Abstract

We study theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in photonic crystal optical fiber. We show that it is possible to engineer two-photon states with specific spectral correlation (“entanglement”) properties suitable for quantum information processing applications. We focus on the case exhibiting no spectral correlations in the two-photon component of the state, which we call factorability, and which allows heralding of single-photon pure-state wave packets without the need for spectral post filtering. We show that spontaneous four wave mixing exhibits a remarkable flexibility, permitting a wider class of two-photon states, including ultra-broadband, highly-anticorrelated states.

© 2007 Optical Society of America

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  1. See, for example, the review by P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling and G. J. Milburn, "Linear optical quantum computing with photonic qubits," Rev. Mod. Phys. 79, 135-174 (2007).
    [CrossRef]
  2. S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of Tunable Optical Parametric Fluorescence," Phys. Rev. Lett. 18, 732-734 (1967).
    [CrossRef]
  3. A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice and M. G. Raymer, "Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion, " Laser Phys. 15, 146-161 (2005).
  4. M. G. Raymer, J. Noh, K. Banaszek and I. A. Walmsley, "Pure-state single-photon wave-packet generation by parmametric down-conversion in a distributed microcavity," Phys. Rev. A 72, 023825 (2005).
    [CrossRef]
  5. A. B. U’Ren, C. Silberhorn, K. Banaszek and I.A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
    [CrossRef] [PubMed]
  6. K. Banaszek, A. B. U’Ren and I. A. Walmsley, "Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides," Opt. Lett. 26, 1367-1369 (2001).
    [CrossRef]
  7. J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007).
    [CrossRef] [PubMed]
  8. J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. St. J. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005).
    [CrossRef] [PubMed]
  9. J. Fan and A. Migdall, "Generation of cross-polarized photon pairs in a microstructure fiber with frequencyconjugate laser pump pulses," Opt. Express 13, 5777-5782 (2005).
    [CrossRef] [PubMed]
  10. X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications: Improved generation of correlated photons," Opt. Express 12, 3737-3744 (2004).
    [CrossRef] [PubMed]
  11. W. P. Grice, A. B. U’Ren and I. A.Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
    [CrossRef]
  12. P. Russell, "Photonic Crystal Fiber," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  13. M. Fiorentino, P. L. Voss, J. E. Sharping and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
    [CrossRef]
  14. R. H. Stolen, "Fundamentals of Raman amplification in fibers," in Raman Amplifiers for Telecommunications 1, edited by M. N. Islam (Springer, 2003), pp. 35-59.
  15. R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. J. McKinstrie, J. Ford, S. Fainman and S. Radic, "Parametric wavelength conversion from conventional near-infrared to visible band," IEEE Photon. Technol. Lett. 18, 2445- 2447 (2006).
    [CrossRef]
  16. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225- 2227 (2003).
    [CrossRef] [PubMed]
  17. M. Yu, C. J. McKinstrie and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
    [CrossRef]
  18. PeterJ.  Mosley, Jeff S. Lundeen, Brian J. Smith, Ian A. Walmsley, Piotr Wasylczyk, Alfred B. U’Ren, Christine Silberhorn, in Coherence and Quantum Optics IX, (Kluwer Academic/Plenum, New York) (accepted).
  19. Z.D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum" Phys. Rev. A 70, 052317 (2004)
    [CrossRef]
  20. J. P. Torres, F. Macia, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled twophoton states by achromatic phase matching" Opt. Lett. 30, 314 (2005)
    [CrossRef] [PubMed]
  21. O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. K¨artner, Phys. Rev. Lett. 94, 083601 (2005)
    [CrossRef] [PubMed]
  22. A.B. U’Ren, K. Banaszek and I. A. Walmsley, "Photon engineering for quantum information processing" Quantum Information and Computation 3, 480 (2003)
  23. A. B. U’Ren, R. Erdmann, M. De la Cruz and I. A.Walmsley, "Generation of two-photon states with an arbitrary degree of entanglement via nonlinear crystal superlattices, " Phys. Rev. Lett. 97, 223602 (2006).
    [CrossRef] [PubMed]
  24. V. Giovanetti, S. Lloyd and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature 412, 417-419 (2001).
    [CrossRef]
  25. M. B. Nasr, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Demonstration of dispersion-canceled quantumoptical coherence tomography," Phys. Rev. Lett. 91, 083601 (2003).
    [CrossRef] [PubMed]
  26. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  27. J. Chen, X. Li and P. Kumar, "Two-photon-state generation via four-wave mixing in optical fibers," Phys. Rev. A 72, 033801 (2005).
    [CrossRef]
  28. J. Chen, K. F. Lee and P. Kumar R, "Quantum theory of degenerate |(3) two-photon state," e-print arXiv:quantph/ 0702176v1.
  29. G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Elsevier, 2007).
  30. C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 15, 8516-8534 (2006). This paper also reviews scalar and vector FWM in strongly-birefringent and randomlybirefringent fibers.
    [CrossRef]
  31. K. P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003).
    [CrossRef] [PubMed]
  32. T. A. Birks, J. C. Knight and P. St. J. Russell. "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  33. G. K. L. Wong, A. Y. H. Chen, S. W. Ha, R. J. Kruhlak, S. G. Murdoch, R. Leonhardt, J. D. Harvey and N. Y. Joly, "Characterization of chromatic dispersion in photonic crystal fibers using scalar modulation instability," Opt. Express 13, 8662-8670 (2005).
    [CrossRef] [PubMed]
  34. A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz and MiguelV. Andres, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
    [CrossRef]
  35. A. L. Berkhoer and V. E. Zakharov, "Self-excitation of waves with different polarizations in nonlinear media," Sov. Phys. JETP 31, 486-493 (1970).
  36. C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
    [CrossRef] [PubMed]
  37. R. H. Stolen, M. A. Bosch and C. Lin, "Phase matching in birefringent fibers," Opt. Lett. 6, 213-215 (1981).
    [CrossRef] [PubMed]
  38. R. J. Kruhlak, G. K. L. Wong, J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly and J. C. Knight, "Polarization modulation instability in photonic crystal fibers," Opt. Lett. 31, 1379-1381 (2006).
    [CrossRef] [PubMed]
  39. S. G. Murdoch, R. Leonhardt and J. D. Harvey, "Polarization modulation instability in weakly birefringent fibers," Opt. Lett. 20, 866-868 (1995).
    [CrossRef] [PubMed]
  40. Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Opt. Lett. 31, 1286-1288 (2006).
    [CrossRef] [PubMed]
  41. Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Phys. Rev. A 75, 023803 (2007).
    [CrossRef]
  42. Such a state is typically referred to as highly entangled, but one should keep in mind that the large vacuum component of the state renders this "entanglement" useful only in a post-selection experiment.
  43. K. A. O’Donnell and A. B. U’Ren, "Observation of ultrabroadband, beamlike parametric downconversion," Opt. Lett. 32, 817-819 (2007).
    [CrossRef] [PubMed]
  44. L. Zhang, A. B. U’Ren, R. Erdmann, K. A. O’Donnell, C. Silberhorn, K. Banaszek and I. A.Walmsley, "Generation of highly entangled photon pairs for continuous variable Bell inequality violation," J. Mod. Opt. 54, 707-719 (2007).
    [CrossRef]
  45. R. Jiang, N. Alic, C. J. McKinstrie and S. Radic,"Two-pump parametric amplifier with 40 dB of equalized gain over a bandwidth of 50 nm, " Proc. OFC 2007, paper OWB2.
  46. J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham and H. L. Fragnito, "Spectrally flat and broadband doublepumped fiber optical parametric amplifiers," Opt. Express 15, 5288-5309 (2007).
    [CrossRef]
  47. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin and G. P. Agrawal, "Record performance of parametric amplifier constructed with highly nonlinear fibre," Electron. Lett. 39, 838-839 (2003).
    [CrossRef]
  48. H. Takesue and K. Inoue, "1.5- m band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber," Opt. Express 13, 7832-7839 (2005).
    [CrossRef] [PubMed]

2007

J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007).
[CrossRef] [PubMed]

See, for example, the review by P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling and G. J. Milburn, "Linear optical quantum computing with photonic qubits," Rev. Mod. Phys. 79, 135-174 (2007).
[CrossRef]

Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Phys. Rev. A 75, 023803 (2007).
[CrossRef]

K. A. O’Donnell and A. B. U’Ren, "Observation of ultrabroadband, beamlike parametric downconversion," Opt. Lett. 32, 817-819 (2007).
[CrossRef] [PubMed]

L. Zhang, A. B. U’Ren, R. Erdmann, K. A. O’Donnell, C. Silberhorn, K. Banaszek and I. A.Walmsley, "Generation of highly entangled photon pairs for continuous variable Bell inequality violation," J. Mod. Opt. 54, 707-719 (2007).
[CrossRef]

J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham and H. L. Fragnito, "Spectrally flat and broadband doublepumped fiber optical parametric amplifiers," Opt. Express 15, 5288-5309 (2007).
[CrossRef]

2006

R. J. Kruhlak, G. K. L. Wong, J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly and J. C. Knight, "Polarization modulation instability in photonic crystal fibers," Opt. Lett. 31, 1379-1381 (2006).
[CrossRef] [PubMed]

A. B. U’Ren, R. Erdmann, M. De la Cruz and I. A.Walmsley, "Generation of two-photon states with an arbitrary degree of entanglement via nonlinear crystal superlattices, " Phys. Rev. Lett. 97, 223602 (2006).
[CrossRef] [PubMed]

C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 15, 8516-8534 (2006). This paper also reviews scalar and vector FWM in strongly-birefringent and randomlybirefringent fibers.
[CrossRef]

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. J. McKinstrie, J. Ford, S. Fainman and S. Radic, "Parametric wavelength conversion from conventional near-infrared to visible band," IEEE Photon. Technol. Lett. 18, 2445- 2447 (2006).
[CrossRef]

Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Opt. Lett. 31, 1286-1288 (2006).
[CrossRef] [PubMed]

2005

J. Chen, X. Li and P. Kumar, "Two-photon-state generation via four-wave mixing in optical fibers," Phys. Rev. A 72, 033801 (2005).
[CrossRef]

H. Takesue and K. Inoue, "1.5- m band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber," Opt. Express 13, 7832-7839 (2005).
[CrossRef] [PubMed]

J. P. Torres, F. Macia, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled twophoton states by achromatic phase matching" Opt. Lett. 30, 314 (2005)
[CrossRef] [PubMed]

O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. K¨artner, Phys. Rev. Lett. 94, 083601 (2005)
[CrossRef] [PubMed]

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. St. J. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005).
[CrossRef] [PubMed]

J. Fan and A. Migdall, "Generation of cross-polarized photon pairs in a microstructure fiber with frequencyconjugate laser pump pulses," Opt. Express 13, 5777-5782 (2005).
[CrossRef] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice and M. G. Raymer, "Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion, " Laser Phys. 15, 146-161 (2005).

M. G. Raymer, J. Noh, K. Banaszek and I. A. Walmsley, "Pure-state single-photon wave-packet generation by parmametric down-conversion in a distributed microcavity," Phys. Rev. A 72, 023825 (2005).
[CrossRef]

G. K. L. Wong, A. Y. H. Chen, S. W. Ha, R. J. Kruhlak, S. G. Murdoch, R. Leonhardt, J. D. Harvey and N. Y. Joly, "Characterization of chromatic dispersion in photonic crystal fibers using scalar modulation instability," Opt. Express 13, 8662-8670 (2005).
[CrossRef] [PubMed]

2004

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz and MiguelV. Andres, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

Z.D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum" Phys. Rev. A 70, 052317 (2004)
[CrossRef]

C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
[CrossRef] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek and I.A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
[CrossRef] [PubMed]

X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications: Improved generation of correlated photons," Opt. Express 12, 3737-3744 (2004).
[CrossRef] [PubMed]

2003

A.B. U’Ren, K. Banaszek and I. A. Walmsley, "Photon engineering for quantum information processing" Quantum Information and Computation 3, 480 (2003)

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225- 2227 (2003).
[CrossRef] [PubMed]

P. Russell, "Photonic Crystal Fiber," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin and G. P. Agrawal, "Record performance of parametric amplifier constructed with highly nonlinear fibre," Electron. Lett. 39, 838-839 (2003).
[CrossRef]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Demonstration of dispersion-canceled quantumoptical coherence tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

K. P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003).
[CrossRef] [PubMed]

2002

M. Fiorentino, P. L. Voss, J. E. Sharping and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

2001

W. P. Grice, A. B. U’Ren and I. A.Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
[CrossRef]

K. Banaszek, A. B. U’Ren and I. A. Walmsley, "Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides," Opt. Lett. 26, 1367-1369 (2001).
[CrossRef]

V. Giovanetti, S. Lloyd and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature 412, 417-419 (2001).
[CrossRef]

1997

1995

S. G. Murdoch, R. Leonhardt and J. D. Harvey, "Polarization modulation instability in weakly birefringent fibers," Opt. Lett. 20, 866-868 (1995).
[CrossRef] [PubMed]

M. Yu, C. J. McKinstrie and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

1981

1970

A. L. Berkhoer and V. E. Zakharov, "Self-excitation of waves with different polarizations in nonlinear media," Sov. Phys. JETP 31, 486-493 (1970).

1967

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of Tunable Optical Parametric Fluorescence," Phys. Rev. Lett. 18, 732-734 (1967).
[CrossRef]

Electron. Lett.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, Q. Lin and G. P. Agrawal, "Record performance of parametric amplifier constructed with highly nonlinear fibre," Electron. Lett. 39, 838-839 (2003).
[CrossRef]

IEEE Photon. Technol. Lett.

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. J. McKinstrie, J. Ford, S. Fainman and S. Radic, "Parametric wavelength conversion from conventional near-infrared to visible band," IEEE Photon. Technol. Lett. 18, 2445- 2447 (2006).
[CrossRef]

M. Fiorentino, P. L. Voss, J. E. Sharping and P. Kumar, "All-fiber photon-pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

A. Ortigosa-Blanch, A. Diez, M. Delgado-Pinar, J. L. Cruz and MiguelV. Andres, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

J. Mod. Opt.

L. Zhang, A. B. U’Ren, R. Erdmann, K. A. O’Donnell, C. Silberhorn, K. Banaszek and I. A.Walmsley, "Generation of highly entangled photon pairs for continuous variable Bell inequality violation," J. Mod. Opt. 54, 707-719 (2007).
[CrossRef]

Laser Phys.

A. B. U’Ren, C. Silberhorn, K. Banaszek, I. A. Walmsley, R. Erdmann, W. P. Grice and M. G. Raymer, "Generation of pure-state single-photon wavepackets by conditional preparation based on spontaneous parametric downconversion, " Laser Phys. 15, 146-161 (2005).

Nature

V. Giovanetti, S. Lloyd and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature 412, 417-419 (2001).
[CrossRef]

Opt. Express

C. J. McKinstrie, H. Kogelnik and L. Schenato, "Four-wave mixing in a rapidly-spun fiber," Opt. Express 15, 8516-8534 (2006). This paper also reviews scalar and vector FWM in strongly-birefringent and randomlybirefringent fibers.
[CrossRef]

K. P. Hansen, "Dispersion flattened hybrid-core nonlinear photonic crystal fiber," Opt. Express 11, 1503-1509 (2003).
[CrossRef] [PubMed]

G. K. L. Wong, A. Y. H. Chen, S. W. Ha, R. J. Kruhlak, S. G. Murdoch, R. Leonhardt, J. D. Harvey and N. Y. Joly, "Characterization of chromatic dispersion in photonic crystal fibers using scalar modulation instability," Opt. Express 13, 8662-8670 (2005).
[CrossRef] [PubMed]

C. J. McKinstrie and S. Radic, "Phase-sensitive amplification in a fiber," Opt. Express 12, 4973-4979 (2004).
[CrossRef] [PubMed]

J. Fan and A. Migdall, "A broadband high spectral brightness fiber-based two-photon source," Opt. Express 15, 2915-2920 (2007).
[CrossRef] [PubMed]

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. St. J. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005).
[CrossRef] [PubMed]

J. Fan and A. Migdall, "Generation of cross-polarized photon pairs in a microstructure fiber with frequencyconjugate laser pump pulses," Opt. Express 13, 5777-5782 (2005).
[CrossRef] [PubMed]

X. Li, J. Chen, P. Voss, J. Sharping, and P. Kumar, "All-fiber photon-pair source for quantum communications: Improved generation of correlated photons," Opt. Express 12, 3737-3744 (2004).
[CrossRef] [PubMed]

J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham and H. L. Fragnito, "Spectrally flat and broadband doublepumped fiber optical parametric amplifiers," Opt. Express 15, 5288-5309 (2007).
[CrossRef]

H. Takesue and K. Inoue, "1.5- m band quantum-correlated photon pair generation in dispersion-shifted fiber: suppression of noise photons by cooling fiber," Opt. Express 13, 7832-7839 (2005).
[CrossRef] [PubMed]

Opt. Lett.

K. A. O’Donnell and A. B. U’Ren, "Observation of ultrabroadband, beamlike parametric downconversion," Opt. Lett. 32, 817-819 (2007).
[CrossRef] [PubMed]

K. Banaszek, A. B. U’Ren and I. A. Walmsley, "Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides," Opt. Lett. 26, 1367-1369 (2001).
[CrossRef]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth and P. St. J. Russell, "Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber," Opt. Lett. 28, 2225- 2227 (2003).
[CrossRef] [PubMed]

R. H. Stolen, M. A. Bosch and C. Lin, "Phase matching in birefringent fibers," Opt. Lett. 6, 213-215 (1981).
[CrossRef] [PubMed]

R. J. Kruhlak, G. K. L. Wong, J. S. Y. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly and J. C. Knight, "Polarization modulation instability in photonic crystal fibers," Opt. Lett. 31, 1379-1381 (2006).
[CrossRef] [PubMed]

S. G. Murdoch, R. Leonhardt and J. D. Harvey, "Polarization modulation instability in weakly birefringent fibers," Opt. Lett. 20, 866-868 (1995).
[CrossRef] [PubMed]

Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation by four-wave mixing in optical fibers," Opt. Lett. 31, 1286-1288 (2006).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight and P. St. J. Russell. "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

J. P. Torres, F. Macia, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled twophoton states by achromatic phase matching" Opt. Lett. 30, 314 (2005)
[CrossRef] [PubMed]

Phys. Rev. A

J. Chen, X. Li and P. Kumar, "Two-photon-state generation via four-wave mixing in optical fibers," Phys. Rev. A 72, 033801 (2005).
[CrossRef]

Q. Lin, F. Yaman and G. P. Agrawal, "Photon-pair generation in optical fibers through four-wave mixing: Role of Raman scattering and pump polarization," Phys. Rev. A 75, 023803 (2007).
[CrossRef]

Z.D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum" Phys. Rev. A 70, 052317 (2004)
[CrossRef]

W. P. Grice, A. B. U’Ren and I. A.Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
[CrossRef]

M. G. Raymer, J. Noh, K. Banaszek and I. A. Walmsley, "Pure-state single-photon wave-packet generation by parmametric down-conversion in a distributed microcavity," Phys. Rev. A 72, 023825 (2005).
[CrossRef]

Phys. Rev. E

M. Yu, C. J. McKinstrie and G. P. Agrawal, "Modulational instabilities in dispersion-flattened fibers," Phys. Rev. E 52, 1072-1080 (1995).
[CrossRef]

Phys. Rev. Lett.

A. B. U’Ren, C. Silberhorn, K. Banaszek and I.A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
[CrossRef] [PubMed]

S. E. Harris, M. K. Oshman, and R. L. Byer, "Observation of Tunable Optical Parametric Fluorescence," Phys. Rev. Lett. 18, 732-734 (1967).
[CrossRef]

A. B. U’Ren, R. Erdmann, M. De la Cruz and I. A.Walmsley, "Generation of two-photon states with an arbitrary degree of entanglement via nonlinear crystal superlattices, " Phys. Rev. Lett. 97, 223602 (2006).
[CrossRef] [PubMed]

O. Kuzucu, M. Fiorentino, M. A. Albota, F. N. C. Wong, and F. X. K¨artner, Phys. Rev. Lett. 94, 083601 (2005)
[CrossRef] [PubMed]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko and M. C. Teich, "Demonstration of dispersion-canceled quantumoptical coherence tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Quantum Information and Computation

A.B. U’Ren, K. Banaszek and I. A. Walmsley, "Photon engineering for quantum information processing" Quantum Information and Computation 3, 480 (2003)

Rev. Mod. Phys.

See, for example, the review by P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling and G. J. Milburn, "Linear optical quantum computing with photonic qubits," Rev. Mod. Phys. 79, 135-174 (2007).
[CrossRef]

Science

P. Russell, "Photonic Crystal Fiber," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Sov. Phys. JETP

A. L. Berkhoer and V. E. Zakharov, "Self-excitation of waves with different polarizations in nonlinear media," Sov. Phys. JETP 31, 486-493 (1970).

Other

Such a state is typically referred to as highly entangled, but one should keep in mind that the large vacuum component of the state renders this "entanglement" useful only in a post-selection experiment.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).

J. Chen, K. F. Lee and P. Kumar R, "Quantum theory of degenerate |(3) two-photon state," e-print arXiv:quantph/ 0702176v1.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Elsevier, 2007).

PeterJ.  Mosley, Jeff S. Lundeen, Brian J. Smith, Ian A. Walmsley, Piotr Wasylczyk, Alfred B. U’Ren, Christine Silberhorn, in Coherence and Quantum Optics IX, (Kluwer Academic/Plenum, New York) (accepted).

R. H. Stolen, "Fundamentals of Raman amplification in fibers," in Raman Amplifiers for Telecommunications 1, edited by M. N. Islam (Springer, 2003), pp. 35-59.

R. Jiang, N. Alic, C. J. McKinstrie and S. Radic,"Two-pump parametric amplifier with 40 dB of equalized gain over a bandwidth of 50 nm, " Proc. OFC 2007, paper OWB2.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Pump envelope function α(ωs ,ωi ) for a fiber characterized by r = 0.67μm, f = 0.52 and L = 30cm. (b) Phasematching function ϕ (νs ,νi ); for a relatively small region of {ωs , ωi } space the phase-matching function contours are essentially straight lines, with slope θsi = - arctan(Ts /Ti }) (with Tμ given by Eq. (5)). (c) Resulting joint spectral intensity.

Fig. 2.
Fig. 2.

(a) Black, solid curve: phase-matching (Δk=0) contour for SFWM in the degenerate pump case. Colored background: phase-matching orientation angle. Black, dashed line: symmetric group velocity matching (GVM) contour. Along the phase-matching contour we have indicated particular orientation angles of interest. (b) Close up, near the lower zero group velocity dispersion frequency.

Fig. 3.
Fig. 3.

Joint spectral intensity (JSI) obtained for the fiber geometry assumed for Fig. 2 (r = 0.616μm and f = 0.6) where the pump central wavelength (λ p0 = 0.7147μm) is obtained by imposing simultaneous phase-matching and group-velocity matching. We consider a pump bandwidth of 0.1nm and a fiber length of 0.25m. The function values are normalized such that white = 1 and black = 0. (a) Pump envelope function α{ωs , ωi ). (b) Phase-matching function ϕ(νs , νi ). (c) Analytic JSI, obtained with approximation from Eq. (4). (d) JSI obtained by numerical integration of Eq. (2).

Fig. 4.
Fig. 4.

Black, solid curve: phase-matching (Δk = 0) contour for SFWM in the non-degenerate pump regime. Colored background: phase-matching orientation angle. Black, dotted line: frequencies that satisfy the group-velocity matching condition (see Eq. (12)). Along the phase-matching contour we have indicated particular angles of orientation of interest.

Fig. 5.
Fig. 5.

Joint spectral intensity (JSI) ∣F(ωs , ωi )∣2 obtained for the fiber geometry assumed for Fig. 4. (a) Pump envelope function α(ωs , ωi ). (b) Phase-matching function ϕ(ωs , ωi ). (c) Analytic JSI. (d) JSI obtained by numerical integration of Eq. (2).

Fig. 6.
Fig. 6.

a) Cross-polarization phase-matching Δk = 0 (thick) and group-velocity matching Ts,i = 0 (thin) curves (f = 0.43, d = 1.75μm, ZDWs = 790 nm, 1404 nm - similar to NL-1.7-790 from Crystal Fiber). With power P = 0, three pairs of curves are plotted with Δd = -0.001,0,0.001 μm, respectively resulting in a birefringence of Δn = -3 × 10-5,0,3 × 10-5 (red, green, blue). Points A through F bound regions in which factorability is possible. b) Full dispersion numerical JSIs for the asymmetric states corresponding to points D (θsi = 0°, λs = 746.4 nm and λi = 949.0 nm, Δλp = 0.30 nm, and L = 30 m) and F (θsi = 90°, λs = 677.1 nm, λi = 834.2 nm, Δλp = 0.30 nm, and L = 30 m).

Fig. 7.
Fig. 7.

Points C through F from Fig. 6 are plotted as a function of the birefringence Δn. Thus, the solid dark blue curves give the pump wavelength λp of asymmetric factorable solutions. The corresponding idler and signal wavelengths λi and λs are given by the magenta dashed curves (for points D and F) and light-blue dash-dotted curves (for points C and E). The shaded regions indicate the range in which factorable states can be generated provide the pump bandwidth is matched to the fiber length. The fiber parameters are the same as in Fig. 6.

Equations (16)

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ψ = 0 s 0 i + κ d ω s d ω i F ω s ω i ω s s ω i i .
F ω s ω i = dω′ α 1 ( ω′ ) α 2 ( ω s + ω i ω′ )
× sin c [ L 2 Δk ω′ ω s ω i ] exp [ i L 2 Δk ω′ ω s ω i ] ,
Δ k ω 1 ω s ω i = k ( ω 1 ) + k ( ω s + ω i ω 1 ) k ( ω s ) k ( ω i ) ( γ 1 P 1 + γ 2 P 2 ) ,
L Δ k lin = L Δ k ( 0 ) + T s ν s + T i ν i ,
τ μ = L [ k 2 ( 1 ) ( ω 2 0 ) k μ ( 1 ) ( ω μ 0 ) ] ,
τ p = L [ k 1 ( 1 ) ( ω 1 0 ) k 2 ( 1 ) ( ω 2 0 ) ] ,
F lin ν s ν i = α ν s ν i ϕ ν s ν i ,
α ν s ν i = exp [ ( ν s + ν i ) 2 σ 1 2 + σ 2 2 ] ,
ϕ ν s ν i = sin c [ L Δ k lin 2 ] exp [ i L Δ k lin 2 ] ,
Φ B x = M π B exp ( B 2 x 2 ) [ erf ( 1 2 B iBx ) + erf ( iBx ) ] ,
T s T i 0 .
2 Γ σ 2 T s T i = 1 ,
2 k 2 ( 1 ) k s ( 1 ) k i ( 1 ) = 2 ( k 1 ( 1 ) k 2 ( 1 ) ) σ 1 2 ( σ 1 2 + σ 2 2 ) .
Δ k ω p Δ s = 2 k x ( ω p ) k y ( ω p + Δ s ) k y ( ω p Δ s ) 2 3 γP
2 k x ( ω p ) k x ( ω p + Δ s ) k x ( ω p Δ s ) + 2 Δ n ω p c 2 3 γP ,

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