Abstract

Many applications in optical quantum information processing benefit from careful spectral shaping of single-photon wave-packets. In this paper we tailor the joint spectral wave-function of photons created in parametric downconversion by engineering the nonlinearity profile of a poled crystal. We design a crystal with an approximately Gaussian nonlinearity profile and confirm successful wave-packet shaping by two-photon interference experiments. We numerically show how our method can be applied for attaining one of the currently most important goals of single-photon quantum optics, the creation of pure single photons without spectral correlations.

© 2011 Optical Society of America

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  1. 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(1), 135 (2007).
    [CrossRef]
  2. N. Gisin, and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
    [CrossRef]
  3. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
    [CrossRef]
  4. T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
    [CrossRef] [PubMed]
  5. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
    [CrossRef]
  6. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
    [CrossRef] [PubMed]
  7. M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).
  8. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
    [CrossRef]
  9. G. Imeshev, M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18(4), 534–539 (2001).
    [CrossRef]
  10. P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
    [CrossRef]
  11. 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(6), 5122–5133 (1994).
    [CrossRef] [PubMed]
  12. The crystal was custom-made by Raicol Crystals Ltd., www.raicol.com.
  13. A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
    [CrossRef]
  14. C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
    [CrossRef] [PubMed]
  15. A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
    [CrossRef]
  16. K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” J. Phys. B 39(18), R293–R324 (2006).
    [CrossRef]
  17. A. Eckstein, and C. Silberhorn, “Broadband frequency mode entanglement in waveguided parametric down conversion,” Opt. Lett. 33(16), 1825–1827 (2008).
    [CrossRef] [PubMed]
  18. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063,815 (2001).
    [CrossRef]
  19. Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49(14–15), 2309–2323 (2002).
    [CrossRef]
  20. 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).
  21. M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
    [CrossRef]
  22. S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
    [CrossRef]
  23. L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
    [CrossRef]
  24. T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
    [CrossRef]
  25. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, and A. Zeilinger, “A wavelength-tunable fiber-coupled source of narrowband entangled photons,” Opt. Express 15(23), 15377–15386 (2007).
    [CrossRef] [PubMed]
  26. K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
    [CrossRef]
  27. M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. Wadsworth, and J. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
    [CrossRef] [PubMed]
  28. W. P. Grice, and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56(2), 1627–1634 (1997).
    [CrossRef]
  29. Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
    [CrossRef]
  30. A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
    [CrossRef]
  31. M. Corona and A. B . U’Ren, “Parametric down-conversion with optimized spectral properties in nonlinear photonic crystals,” Phys. Rev. A 76(4), 043829 (2007).
    [CrossRef]
  32. A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
    [CrossRef]
  33. O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
    [CrossRef] [PubMed]
  34. P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
    [CrossRef] [PubMed]
  35. K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
    [CrossRef]
  36. A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-IPDC with backward-wave amplification,” Opt. Express 17(5), 3441–3446 (2009).
    [CrossRef] [PubMed]
  37. M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
    [CrossRef]

2010

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
[CrossRef]

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

2009

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
[CrossRef]

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-IPDC with backward-wave amplification,” Opt. Express 17(5), 3441–3446 (2009).
[CrossRef] [PubMed]

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. Wadsworth, and J. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17, 4670–4676 (2009).
[CrossRef] [PubMed]

2008

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

A. Eckstein, and C. Silberhorn, “Broadband frequency mode entanglement in waveguided parametric down conversion,” Opt. Lett. 33(16), 1825–1827 (2008).
[CrossRef] [PubMed]

2007

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(1), 135 (2007).
[CrossRef]

N. Gisin, and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

M. Corona and A. B . U’Ren, “Parametric down-conversion with optimized spectral properties in nonlinear photonic crystals,” Phys. Rev. A 76(4), 043829 (2007).
[CrossRef]

A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
[CrossRef]

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[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(23), 15377–15386 (2007).
[CrossRef] [PubMed]

2006

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” J. Phys. B 39(18), R293–R324 (2006).
[CrossRef]

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
[CrossRef]

2005

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 parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
[CrossRef]

2004

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[CrossRef]

2002

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49(14–15), 2309–2323 (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. A64(6), 063,815 (2001).
[CrossRef]

G. Imeshev, M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18(4), 534–539 (2001).
[CrossRef]

2000

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

1997

W. P. Grice, and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56(2), 1627–1634 (1997).
[CrossRef]

1994

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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

1992

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

1987

C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Alibart, O.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Aspelmeyer, M

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
[CrossRef]

Banaszek, K

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).

Banaszek, K.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

Barbieri, M

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
[CrossRef]

Bartlett, S. D.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

Berry, D. W.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Branczyk, M. A.

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Brida, G.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

Carrasco, S.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Cecena-Alvarez, H

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Cemlyn, B.

Cer´e, A.

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

Christ, A.

Clark, A.

Cohen, O.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Corona, M.

M. Corona and A. B . U’Ren, “Parametric down-conversion with optimized spectral properties in nonlinear photonic crystals,” Phys. Rev. A 76(4), 043829 (2007).
[CrossRef]

Cussey, J.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

de la Cruz-Gutierrez, M

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

Dowling, J. P.

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(1), 135 (2007).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Eckstein, A.

Emplit, P.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Erdmann, R.

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).

Erdmann, R. K

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

Fedrizzi, A.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (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(23), 15377–15386 (2007).
[CrossRef] [PubMed]

Fejer, M.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

G. Imeshev, M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18(4), 534–539 (2001).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

Fiorentino, M.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
[CrossRef]

Fulconis, J.

Galvanauskas, A.

Garay-Palmett, K.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Garcia-Gracia, H

A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
[CrossRef]

Genovese, M.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
[CrossRef]

Ghosh, S.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Gisin, N.

N. Gisin, and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

Gomez-Gonzalez, R

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Grice, W. P.

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).

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49(14–15), 2309–2323 (2002).
[CrossRef]

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063,815 (2001).
[CrossRef]

W. P. Grice, and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56(2), 1627–1634 (1997).
[CrossRef]

Halder, M.

Harter, D.

Helwig, W

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

Herbst, T.

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (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(23), 15377–15386 (2007).
[CrossRef] [PubMed]

Higgins, B. L.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

Hong, C.

C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Hum, D.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Huy, K.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Imeshev, G.

Jennewein, T.

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (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(23), 15377–15386 (2007).
[CrossRef] [PubMed]

Jeronimo-Moreno, Y

A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

Kim, T.

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
[CrossRef]

Kim, Y.-H.

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49(14–15), 2309–2323 (2002).
[CrossRef]

Klyshko, D. N.

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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

Kok, P.

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(1), 135 (2007).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Kurimura, S.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Kuzucu, O.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

Langford, N. K.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

Lugani, J.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

Mandel, L.

C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Martin, A.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Massar, S.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

McGuinness, H. J.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

McKinstrie, C. J.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Merolla, J.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Milburn, G. J.

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(1), 135 (2007).
[CrossRef]

Molina-Terriza, G.

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

Mosley, P. J.

A. Christ, A. Eckstein, P. J. Mosley, and C. Silberhorn, “Pure single photon generation by type-IPDC with backward-wave amplification,” Opt. Express 17(5), 3441–3446 (2009).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

Munro, W. J.

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(1), 135 (2007).
[CrossRef]

Nagata, T.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Nasr, M.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Nemoto, K.

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(1), 135 (2007).
[CrossRef]

Nguyen, A.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Nielsen, M. A.

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
[CrossRef]

Noh, J.

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

O’Brien, J. L.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Okamoto, R.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Olislager, L.

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Ostrowsky, D. B.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Ou, Z.

C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

Peimbert-Torres, A

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

Poppe, A.

Pryde, G. J.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

Radic, S.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Ralph, T. C.

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

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(1), 135 (2007).
[CrossRef]

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
[CrossRef]

Ramelow, S.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

Rangel-Rojo, R.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

Rarity, J.

Ratschbacher, L.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

Raymer, M. G.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

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).

Rohde, P. P.

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
[CrossRef]

Rubin, M. H.

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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

Ruo Berchera, I.

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
[CrossRef]

Saleh, B.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Saleh, B. E. A.

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[CrossRef]

Sasaki, K.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Sergienko, A.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Sergienko, A. V.

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

Shi, X.

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

Shih, Y. H.

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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

Silberhorn, C

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[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).

Silberhorn, C.

Sinha, K.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Smith, B. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

Takeuchi, S.

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Tanzilli, S.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Teich, M.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Teich, M. C.

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[CrossRef]

Thew, R.

N. Gisin, and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

Thyagarajan, K.

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

Torner, L.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Torres, J.

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

Torres, J. P.

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

Tovstonog, S.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

U’Re, A. B

A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
[CrossRef]

U’Ren, A. B

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

M. Corona and A. B . U’Ren, “Parametric down-conversion with optimized spectral properties in nonlinear photonic crystals,” Phys. Rev. A 76(4), 043829 (2007).
[CrossRef]

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

U’ren, A. B.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063,815 (2001).
[CrossRef]

U’Ren,, A. B

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).

Valencia, A.

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

Wadsworth, W.

Walmsley, I. A

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

Walmsley, I. A.

K. Garay-Palmett, H. J. McGuinness, O. Cohen, J. S. Lundeen, R. Rangel-Rojo, A. B. U’ren, M. G. Raymer, C. J. McKinstrie, S. Radic, and I. A. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14,870–14,886 (2007).
[CrossRef]

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

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).

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063,815 (2001).
[CrossRef]

W. P. Grice, and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56(2), 1627–1634 (1997).
[CrossRef]

Walton, Z. D.

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[CrossRef]

Wang, K.

K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” J. Phys. B 39(18), R293–R324 (2006).
[CrossRef]

Wasylczyk, P.

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Wiseman, H. M.

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

Wong, F. N. C.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
[CrossRef]

Xiong, C.

Zeilinger, A

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
[CrossRef]

Zeilinger, A.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (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(23), 15377–15386 (2007).
[CrossRef] [PubMed]

IEEE J. Quantum Electron.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. QE-28, 2631–2654 (1992).
[CrossRef]

J. Mod. Opt.

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49(14–15), 2309–2323 (2002).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

K. Wang, “Quantum theory of two-photon wavepacket interference in a beamsplitter,” J. Phys. B 39(18), R293–R324 (2006).
[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).

Nat. Photonics

N. Gisin, and R. Thew, “Quantum communication,” Nat. Photonics 1(3), 165–171 (2007).
[CrossRef]

G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nat. Photonics 4(4), 227–230 (2010).
[CrossRef]

Nature

B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberglimited phase estimation,” Nature 450(7168), 393–396 (2007).
[CrossRef]

New J. Phys

M. A. Branczyk, T. C. Ralph, W . Helwig, and C . Silberhorn, “Optimised generation of heralded Fock states using parametric down conversion,” New J. Phys.  12, 063,001 (2010).
[CrossRef]

A. Fedrizzi, T. Herbst, M . Aspelmeyer, M . Barbieri, T. Jennewein, and A . Zeilinger, “Anti-symmetrization reveals hidden entanglement,” New J. Phys. 11, 103,052 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

K. Thyagarajan, J. Lugani, S. Ghosh, K. Sinha, A. Martin, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, “Generation of polarization-entangled photons using type-II doubly periodically poled lithium niobate waveguides,” Phys. Rev. A 80, 052321 (2009).
[CrossRef]

M. G. Raymer, J. Noh, K. Banaszek, and I. A. Walmsley, “Pure-state single-photon wave-packet generation by parametric down-conversion in a distributed microcavity,” Phys. Rev. A 72(2), 023,825 (2005).
[CrossRef]

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A64(6), 063,815 (2001).
[CrossRef]

L. Olislager, J. Cussey, A. Nguyen, P. Emplit, S. Massar, J. Merolla, K. Huy, H . Cecena-Alvarez, A . Peimbert-Torres, R . Gomez-Gonzalez, et al., “Frequency-bin entangled photons,” Phys. Rev. A 82(1), 13,804 (2010).
[CrossRef]

T. Kim, M. Fiorentino, and F. N. C. Wong, “Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer,” Phys. Rev. A 73(1), 12,316 (2006).
[CrossRef]

W. P. Grice, and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56(2), 1627–1634 (1997).
[CrossRef]

Z. D. Walton, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Generation of polarization-entangled photon pairs with arbitrary joint spectrum,” Phys. Rev. A 70(5), 052,317 (2004).
[CrossRef]

M. Corona and A. B . U’Ren, “Parametric down-conversion with optimized spectral properties in nonlinear photonic crystals,” Phys. Rev. A 76(4), 043829 (2007).
[CrossRef]

A. B . U’Ren, Y . Jeronimo-Moreno, and H . Garcia-Gracia, “Generation of Fourier-transform-limited heralded single photons,” Phys. Rev. A 75(2), 023810 (2007).
[CrossRef]

P. P. Rohde, T. C. Ralph, and M. A. Nielsen, “Optimal photons for quantum-information processing,” Phys. Rev. A72(5), 052,332 (2005).
[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(6), 5122–5133 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett

M. Nasr, S. Carrasco, B. Saleh, A. Sergienko, M. Teich, J. Torres, L. Torner, D. Hum, and M. Fejer, “Ultrabroadband biphotons generated via chirped quasi-phase-matched optical parametric down-conversion,” Phys. Rev. Lett.  100(18), 183,601 (2008).

A. B . U’Ren, R. K . Erdmann, M . de la Cruz-Gutierrez, and I. A . Walmsley, “Generation of Two-Photon States with an Arbitrary Degree of Entanglement Via Nonlinear Crystal Superlattices,” Phys. Rev. Lett.  97(22), 223,602 (2006).
[CrossRef]

Phys. Rev. Lett.

O. Kuzucu, F. N. C. Wong, S. Kurimura, and S. Tovstonog, “Joint Temporal Density Measurements for Two-Photon State Characterization,” Phys. Rev. Lett. 101(15), 153602 (2008).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, and P. Wasylczyk, A. B . U’Ren, C . Silberhorn, and I. A . Walmsley, “Heralded Generation of Ultrafast Single Photons in Pure Quantum States,” Phys. Rev. Lett. 100(13), 133601 (2008).
[CrossRef] [PubMed]

A. Valencia, A. Cere, X. Shi, G. Molina-Terriza, and J. P. Torres, “Shaping theWaveform of Entangled Photons,” Phys. Rev. Lett. 99(24), 243,601 (2007).
[CrossRef]

C. Hong, Z. Ou, and L. Mandel, “Measurement of Subpicosecond Time Intervals between Two Photons by Interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[CrossRef] [PubMed]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103(25), 253601 (2009).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85(13), 2733–2736 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys

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(1), 135 (2007).
[CrossRef]

Science

T. Nagata, R. Okamoto, J. L. O’Brien, K. Sasaki, and S. Takeuchi, “Beating the Standard Quantum Limit with Four-Entangled Photons,” Science 316(5825), 726 (2007).
[CrossRef] [PubMed]

Other

The crystal was custom-made by Raicol Crystals Ltd., www.raicol.com.

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Figures (5)

Fig. 1
Fig. 1

a) Nonlinearity profile for the cpKTP crystal χT(z) (orange line) and target Gaussian profile χG(z) = exp(−(z/Leff)2/γ) (black dashed line) with effective length Leff = 5.67mm (green dot-dashed line) and γ ≈ 0.193 (see Appendix C). b) Phase-matching function amplitudes and intensities (inset) for the cpKTP (orange line) compared to a pp-KTP of the same effective length Leff (green dot-dashed line) and target Gaussian profile ΦG(ωi, ωs) = exp(−γkL/2)2) (black dashed line). c) Magnified image of part of the custom-poled KTP crystal. Vertical lines separate sections with constant effective nonlinearity, with their poling order m, length L and poling duty cycle D. d) Magnified view of the transition from poling order m=1 to m=2 [12]. Due to a slight mismatch between design and actual domain lengths, the crystal was shortened by a few tens of μm on one side.

Fig. 2
Fig. 2

a) Experimental scheme. The crystals (cpKTP, ppKTP) were temperature-stabilised (TEC) and pumped by a 410 nm, grating-stabilised diode laser. The emitted orthogonally polarised photon pairs were split at a polarising beamsplitter (PBS) and coupled into single-mode fibres equipped with polarisation-controllers (POL). They were then superposed at a 50/50 fiber beamsplitter (BS) and detected in coincidence. We obtained two-photon interference patterns by changing the delay Δt with a motorised translation stage. The only filters in use were two RG715 long-pass filters (LP). b) Two-photon interference patterns for the cpKTP (red circles) compared to a standard ppKTP (green diamonds). The solid lines show the theoretical values, calculated from the respective PMF for each crystal. The reduced chi-square values of these fits are 3.07 and 5.51, respectively. The dashed lines show least-square fits of a triangular pattern to the tailored crystal data and a Gaussian fitted to the normal crystal, with reduced chi-square values of 50.59 and 23.10, underlining the strong divergence from these shapes. c) Spatial quantum beating for various center-frequency detunings Δω = ωiωs. The lines show the ideal values, calculated from the respective PMF. All probabilities pc for b) and c) were obtained by normalising detected pairs to twice the averaged counts outside the coherence length. The only free parameter for theory values was the interference visibility of ∼ 95%. All error bars are smaller than symbol size.

Fig. 3
Fig. 3

Phase matching functions generated from the basic model (black solid line) and the detailed model (light red line). The inset shows a magnified portion of the PMFs, detailing the deviation between the models.

Fig. 4
Fig. 4

a) Nonlinearity profiles and b) corresponding PMFs for: m = 1 tailored crystal (solid black line); m = 2 tailored crystal (dot-dashed black line); and an ideal crystal with a Gaussian profile (dashed red line). The corresponding sinc PMF (thin dotted line) has been included for comparison.

Fig. 5
Fig. 5

a) Examples of tailored nonlinearity profiles, and corresponding phasematching functions, for a) a triangular phase-matching function and b) a top-hat function. The dashed red line shows the target functions and the black line the results of the discrete approximation.

Tables (1)

Tables Icon

Table 1 Numerical comparison of the purity P of heralded single-photons of a standard crystal and two cpKTP crystals of length L, in a group-velocity-matched scenario. The effective length of both cpKTP crystals is Leff=24.2mm.

Equations (9)

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

| ψ = d ω i d ω s f ( ω i , ω s ) a ^ i ( ω i ) a ^ s ( ω s ) | 0 ,
Φ ( ω i , ω s ) = 2 π χ ( z ) e i Δ k ( ω i , ω s ) z d z ,
H ( t ) = A d ω i d ω s d ω p α ( ω p ) e i Δ ω t a ^ i ( ω i ) a ^ s ( ω s ) × L / 2 L / 2 d z χ ( 2 ) e i Δ k ( ω i , ω s , ω p ) z + H . c . ,
H ( t ) = A L d ω i d ω s d ω p α ( ω p ) Φ ( Δ k ( ω i , ω s , ω s ) ) × e i Δ ω t a ^ i ( ω i ) a ^ s ( ω s ) + H . c . ,
Φ ( Δ k ( ω i , ω s , ω p ) ) = sinc ( 1 2 Δ k ( ω i , ω s , ω p ) L )
| ψ = d ω i d ω s f ( ω i , ω s ) a ^ i ( ω i ) a ^ s ( ω s ) | 0 ,
χ T ( z ) = s = 1 21 1 m s u ( 1 2 r = 1 s m r n r Λ z ) × u ( z 1 2 r = 1 s 1 m r n r Λ ) ,
Φ D ( Δ k p ) = χ ( 2 ) j s j ( e i Δ k p z j e i Δ k p z j 1 ) ,
f ( ω i , ω s ) exp ( ( ω i + ω s 2 μ ) 2 2 σ p 2 ) × exp ( γ Δ k 2 L 2 4 ) ,

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