Abstract

We present a simple method of simulating the effect of the pumping process in spontaneous parametric down-conversion (SPDC) by modulating a classical laser beam with two spatial light modulators through a back projection setup. We simulate a wide range of pump beams for quantum state engineering and confirm that the results are in agreement with theory. Our approach offers high photon count rates, is quick to yield results and can easily be converted back to a SPDC setup. It is likely to be a useful tool before starting more complicated SPDC experiments with custom pump profiles.

© 2014 Optical Society of America

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  1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
    [CrossRef]
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  3. B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
    [CrossRef]
  4. J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
    [CrossRef] [PubMed]
  5. A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
    [CrossRef]
  6. J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
    [CrossRef]
  7. L. Chen and J. Romero, “Hardy’s nonlocality proof using twisted photons,” Opt. Express 20, 21687–21692 (2012).
    [CrossRef] [PubMed]
  8. E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
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  10. M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
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  11. M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
    [CrossRef] [PubMed]
  12. M. Mclaren, J. Romero, M. J. Padgett, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
    [CrossRef]
  13. M. Mclaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nature Commun. 5, 3248 (2014).
    [CrossRef]
  14. M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
    [CrossRef]
  15. H. Di Lorenzo Pires, H. Florijn, and M. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
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  16. J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
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  17. J. Barreiro, N. Langford, N. Peters, and P. Kwiat, “Generation of hyper-entangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
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  18. M. Malik, M. Mirhosseini, M. Lavery, J. Leach, M. Padgett, and R. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nature Commun. 5, 3115 (2014).
    [CrossRef]
  19. R. Fickler, R. Lapkiewicz, M. Huber, M. Lavery, M. Padgett, and A. Zeilinger, “Interface between path and OAM entanglement for high-dimensional photonic quantum information,” arXiv:1402.2423v2 (2014).
  20. D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
    [CrossRef]
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    [CrossRef]
  22. B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
    [CrossRef]
  23. M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).
  24. K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors,” Scientific Reports 3, 3548 (2013).
    [CrossRef] [PubMed]
  25. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65, 033823 (2002).
    [CrossRef]
  26. J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
    [CrossRef]
  27. E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868 (1999).
    [CrossRef]
  28. S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
    [CrossRef]
  29. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
    [CrossRef]
  30. T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
    [CrossRef]
  31. R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
    [CrossRef] [PubMed]
  32. J. Romero, D. Giovannini, M. G. Mclaren, E. J. Galvez, A. Forbes, and M. J. Padgett, “Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam,” J. Opt. 14, 085401 (2012).
    [CrossRef]
  33. D. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the EinsteinPodolskyRosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74 (1988)
    [CrossRef]
  34. R. S. Aspden, D. S. Tasca, A. Forbes, R. W. Boyd, and M. J. Padgett, “Experimental demonstration of Klyshkos advanced-wave picture using a coincidence-count based, camera-enabled imaging system,” J. Mod. Opt. 10.1080/09500340.2014.899645 (2014).
    [CrossRef]
  35. F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
    [CrossRef]
  36. Y. Zhang and F. S. Roux, “Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching,” Phys. Rev. A 89, 063802 (2014).
    [CrossRef]
  37. Y. Zhang, F. S. Roux, M. Mclaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
    [CrossRef]
  38. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
    [CrossRef]
  39. T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of LaguerreGaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett. 34, 34–36 (2009)
    [CrossRef]

2014 (5)

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

M. Mclaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nature Commun. 5, 3248 (2014).
[CrossRef]

M. Malik, M. Mirhosseini, M. Lavery, J. Leach, M. Padgett, and R. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nature Commun. 5, 3115 (2014).
[CrossRef]

Y. Zhang and F. S. Roux, “Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching,” Phys. Rev. A 89, 063802 (2014).
[CrossRef]

Y. Zhang, F. S. Roux, M. Mclaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[CrossRef]

2013 (5)

K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors,” Scientific Reports 3, 3548 (2013).
[CrossRef] [PubMed]

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[CrossRef]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. Mclaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lutkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[CrossRef]

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
[CrossRef]

M. Mclaren, J. Romero, M. J. Padgett, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[CrossRef]

2012 (4)

M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[CrossRef] [PubMed]

L. Chen and J. Romero, “Hardy’s nonlocality proof using twisted photons,” Opt. Express 20, 21687–21692 (2012).
[CrossRef] [PubMed]

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
[CrossRef]

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

2011 (2)

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
[CrossRef]

2010 (4)

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[CrossRef]

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
[CrossRef]

H. Di Lorenzo Pires, H. Florijn, and M. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

2009 (3)

B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
[CrossRef]

T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of LaguerreGaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett. 34, 34–36 (2009)
[CrossRef]

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

2007 (4)

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

2005 (2)

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[CrossRef]

J. Barreiro, N. Langford, N. Peters, and P. Kwiat, “Generation of hyper-entangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

2004 (1)

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[CrossRef]

2003 (1)

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[CrossRef]

2002 (1)

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65, 033823 (2002).
[CrossRef]

2001 (1)

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

1999 (1)

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

1988 (1)

D. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the EinsteinPodolskyRosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74 (1988)
[CrossRef]

Abouraddy, A. F.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

Agnew, M.

M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[CrossRef] [PubMed]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
[CrossRef]

Aiello, A.

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[CrossRef]

Alexandrescu, A.

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[CrossRef]

Allen, L.

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Almeida, M.

B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
[CrossRef]

Ando, T.

Arrizón, V.

Aspden, R. S.

R. S. Aspden, D. S. Tasca, A. Forbes, R. W. Boyd, and M. J. Padgett, “Experimental demonstration of Klyshkos advanced-wave picture using a coincidence-count based, camera-enabled imaging system,” J. Mod. Opt. 10.1080/09500340.2014.899645 (2014).
[CrossRef]

Barbieri, M.

B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
[CrossRef]

Barnett, S. M.

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
[CrossRef]

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
[CrossRef]

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65, 033823 (2002).
[CrossRef]

Barreiro, J.

J. Barreiro, N. Langford, N. Peters, and P. Kwiat, “Generation of hyper-entangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

Boyd, R.

M. Malik, M. Mirhosseini, M. Lavery, J. Leach, M. Padgett, and R. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nature Commun. 5, 3115 (2014).
[CrossRef]

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[CrossRef] [PubMed]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
[CrossRef]

Boyd, R. W.

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

R. S. Aspden, D. S. Tasca, A. Forbes, R. W. Boyd, and M. J. Padgett, “Experimental demonstration of Klyshkos advanced-wave picture using a coincidence-count based, camera-enabled imaging system,” J. Mod. Opt. 10.1080/09500340.2014.899645 (2014).
[CrossRef]

Cardano, F.

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

Cardano, M.

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

Carrada, R.

Chen, L.

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
[CrossRef]

de Lisio, C.

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

de Oliveira, A. N.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[CrossRef]

Di Lorenzo Pires, H.

H. Di Lorenzo Pires, H. Florijn, and M. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

Dudley, A.

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[CrossRef]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. Mclaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lutkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[CrossRef]

Eliel, E. R.

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[CrossRef]

Fickler, R.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
[CrossRef]

R. Fickler, R. Lapkiewicz, M. Huber, M. Lavery, M. Padgett, and A. Zeilinger, “Interface between path and OAM entanglement for high-dimensional photonic quantum information,” arXiv:1402.2423v2 (2014).

Florijn, H.

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M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
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[CrossRef]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. Mclaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lutkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
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[CrossRef]

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[CrossRef]

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
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J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
[CrossRef]

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[CrossRef]

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[CrossRef]

M. Mclaren, J. Romero, M. J. Padgett, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[CrossRef]

L. Chen and J. Romero, “Hardy’s nonlocality proof using twisted photons,” Opt. Express 20, 21687–21692 (2012).
[CrossRef] [PubMed]

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
[CrossRef]

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

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[CrossRef]

J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
[CrossRef]

Roux, F.

M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[CrossRef] [PubMed]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
[CrossRef]

Roux, F. S.

M. Mclaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nature Commun. 5, 3248 (2014).
[CrossRef]

Y. Zhang, F. S. Roux, M. Mclaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[CrossRef]

Y. Zhang and F. S. Roux, “Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching,” Phys. Rev. A 89, 063802 (2014).
[CrossRef]

Ruiz, U.

Saleh, B. E. A.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

Salles, A.

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

Santamato, E.

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

Sciarrino, F.

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

Slussarenko, S.

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

Souto Ribeiro, P. H.

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

Tasca, D. S.

R. S. Aspden, D. S. Tasca, A. Forbes, R. W. Boyd, and M. J. Padgett, “Experimental demonstration of Klyshkos advanced-wave picture using a coincidence-count based, camera-enabled imaging system,” J. Mod. Opt. 10.1080/09500340.2014.899645 (2014).
[CrossRef]

Teich, M. C.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

Thebaldi, R. S.

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[CrossRef]

Toscano, F.

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

van Exter, M.

H. Di Lorenzo Pires, H. Florijn, and M. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

Vaziri, A.

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

Walborn, S. P.

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[CrossRef]

Weihs, G.

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

White, A.

B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
[CrossRef]

Woerdman, J. P.

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[CrossRef]

Yao, A. M.

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[CrossRef]

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

Yarnall, T.

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

Zeilinger, A.

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
[CrossRef]

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

R. Fickler, R. Lapkiewicz, M. Huber, M. Lavery, M. Padgett, and A. Zeilinger, “Interface between path and OAM entanglement for high-dimensional photonic quantum information,” arXiv:1402.2423v2 (2014).

Zhang, Y.

Y. Zhang and F. S. Roux, “Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching,” Phys. Rev. A 89, 063802 (2014).
[CrossRef]

Y. Zhang, F. S. Roux, M. Mclaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[CrossRef]

J. Opt. (1)

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

J. Opt. Soc. Am. A (1)

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

Nature (London) (1)

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

Nature Commun. (2)

M. Mclaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nature Commun. 5, 3248 (2014).
[CrossRef]

M. Malik, M. Mirhosseini, M. Lavery, J. Leach, M. Padgett, and R. Boyd, “Direct measurement of a 27-dimensional orbital-angular-momentum state vector,” Nature Commun. 5, 3115 (2014).
[CrossRef]

Nature Physics (1)

B. Lanyon, M. Barbieri, M. Almeida, T. Jennewein, T. Ralph, K. Resch, G. Pryde, J. O’Brien, A. Gilchrist, and A. White, “Simplifying quantum logic using higher-dimensional Hilbert spaces,” Nature Physics 5, 134–140 (2009).
[CrossRef]

New J. Phys. (1)

J. Romero, J. Leach, B. Jack, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Violation of Leggett inequalities in orbital angular momentum subspaces,” New J. Phys. 12, 123007 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (14)

F. M. Miatto, A. M. Yao, and S. M. Barnett, “Full characterization of the quantum spiral bandwidth of entangled biphotons,” Phys. Rev. A 83, 033816 (2011).
[CrossRef]

Y. Zhang and F. S. Roux, “Modal spectrum in spontaneous parametric down-conversion with noncollinear phase matching,” Phys. Rev. A 89, 063802 (2014).
[CrossRef]

Y. Zhang, F. S. Roux, M. Mclaren, and A. Forbes, “Radial modal dependence of the azimuthal spectrum after parametric down-conversion,” Phys. Rev. A 89, 043820 (2014).
[CrossRef]

S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, “Two-photon entanglement of orbital angular momentum states,” Phys. Rev. A 65, 033823 (2002).
[CrossRef]

J. P. Torres, A. Alexandrescu, and L. Torner, “Quantum spiral bandwidth of entangled two-photon states,” Phys. Rev. A 68, 050301 (2003).
[CrossRef]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. Mclaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lutkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[CrossRef]

S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, “Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,” Phys. Rev. A 69, 023811 (2004).
[CrossRef]

M. Mclaren, J. Romero, M. J. Padgett, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[CrossRef]

M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-gauss modes,” Phys. Rev. A 87, 012326 (2013).
[CrossRef]

J. Romero, D. Giovannini, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Increasing the dimension in high-dimensional two-photon orbital angular momentum entanglement,” Phys. Rev. A 86, 012334 (2012).
[CrossRef]

E. Karimi, F. Cardano, M. Maffei, C. de Lisio, L. Marrucci, R. Boyd, and E. Santamato, “Hardy’s paradox tested in the spin-orbit hilbert space of single photons,” Phys. Rev. A 89, 032122 (2014).
[CrossRef]

M. Agnew, J. Leach, M. McLaren, F. Roux, and R. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 062101 (2011).
[CrossRef]

B. Jack, A. M. Yao, J. Leach, J. Romero, S. Franke-Arnold, D. G. Ireland, S. M. Barnett, and M. J. Padgett, “Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces,” Phys. Rev. A 81, 043844 (2010).
[CrossRef]

A. Aiello, S. S. R. Oemrawsingh, E. R. Eliel, and J. P. Woerdman, “Nonlocality of high-dimensional two-photon orbital angular momentum states,” Phys. Rev. A 72, 052114 (2005).
[CrossRef]

Phys. Rev. Lett. (7)

J. Barreiro, N. Langford, N. Peters, and P. Kwiat, “Generation of hyper-entangled photon pairs,” Phys. Rev. Lett. 95, 260501 (2005).
[CrossRef]

H. Di Lorenzo Pires, H. Florijn, and M. van Exter, “Measurement of the spiral spectrum of entangled two-photon states,” Phys. Rev. Lett. 104, 020505 (2010).
[CrossRef] [PubMed]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Experimental violation of Bells inequality in spatial-parity space,” Phys. Rev. Lett. 99, 170408 (2007).
[CrossRef]

T. Yarnall, A. F. Abouraddy, B. E. A. Saleh, and M. C. Teich, “Synthesis and analysis of entangled photonic qubits in spatial-parity space,” Phys. Rev. Lett. 99, 250502 (2007).
[CrossRef]

R. M. Gomes, A. Salles, F. Toscano, P. H. Souto Ribeiro, and S. P. Walborn, “Observation of a nonlocal optical vortex,” Phys. Rev. Lett. 103, 033602 (2009).
[CrossRef] [PubMed]

D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, “Characterization of high-dimensional entangled systems via mutually unbiased measurements,” Phys. Rev. Lett. 110, 143601 (2013).
[CrossRef]

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82, 2868 (1999).
[CrossRef]

Science (1)

J. Leach, B. Jack, J. Romero, A. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angleorbital angular momentum variables,” Science 329, 662–665 (2010).
[CrossRef] [PubMed]

Scientific Reports (1)

K. Goyal and T. Konrad, “Teleporting photonic qudits using multimode quantum scissors,” Scientific Reports 3, 3548 (2013).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

D. Klyshko, “A simple method of preparing pure states of an optical field, of implementing the EinsteinPodolskyRosen experiment, and of demonstrating the complementarity principle,” Sov. Phys. Usp. 31, 74 (1988)
[CrossRef]

Other (4)

R. S. Aspden, D. S. Tasca, A. Forbes, R. W. Boyd, and M. J. Padgett, “Experimental demonstration of Klyshkos advanced-wave picture using a coincidence-count based, camera-enabled imaging system,” J. Mod. Opt. 10.1080/09500340.2014.899645 (2014).
[CrossRef]

M. Cardano, F. Francesco, E. Karimi, S. Slussarenko, D. Paparo, C. de Lisio, F. Sciarrino, E. Santamato, and L. Marrucci, “Photonic quantum walk in a single beam with twisted light,” arXiv:1403.4857v1 (2014).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2010).
[CrossRef]

R. Fickler, R. Lapkiewicz, M. Huber, M. Lavery, M. Padgett, and A. Zeilinger, “Interface between path and OAM entanglement for high-dimensional photonic quantum information,” arXiv:1402.2423v2 (2014).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of a typical back-projection setup (a) compared to that of a SPDC setup (b). Back-projection setup to simulate the pump profile is shown in (c) where the mirror in (a) is replaced by a SLM.

Fig. 2
Fig. 2

Generated hologram on the SLM with m p ( x ) m i , s * ( x ) encoded for a flat-top pump and LG signal and idler modes with p = 2, = 4. (a) and (b) uses Eq. (10) as m i , s * ( x ) with w = wp = 0.250 mm for (a) and w = wp = 0.450 mm for (b). (c) and (d) uses Eq. (7) as m i , s * ( x ) with w = wp = 0.250 mm for (c) and w = wp = 0.450 mm for (d).

Fig. 3
Fig. 3

Spiral bandwidth plots from the back-projection experiment for p = −4 and p = 6 is shown in (a) and (b) respectively. A cross-section along the diagonal of (a) and (b) is shown in (c) and (d) respectively with the circles representing experimental data and the solid line being the theory. Due to the high count rate of the back-projection experiment, error from the Poisson distribution of the count rate is negligible and is therefore not visible.

Fig. 4
Fig. 4

Spiral bandwidth plots measured for a flat-top pump in the LG basis. (a) is measured for the radial index pi = ps = 0 and (b) is for pi = 3 and ps = 4, the diagonals are shown in (c) and (d) respectively with circles representing experimental data and the solid line being the theory. Due to the high count rate of the back-projection experiment, error from the Poisson distribution of the count rate is negligible and is therefore not visible.

Fig. 5
Fig. 5

Comparison of spiral bandwidth plots for experiment and theory (shown as small inset) of a HG pump in the LG basis. (a), (b) and (c) are the experimental results for a HG11, HG22 and HG31 pump respectively with pi = ps = 0.

Equations (11)

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

= Ω 0 M s * ( q s ) M i * ( q i ) M p ( q s + q i ) S ( q s q i ) d 2 q s ( 2 π ) 2 d 2 q i ( 2 π ) 2
S ( q s q i ) = sinc = ( n o L w p 2 8 z R | q s q i | 2 ) ,
= Ω 0 m p ( x ) m s * ( x ) m i * ( x ) d 2 x ,
m p ( x ) = 1 w p ( 2 | p | | p | ! ) 1 / 2 ( r w p ) | p | exp ( r 2 w p 2 ) exp ( i p ϕ ) ,
m p ( x ) = { 1 π w p for r < w p 0 for r > w p ,
m p m , n ( x ) = 1 w p ( 1 2 n + m n ! m ! ) 1 / 2 exp ( x 2 + y 2 w p 2 ) H n ( 2 x w p ) H m ( 2 y w p ) ,
m s , i , p ( q ) = 1 w [ 2 | | p ! ( p + | | ) ! ] 1 / 2 ( r w ) | | exp ( r 2 w 2 ) L p | | ( 2 r 2 w 2 ) exp ( i ϕ ) ,
= Ω 0 m p ( x ) m s * ( x ) m i * ( x ) G 2 ( x ) d 2 x ,
G ( x ) = ( 2 π ) 1 / 2 1 w 0 exp ( x 2 + y 2 w 0 2 )
m s , i , p ( q ) = 1 w [ 2 | | p ! ( p + | | ) ! ] 1 / 2 ( r w ) | | exp ( r 2 ( w ) 2 ) L p | | ( 2 r 2 w 2 ) exp ( i ϕ ) ,
1 ( w ) 2 = 1 w 2 1 w 0 2 .

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