i ω i 0 ) z 0 / c E p χ eff 2 ω s 0 ω i 0 8 ϵ 0 c 3 n p n s n i ,
Ω 2 = d ω s 2 π d ω i 2 π | p ( ω s + ω i ω p 0 ) × F ( ω s ω s 0 ) F ( ω i ω i 0 ) | 2
K 2 = | d 2 κ s ( 2 π ) 2 d 2 κ i ( 2 π ) 2 p ( κ s + κ i , 0 ) × Ŏ 0 ( κ s , z 0 ) Ŏ 0 ( κ i , z 0 ) e i z 0 ( n p n s | κ s | 2 k p 0 + n p n i | κ i | 2 k p 0 ) × L sinc ( Δ K ( κ s , κ i ) L 2 ) | 2 ,
Ω 2 = | p | 2 * | F | 2 * | F | 2 ( ω s 0 + ω i 0 ω p 0 ) .
P 1 = ψ 1 | ψ 1
| ψ 1 = s , i γ 0 ( s , i ) γ T ( 1 ) ( s ) γ S ( 1 ) ( s ) o ^ ω s a ^ i | 0 ignored zero-photon terms ,
γ T ( 1 ) = F ( ω s ω s 0 , κ s ) ,
γ S ( 1 ) = 1 S Ŏ 0 * ( κ s , z 0 ) e i k z , s z 0 ,
P 1 = | C | 2 Ω 1 K 1 ,
Ω 1 = d ω s 2 π d ω i 2 π | p ( ω s + ω i ω p 0 ) F ( ω s ω s 0 ) | 2 ,
K 1 = d 2 κ i ( 2 π ) 2 | d 2 κ s ( 2 π ) 2 p ( κ s + κ i , 0 ) Ŏ 0 ( κ s , z 0 ) × e i z 0 n p n s | κ s | 2 k p 0 L sinc Δ K L 2 | 2 .
Ω 1 = d ω 2 π | F ( ω ) | 2 ,
Γ 2 | 1 = K 2 K 1 .
S p ( ρ , 0 ) = 2 π w 0 2 e | ρ | 2 / w 0 2 ,
p ( κ , 0 ) = 2 π w 0 2 e | κ | 2 w 0 2 / 4 .
Δ K Δ k 0 + w 0 2 4 z R [ | κ s + κ i | 2 2 ( 1 δ ω ω p 0 ) n p n s | κ s | 2 2 ( 1 + δ ω ω p 0 ) n p n i | κ i | 2 ] .
O 0 ( ρ , z 0 ) = 2 π a 0 2 e | ρ | 2 / a 0 2 ,
Ŏ 0 ( κ , z 0 ) = 2 π a 0 2 e | κ | 2 a 0 2 / 4 .
P 2 = E p χ eff 2 L Δ ω F ω s 0 ω i 0 ω p 0 8 ϵ 0 c 4 n s n i · Ω 2 Δ ω F ( δ ) · K 2 k p 0 L ( ξ , α , ζ , φ 0 ) ,
T p ( t ) = [ 4 ln 2 π Δ t p 2 ] 1 4 e 2 ln 2 t 2 / Δ t p 2 ,
p ( ω ) = [ π Δ t p 2 ln 2 ] 1 4 e ω 2 Δ t p 2 / ( 8 ln 2 ) ,
F ( ω ) = e 2 ln 2 ω 2 / Δ ω F 2 ,
Ω 2 Δ ω F ( δ ) = π / ( 8 ln 2 ) 1 + δ 2 2 .
K 2 k p 0 L ( ξ , α , ζ , φ 0 ) = 8 π 5 ξ α 4 | d 2 φ s d 2 φ i Q 2 | 2
Q 2 = exp { | φ s + φ i | 2 } × exp { α 2 ( | φ s | 2 + | φ i | 2 ) } × exp i { 4 ξ ζ ( n p n s | φ s | 2 + n p n i | φ i | 2 ) } × sinc { φ 0 2 + ξ [ | φ s + φ i | 2 2 n p n s | φ s | 2 2 n p n i | φ i | 2 ] } .
d 2 φ s d 2 φ i Q 2 2 π 0 ρ s d ρ s 0 ρ i d ρ i 0 2 π d ( θ s θ i ) Q 2
Q 2 = exp { ( 1 + α 2 ) ( ρ s 2 + ρ i 2 ) } × exp { 2 ρ s ρ i cos ( θ s θ i ) } × exp i { 4 ξ ζ ( n p n s ρ s 2 + n p n i ρ i 2 ) } × sinc { φ 0 2 + ξ [ ( 1 2 n p n s ) ρ s 2 + ( 1 2 n p n s ) ρ i 2 + 2 ρ s ρ i cos ( θ s θ i ) ] } .
P 1 = E p χ eff 2 L Δ ω F ω s 0 ω i 0 ω p 0 8 ϵ 0 c 4 n s n i · Ω 1 Δ ω F ( δ ) · K 1 k p 0 L ( ξ , α , ζ , φ 0 ) ,
K 1 k p 0 L = 4 π 4 ξ α 2 d 2 φ s | d 2 φ i Q 1 | 2
Q 1 = exp { | φ s + φ i | 2 } × exp { α 2 | φ s | 2 } × exp i { 4 ξ ζ n p n s | φ s | 2 } × sinc { φ 0 2 ξ [ | φ s + φ i | 2 2 n p n s | φ s | 2 2 n p n i | φ i | 2 ] } ,
Γ 2 | 1 = K 2 K 1 = Ω 1 Ω 2 P 2 P 1 .
P A B = T A T B P 2 , P I = T I P 1 ,
Γ 2 | 1 = Ω 1 Ω 2 T I T A T B P A B P I .
| 1 r = k e i k · r V | 1 k .
| ψ = V d 3 r ψ ( r ) | 1 r ,
P ( V ) = V d 3 r | 1 r | ψ | 2 = V d 3 r | ψ ( r ) | 2 .
P ( V ) = V d 3 r | ψ ( r ) | 2 = ψ | ψ = k | ψ k | 2 = 1 .
O ω , j = 0 ( ρ , z z 0 ) = O ω , 0 ( ρ , z 0 ) e i β ω ( z z 0 ) .
| O ω , j = 1 L d 3 r O ω , j ( r ) | 1 r
| 1 = d 3 r f ( r ) | 1 r
= d 3 r ( Θ ( z 0 z ) e i k · r V + Θ ( z z 0 ) j g j ( ) O ω , j ( r ) L ) | 1 r ,
j g j ( ) O ω , j ( ρ , z 0 ) L = e i κ · ρ e i k z , · z 0 V .
κ κ = | k | sin θ | k | sin θ = 1 k z k z = | k | cos θ | k | cos θ n n ,
g j ( ) = d 2 ρ O ω , j * ( ρ , z 0 ) e i κ · ρ e i k z , · z 0 V L = 1 S e i k z , · z 0 Ŏ ω , j * ( κ , z 0 ) ,
| Ψ ( t 1 ) = j μ e i k z , · z 0 1 S Ŏ ω , j * ( κ , z 0 ) | O ω , j .
| Ψ ( t 1 ) = μ e i k z , · z 0 1 S Ŏ ω , 0 * ( κ , z 0 ) | O ω , 0 ignored zero-photon terms .

Metrics