Abstract

This work proposes and analyses a novel approach for the generation of separable (quantum uncorrelated) photon pairs based on spontaneous parametric down-conversion in Bragg reflection waveguides composed of semiconductor AlGaN layers. This platform allows the removal of any spectral correlation between paired photons that propagate in different spatial modes. The photons can be designed to show equal or different spectra by tuning the structural parameters and hence the dispersion of the waveguide.

© 2011 Optical Society of America

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  1. P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
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  2. I. A. Walmsley, and M. G. Raymer, "Toward quantum-information processing with photons," Science 307, 1733 (2005).
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  3. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
    [CrossRef]
  4. L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
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  5. T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
    [CrossRef]
  6. W. P. Grice, A. B. U’Ren, and I. A. Walmsley, "Eliminating frequency and space-time correlation in multiphoton states," Phys. Rev. A 64, 063815 (2001).
    [CrossRef]
  7. P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
    [CrossRef] [PubMed]
  8. J. P. Torres, F. Macià, S. Carrasco, and L. Torner, "Engineering the frequency correlations of entangled two photon states by achromatic phase matching," Opt. Lett. 30, 314 (2005).
    [CrossRef] [PubMed]
  9. M. Hendrych, M. Mičuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339 (2007).
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  12. A. B. U’Ren, K. Banaszek, and I. A. Walmsley, "Photon engineering for quantum information processing," Quantum Inf. Comput. 3, 480 (2003).
  13. S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
    [CrossRef]
  14. A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (2007).
    [CrossRef]
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    [CrossRef]
  17. B. R. West, and A. S. Helmy, "Dispersion tailoring of the quarter-wave Bragg reflection waveguide," Opt. Express 14, 4073 (2006).
    [CrossRef] [PubMed]
  18. P. Abolghasem, M. Hendrych, X. Shi, J. P. Torres, and A. Helmy, "Bandwidth control of paired photons generated in monolithic Bragg reflection waveguides," Opt. Lett. 34, 2000 (2009).
    [CrossRef] [PubMed]
  19. Notice that here Ep(ωs + ωi) refers to the spectral amplitude of the pump beam at the input face of the waveguide, while the operators as(ω0s + Ωs) and ai(ω0i + Ωi) refer to the quantum state at the output face of the waveguide. Under these conditions (see [8]), the exponential factor contained in the biphoton amplitude is of the form exp(iskL/2). Different definitions of Ep and as and ai lead to slightly different expressions for the exponential factor of the biphoton amplitude. This is the case, for instance, in [6], where Ep refers to the spectral amplitude of the pump beam at the output face of the nonlinear crystal, while the same definition of the quantum operators as and ai is used. Now the exponential factor contained in the biphoton amplitude is of the form exp(−iΔkL/2). Indeed, when Ep and the quantum operators are referred to the center of the nonlinear crystal, there is no exponential factor at all [see S. P. Walborn, A. N. de Oliveira, S. Padua, and C. H. Monken, "Multimode Hong-Ou-Mandel interference," Phys. Rev. Lett. 90, 143601 (2003)]. Of course, all of these expressions are related and should yield the same result when calculating correlation functions, since the electric field operators should also be correspondingly modified in each case.
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  23. G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
    [CrossRef]
  24. S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
    [CrossRef]
  25. M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, 2000).

2010 (2)

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

J. P. Torres, M. Hendrych, and A. Valencia, "Angular dispersion: an enabling tool in nonlinear and quantum optics," Adv. Opt. Photon. 2, 319 (2010).
[CrossRef]

2009 (1)

2008 (2)

X. Shi, A. Valencia, M. Hendrych, and J. Torres, "Generation of indistinguishable and pure heralded single photons with tunable bandwidth," Opt. Lett. 33, 875 (2008).
[CrossRef] [PubMed]

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

2007 (3)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (2007).
[CrossRef]

M. Hendrych, M. Mičuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339 (2007).
[CrossRef]

2006 (3)

J. H. Eberly, "Schmidt analysis of pure-state entanglement," Laser Phys. 16, 921 (2006).
[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, 223602 (2006).
[CrossRef]

B. R. West, and A. S. Helmy, "Dispersion tailoring of the quarter-wave Bragg reflection waveguide," Opt. Express 14, 4073 (2006).
[CrossRef] [PubMed]

2005 (4)

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

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

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

I. A. Walmsley, and M. G. Raymer, "Toward quantum-information processing with photons," Science 307, 1733 (2005).
[CrossRef] [PubMed]

2004 (1)

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

2003 (2)

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

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

2002 (1)

T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
[CrossRef]

2001 (2)

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

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

1995 (1)

A. Ekert, and P. L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415 (1995).
[CrossRef]

Abolghasem, P.

Aichele, T.

T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
[CrossRef]

Banaszek, K.

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

Booth, M. C.

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

Carrasco, S.

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

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Ceré, A.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (2007).
[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, 223602 (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," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

Eberly, J. H.

J. H. Eberly, "Schmidt analysis of pure-state entanglement," Laser Phys. 16, 921 (2006).
[CrossRef]

Ekert, A.

A. Ekert, and P. L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415 (1995).
[CrossRef]

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, 223602 (2006).
[CrossRef]

Grandjean, N.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Grice, W. P.

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

Harrison, I.

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Helmy, A.

Helmy, A. S.

Hendrych, M.

Knight, P. L.

A. Ekert, and P. L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415 (1995).
[CrossRef]

Kok, P.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

Larkins, E. C.

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Laws, G. M.

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Lundeen, J. S.

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

Lvovsky, A. I.

T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
[CrossRef]

Macià, F.

Massies, J.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Micuda, M.

Milburn, G. J.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

Molina-Terriza, G.

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (2007).
[CrossRef]

Molloy, C.

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Mosley, P. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 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," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

Nemoto, K.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

O’Brien, J. L.

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

Osorio, C. I.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

Pezzagna, S.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Pryde, G. J.

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

Ralph, T. C.

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

Rangarajan, R.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

Raymer, M. G.

I. A. Walmsley, and M. G. Raymer, "Toward quantum-information processing with photons," Science 307, 1733 (2005).
[CrossRef] [PubMed]

Rohde, P. P.

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

Saleh, B. E.

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Saleh, B. E. A.

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

Schiller, S.

T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
[CrossRef]

Sergienko, A. V.

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

Shi, X.

Silberhorn, C.

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

Smith, B. J.

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

Somerford, D.

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Teich, M. C.

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

Torner, L.

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

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Torres, J.

Torres, J. P.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

J. P. Torres, M. Hendrych, and A. Valencia, "Angular dispersion: an enabling tool in nonlinear and quantum optics," Adv. Opt. Photon. 2, 319 (2010).
[CrossRef]

P. Abolghasem, M. Hendrych, X. Shi, J. P. Torres, and A. Helmy, "Bandwidth control of paired photons generated in monolithic Bragg reflection waveguides," Opt. Lett. 34, 2000 (2009).
[CrossRef] [PubMed]

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (2007).
[CrossRef]

M. Hendrych, M. Mičuda, and J. P. Torres, "Tunable control of the frequency correlations of entangled photons," Opt. Lett. 32, 2339 (2007).
[CrossRef]

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

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

U’Ren, A. B.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 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, 223602 (2006).
[CrossRef]

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

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

Valencia, A.

Vennéguès, P.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Vicent, L. E.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

Walmsley, I. A.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 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, 223602 (2006).
[CrossRef]

I. A. Walmsley, and M. G. Raymer, "Toward quantum-information processing with photons," Science 307, 1733 (2005).
[CrossRef] [PubMed]

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

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

Walton, Z. D.

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

Wasylczyk, P.

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

West, B. R.

Wieck, A. D.

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Zhang, L.

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

Adv. Opt. Photon. (1)

Am. J. Phys. (1)

A. Ekert, and P. L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

S. Pezzagna, P. Vennéguès, N. Grandjean, A. D. Wieck, and J. Massies, "Submicron periodic poling and chemical patterning of GaN," Appl. Phys. Lett. 87, 062106 (2005).
[CrossRef]

Eur. Phys. J. D (1)

T. Aichele, A. I. Lvovsky, and S. Schiller, "Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state," Eur. Phys. J. D 18, 237 (2002).
[CrossRef]

J. Appl. Phys. (1)

G. M. Laws, E. C. Larkins, I. Harrison, C. Molloy, and D. Somerford, "Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys," J. Appl. Phys. 89, 1108 (2001).
[CrossRef]

Laser Phys. (1)

J. H. Eberly, "Schmidt analysis of pure-state entanglement," Laser Phys. 16, 921 (2006).
[CrossRef]

N. J. Phys. (1)

L. E. Vicent, A. B. U’Ren, R. Rangarajan, C. I. Osorio, J. P. Torres, L. Zhang, and I. A. Walmsley, "Design of bright, fiber-coupled and fully factorable photon pair sources," N. J. Phys. 12, 093027 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (4)

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

P. P. Rohde, G. J. Pryde, J. L. O’Brien, and T. C. Ralph, "Quantum gate characterization in an extended Hilbert space," Phys. Rev. A 72, 032306 (2005).
[CrossRef]

Z. D. Walton, M. C. Booth, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, "Controllable frequency entanglement via auto-phase-matched spontaneous parametric down-conversion," Phys. Rev. A 67, 053810 (2003).
[CrossRef]

S. Carrasco, J. P. Torres, L. Torner, A. V. Sergienko, B. E. Saleh, and M. C. Teich, "Spatial-to-spectral mapping in spontaneous parametric down-conversion," Phys. Rev. A 70, 043817 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

A. Valencia, A. Ceré, X. Shi, G. Molina-Terriza, and J. P. Torres, "Shaping the waveform of entangled photons," Phys. Rev. Lett. 99, 243601 (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, 223602 (2006).
[CrossRef]

P. J. Mosley, J. S. Lundeen, B. J. Smith, 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, 133601 (2008).
[CrossRef] [PubMed]

Quantum Inf. Comput. (1)

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

Rev. Mod. Phys. (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, "Linear optical quantum computing," Rev. Mod. Phys. 79, 135 (2007).
[CrossRef]

Science (1)

I. A. Walmsley, and M. G. Raymer, "Toward quantum-information processing with photons," Science 307, 1733 (2005).
[CrossRef] [PubMed]

Other (3)

Notice that here Ep(ωs + ωi) refers to the spectral amplitude of the pump beam at the input face of the waveguide, while the operators as(ω0s + Ωs) and ai(ω0i + Ωi) refer to the quantum state at the output face of the waveguide. Under these conditions (see [8]), the exponential factor contained in the biphoton amplitude is of the form exp(iskL/2). Different definitions of Ep and as and ai lead to slightly different expressions for the exponential factor of the biphoton amplitude. This is the case, for instance, in [6], where Ep refers to the spectral amplitude of the pump beam at the output face of the nonlinear crystal, while the same definition of the quantum operators as and ai is used. Now the exponential factor contained in the biphoton amplitude is of the form exp(−iΔkL/2). Indeed, when Ep and the quantum operators are referred to the center of the nonlinear crystal, there is no exponential factor at all [see S. P. Walborn, A. N. de Oliveira, S. Padua, and C. H. Monken, "Multimode Hong-Ou-Mandel interference," Phys. Rev. Lett. 90, 143601 (2003)]. Of course, all of these expressions are related and should yield the same result when calculating correlation functions, since the electric field operators should also be correspondingly modified in each case.
[CrossRef] [PubMed]

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley-IEEE Press, 2002).

M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, 2000).

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Figures (6)

Fig. 1
Fig. 1

General scheme for generating frequency-uncorrelated photon pairs. The waveguide is pumped by a TIR mode with TE polarization. The down-converted photons with TE polarization propagate in a Bragg mode, while the down-converted photons with TM polarization propagate in a TIR mode. The two structures presented in Section 3 make use of the same combination of modes and the spatial shapes of the modes are almost identical for both structures. The Bragg and TIR modes have different group velocities that can be properly engineered by modifying the waveguide structure.

Fig. 2
Fig. 2

(a) Profile of the refractive index along the y-axis of the Bragg reflection waveguide. tc - core thickness; t1,2 - thicknesses of the alternating layers of the Bragg reflector; xc - aluminium concentration in the core; x1,2 - aluminium concentration in the reflector’s layers; Λ- quasi-phase-matching period. Both structures are 4 mm long and they are optimized for type-II SPDC.

Fig. 3
Fig. 3

The Schmidt number K as a function of the bandwidth of the pump beam Δλp.

Fig. 4
Fig. 4

(a) Joint spectral intensity of the biphoton generated in Structure 1 for Δλp=10 nm. (b) The Schmidt decomposition corresponding to this quantum state.

Fig. 5
Fig. 5

The Schmidt number K of the state generated in Structure 2 as a function of pump bandwidth Δλp.

Fig. 6
Fig. 6

Joint spectral intensity of photons generated in Structure 2 for different pump bandwidths: a) Δλp = 1.3 nm, b) Δλp = 0.3 nm and c) Δλp = 4.8 nm. Plots (d), (e) and (f) in the second line are the corresponding Schmidt decompositions.

Equations (5)

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| Ψ = d Ω s d Ω i Φ ( Ω s , Ω i ) a ^ s ( ω s 0 + Ω s ) a ^ i ( ω i 0 + Ω i ) | 0 s | 0 i ,
Φ ( Ω s , Ω i ) = 𝒩 E p ( ω s + ω i ) sinc ( Δ k L 2 ) exp ( i s k L 2 ) ,
Φ ( Ω s , Ω i ) = 𝒩 exp { ( Ω s + Ω i ) 2 Δ w p 2 } sinc { [ ( N p N s ) Ω s + ( N p N i ) Ω i ] L 2 } × exp { i [ ( N p + N s ) Ω s + ( N p + N i ) Ω i ] L 2 } .
Δ ω p 2 α L N s N p N p N i .
Γ = d x u p ( x ) u s * ( x ) u i * ( x ) ,

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