Abstract

Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. While the polarization degree of freedom of the photon is a common choice for many studies, it is restricted to only two orthogonal states, hence qubits for manipulation. In this paper, we theoretically model as well as experimentally verify a novel scheme of approximating photonic qutrits by modulating the pump beam in a spontaneous parametric down conversion process using a three-slit aperture. The emerging bi-photon fields behave like qutrits and are found to be highly correlated in the spatial degree of freedom and effectively represent spatially correlated qutrits with a Pearson coefficient as high as 0.9. In principle, this system provides us a scalable architecture for generating and experimenting with higher dimensional correlated qudits.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
    [Crossref] [PubMed]
  2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 1st ed. (Cambridge University Press, 2000).
  3. C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
    [Crossref] [PubMed]
  4. C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
    [Crossref]
  5. A. Gajewski and P. Kolenderski, “Spectral correlation control in down-converted photon pairs,” Phys. Rev. A 94, 013838 (2016).
    [Crossref]
  6. V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
    [Crossref]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [Crossref] [PubMed]
  8. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [Crossref]
  9. G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
    [Crossref]
  10. M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195 (2012).
    [Crossref] [PubMed]
  11. L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
    [Crossref]
  12. L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
    [Crossref] [PubMed]
  13. L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
    [Crossref]
  14. G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
    [Crossref]
  15. A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
    [Crossref] [PubMed]
  16. P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
    [Crossref]
  17. R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
    [Crossref] [PubMed]
  18. P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
    [Crossref] [PubMed]
  19. P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”
  20. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
    [Crossref]
  21. P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
    [Crossref]
  22. K. Pearson, “Notes on regression and inheritance in the case of two parents,” Proc. Royal Soc. Lond. 58, 240–242 (1895).
    [Crossref]
  23. R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
    [Crossref]

2016 (3)

A. Gajewski and P. Kolenderski, “Spectral correlation control in down-converted photon pairs,” Phys. Rev. A 94, 013838 (2016).
[Crossref]

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
[Crossref] [PubMed]

2015 (1)

A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
[Crossref] [PubMed]

2014 (2)

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

2012 (2)

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

M. Malik, M. O’Sullivan, B. Rodenburg, M. Mirhosseini, J. Leach, M. P. J. Lavery, M. J. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding,” Opt. Express 20, 13195 (2012).
[Crossref] [PubMed]

2010 (1)

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

2009 (2)

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
[Crossref]

2007 (3)

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

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
[Crossref]

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

2005 (1)

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

2004 (1)

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

2001 (1)

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

2000 (1)

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

1999 (1)

R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
[Crossref]

1998 (1)

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

1895 (1)

K. Pearson, “Notes on regression and inheritance in the case of two parents,” Proc. Royal Soc. Lond. 58, 240–242 (1895).
[Crossref]

Aguirre Gómez, J. G.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

Banaszek, K.

P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
[Crossref]

Bellisai, S.

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Boeuf, N.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Boyd, R. W.

Bramon, A.

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
[Crossref]

Branning, D.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Cabello, A.

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

Calvo, G. F.

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
[Crossref]

Chaperot, I.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 1st ed. (Cambridge University Press, 2000).

Couteau, C.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

Cruz-Ramírez, H.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Dauler, E.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Davidovich, L.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

Dougakiuchi, T.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Fonseca, E. J. S.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

Gajewski, A.

A. Gajewski and P. Kolenderski, “Spectral correlation control in down-converted photon pairs,” Phys. Rev. A 94, 013838 (2016).
[Crossref]

Guerin, S.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Hamel, D.

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Hamel, D. R.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Hofmann, H. F.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Holloway, C.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Iinuma, M.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Jaeger, G.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Jáuregui-Renaud, R.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Jennewein, T.

C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Jerónimo-Moreno, Y.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Johnsen, K. D.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Kadoya, Y.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Kolenderski, P.

A. Gajewski and P. Kolenderski, “Spectral correlation control in down-converted photon pairs,” Phys. Rev. A 94, 013838 (2016).
[Crossref]

C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
[Crossref]

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Laflamme, R.

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

Lavery, M. P. J.

Leach, J.

Lima, G.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

Mair, A.

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

Malik, M.

Migdall, A. L.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Mirhosseini, M.

Molina-Terriza, G.

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

Monken, C. H.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Muller, A.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Neves, L.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 1st ed. (Cambridge University Press, 2000).

O’Sullivan, M.

Padgett, M. J.

Pádua, S.

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Pearson, K.

K. Pearson, “Notes on regression and inheritance in the case of two parents,” Proc. Royal Soc. Lond. 58, 240–242 (1895).
[Crossref]

Picón, A.

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
[Crossref]

Pugh, C. J.

Ramírez-Alarcón, R.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Resch, K.

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Resch, K. J.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Ribeiro, P. H. S.

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

Rodenburg, B.

Saavedra, C.

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

Samuel, J.

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

Santiago, J. T.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Sawant, R.

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

Scarcella, C.

C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Shalm, L. K.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Sinha, A.

A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
[Crossref] [PubMed]

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

Sinha, S.

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

Sinha, U.

A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
[Crossref] [PubMed]

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

Taguchi, G.

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

Tisa, S.

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Torner, L.

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

Torres, J. P.

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

Tosi, A.

C. J. Pugh, P. Kolenderski, C. Scarcella, A. Tosi, and T. Jennewein, “Towards correcting atmospheric beam wander via pump beam control in a down conversion process,” Opt. Express 24, 20947–20955 (2016).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

Uren, A. B.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Vaziri, A.

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

Vicuña-Hernández, V.

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

Vijay, A. H.

A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
[Crossref] [PubMed]

Volpini, M.

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

Wasilewski, W.

P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
[Crossref]

Weihs, G.

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

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

Youning, L.

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

Zeilinger, A.

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

Zhao, T.

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

J. Mod. Opt. (1)

R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46, 367–378 (1999).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

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

Opt. Eng. (1)

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. L. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Opt. Express (2)

Phys, Rev, A (1)

L. Neves, G. Lima, E. J. S. Fonseca, L. Davidovich, and S. Pádua, “Characterizing entanglement in qubits created with spatially correlated twin photons,” Phys, Rev, A 76, 032314 (2007).
[Crossref]

Phys. Rev. A (8)

G. Taguchi, T. Dougakiuchi, M. Iinuma, H. F. Hofmann, and Y. Kadoya, “Reconstruction of spatial qutrit states based on realistic measurement operators,” Phys. Rev. A 80, 062102 (2009).
[Crossref]

L. Neves, S. Pádua, and C. Saavedra, “Controlled generation of maximally entangled qudits using twin photons,” Phys. Rev. A 69, 042305 (2004).
[Crossref]

P. Kolenderski, U. Sinha, L. Youning, T. Zhao, M. Volpini, A. Cabello, R. Laflamme, and T. Jennewein, “Playing the Aharon-Vaidman quantum game with a young type photonic qutrit,” Phys. Rev. A 86, 012321 (2012).
[Crossref]

C. H. Monken, P. H. S. Ribeiro, and S. Pádua, “Transfer of angular spectrum and image formation in spontaneous parametric down-conversion,” Phys. Rev. A 57, 3123–3126 (1998).
[Crossref]

A. Gajewski and P. Kolenderski, “Spectral correlation control in down-converted photon pairs,” Phys. Rev. A 94, 013838 (2016).
[Crossref]

V. Vicuña-Hernández, J. T. Santiago, Y. Jerónimo-Moreno, R. Ramírez-Alarcón, H. Cruz-Ramírez, A. B. Uren, and R. Jáuregui-Renaud, “Double transverse wave-vector correlations in photon pairs generated by spontaneous parametric down-conversion pumped by Bessel-Gauss beams,” Phys. Rev. A 94, 063863 (2016).
[Crossref]

G. F. Calvo, A. Picón, and A. Bramon, “Measuring two-photon orbital angular momentum entanglement,” Phys. Rev. A 75,, 012319 (2007).
[Crossref]

P. Kolenderski, W. Wasilewski, and K. Banaszek, “Modelling and optimization of photon pair sources based on spontaneous parametric down-conversion,” Phys. Rev. A 80, 013811 (2009).
[Crossref]

Phys. Rev. Lett. (2)

R. Sawant, J. Samuel, A. Sinha, S. Sinha, and U. Sinha, “Nonclassical paths in quantum interference experiments,” Phys. Rev. Lett. 113, 120406 (2014).
[Crossref] [PubMed]

L. Neves, G. Lima, J. G. Aguirre Gómez, C. H. Monken, C. Saavedra, and S. Pádua, “Generation of entangled states of qudits using twin photons,” Phys. Rev. Lett. 94, 100501 (2005).
[Crossref] [PubMed]

Proc. Royal Soc. Lond. (1)

K. Pearson, “Notes on regression and inheritance in the case of two parents,” Proc. Royal Soc. Lond. 58, 240–242 (1895).
[Crossref]

Sci. Rep (2)

A. Sinha, A. H. Vijay, and U. Sinha, “On the superposition principle in interference experiments,” Sci. Rep.  5, 10304 (2015).
[Crossref] [PubMed]

P. Kolenderski, C. Scarcella, K. D. Johnsen, D. R. Hamel, C. Holloway, L. K. Shalm, S. Tisa, A. Tosi, K. J. Resch, and T. Jennewein, “Time-resolved double-slit interference pattern measurement with entangled photons,” Sci. Rep.  4, 4685 (2014).
[Crossref] [PubMed]

Science (1)

U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, and G. Weihs, “Ruling out multi-order interference in quantum mechanics,” Science 329, 418–421 (2010).
[Crossref] [PubMed]

Other (2)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 1st ed. (Cambridge University Press, 2000).

P. Kolenderski, K. D. Johnsen, C. Scarcella, D. Hamel, S. Bellisai, A. Tosi, K. Resch, and T. Jennewein are preparing a manuscript to be called “Experimental quantum bit state estimation using a simple 28-element quantum measurement.”

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Figures (7)

Fig. 1
Fig. 1 Schematic of the experimental set-up. Horizontal pump beam is made incident on a triple slit aperture. Lens L1 is used to transfer the image of the pump beam on the Type-1 BBO crystal. After appropriate filtering of the blue pump beam, another lens L2 is used to transfer the signal and idler spatial profiles to actuated detectors placed on either side of a beam splitter. The spatial profiles of the signal and idler photons are measured using detectors D1 and D2 and the spatial correlation is measured using an appropriate co-incidence logic unit.
Fig. 2
Fig. 2 The top figure represents the pump beam modulation scenario whereas the bottom figure represents the alternative technique of discretizing the Hilbert space with slit after the crystal. The action of the slit is represented by an operator S with a linearity α. The action of the crystal is represented by an operator C which is non-linear and has non-linearity β. In case of pump beam modulation, with intensity I of pump beam, the output after the crystal (for the part which interacts with the non-linearity) is (αI)β. In the second case of slit after the crystal, the output after the slit is α(I)β.
Fig. 3
Fig. 3 (a) Coincidence counts, RC measured as a function of position of detectors D1 and D2. A comparison between experimental (Red circle) and theoretically predicted coincidence counts (Blue rectangle) when detector D1 is fixed at peaks of slit (b) A, (c) B, (d) C and the detector D2 is scanning. (e) Single counts, RS measured at detector D1. Each data point has a measurement time of 3 minutes.
Fig. 4
Fig. 4 Second order correlation experiment using the classical pump laser light. (a) Coincidence counts, RC measured as a function of position of detectors D1 and D2. The plot clearly indicates that the classical light shows no photon-photon correlation. Red circles represent coincidence counts when detector D1 is fixed at peaks of slit (b) A, (c) B, (d) C and the detector D2 is scanned. (e) Single counts, RS measured at detector D1. The blue lines are guides to the eye. Each data point has a measurement time of 30 seconds, and the coincidence time window has been kept at the same value as for the SPDC experiments. Note that the coincidence measurements strictly overlap with the singles-count measurement, indicating again the lack of photon-photon correlation in classical light.
Fig. 5
Fig. 5 Variation of Pearson coefficient ρ with increasing slit width and increasing inter-slit distance respectively. Simulations have been done by varying one parameter while keeping the other parameters constant. When slit width w is varied, inter-slit distance is kept fixed at 100µm whereas when inter-slit distance is varied, slit width w is kept constant at 30µm. The crystal length LZ has been kept fixed at 10mm for both these simulations.
Fig. 6
Fig. 6 Variation of ρ with Lz. As crystal length increases, the Pearson coefficient is seen to decrease.
Fig. 7
Fig. 7 Figure on left shows the theoretically simulated pump profile. When the lens is used for image transfer experimentally, a magnification is introduced in the system, which has also been incorporated in theory. While the y-axis denotes the crystal length along beam propagation direction, the x-axis denotes the image along the transverse crystal direction. The figure on the right is the experimentally measured image of the modulated pump at the position corresponding to center of the crystal using a lens.

Tables (1)

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Table 1 Comparing the Pearson Coefficients Varying Slit Width w, Inter-Slit Distance d, and Crystal Longitudinal Length Lz

Equations (6)

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Δ k = k p ( ω p , α , n e ( θ ) ) k s ( ω s , α , n o ) k i ( ω i , α , n o ) .
| s i n c ( Δ k x L x ) s i n c ( Δ k z L z ) | 2 ,
A V d 3 r d k s d k i A p ( x , y , z ) exp ( i ( k p k s k i ) . r )
A ( k s , k i ) = V d 3 r A p ( x , y , z ) Π i = x , y , z s i n c ( Δ k i ( Δ r ) L i )
H ( x i , z i ; x o , z o ) = R R e 1 2 i k x o 2 z o e 1 2 i k ( 1 z o + 1 z i 1 f ) x l 2 e i k ( x o z o + x i z i ) x l λ 2 z o z i d x l .
U ( x i ; z i ) = d x 0 U ( x 0 ; z 0 ) H ( x i , z i ; x 0 , z 0 )

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