Abstract

We image with cameras entangled photon light transmitted through a thin scattering medium. Near-field and far-field spatial quantum correlations show that entangled photon pairs (bi-photons) generated by spontaneous optical parametric down-conversion exhibit speckle patterns. In contrast, no information from the thin scattering medium can be extracted using incoherent light issued from one photon of the pair.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  32. A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
    [Crossref]
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    [Crossref]
  34. O. Lib, G. Hasson, and Y. Bromberg, “Wavefront Shaping of Spatially Entangled Photons Scattered by Dynamic Random Media,” arXiv:1902.06653 [physics, physics:quant-ph] (2019).ArXiv:1902.06653.

2019 (3)

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

D. Li, Y. Yao, and M. Li, “Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium,” Opt. Commun. 446, 106–112 (2019).
[Crossref]

H. Defienne and S. Gigan, “Spatially-entangled Photon-pairs Generation Using Partial Spatially Coherent Pump Beam,” Phys. Rev. A 99(5), 053831 (2019).
[Crossref]

2018 (1)

H. Defienne, M. Reichert, and J. W. Fleischer, “Adaptive Quantum Optics with Spatially Entangled Photon Pairs,” Phys. Rev. Lett. 121(23), 233601 (2018).
[Crossref]

2015 (1)

2014 (2)

P.-A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113(16), 160401 (2014).
[Crossref]

M. Candé, A. Goetschy, and S. E. Skipetrov, “Transmission of quantum entanglement through a random medium,” Euro. Phys. Lett. 107, 54004 (2014).
[Crossref]

2013 (1)

M. Candé and S. E. Skipetrov, “Quantum versus classical effects in two-photon speckle patterns,” Phys. Rev. A 87(1), 013846 (2013).
[Crossref]

2012 (4)

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Statistical properties of two-photon speckles,” Phys. Rev. A 85(3), 033807 (2012).
[Crossref]

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

2010 (2)

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of Two-Photon Speckle Patterns,” Phys. Rev. Lett. 104(17), 173601 (2010).
[Crossref]

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

2009 (2)

C. W. J. Beenakker, J. W. F. Venderbos, and M. P. van Exter, “Two-photon speckle as a probe of multi-dimensional entanglement,” Phys. Rev. Lett. 102(19), 193601 (2009).
[Crossref]

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

2008 (1)

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

2007 (1)

S. E. Skipetrov, “Quantum theory of dynamic multiple light scattering,” Phys. Rev. A 75(5), 053808 (2007).
[Crossref]

2006 (2)

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

S. Brustlein, F. Devaux, and E. Lantz, “Limits of amplification of weaks images,” J. Mod. Opt. 53(5-6), 799–807 (2006).
[Crossref]

2004 (3)

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

2002 (1)

2001 (1)

E. Lantz and F. Devaux, “Numerical simulation of spatial fluctuations in parametric image amplification,” Eur. Phys. J. D 17(1), 93–98 (2001).
[Crossref]

2000 (2)

F. Devaux and E. Lantz, “Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal,” Eur. Phys. J. D 8(1), 117–124 (2000).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

1998 (1)

C. W. J. Beenakker, “Thermal Radiation and Amplified Spontaneous Emission from a Random Medium,” Phys. Rev. Lett. 81(9), 1829–1832 (1998).
[Crossref]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

1970 (1)

C. David Burnham and L. Donald Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25(2), 84–87 (1970).
[Crossref]

Abouraddy, A. F.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19(5), 1174 (2002).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

Agnew, M.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Andersen, U. L.

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

Bache, M.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

Bassignot, F.

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

Beenakker, C. W. J.

C. W. J. Beenakker, J. W. F. Venderbos, and M. P. van Exter, “Two-photon speckle as a probe of multi-dimensional entanglement,” Phys. Rev. Lett. 102(19), 193601 (2009).
[Crossref]

C. W. J. Beenakker, “Thermal Radiation and Amplified Spontaneous Emission from a Random Medium,” Phys. Rev. Lett. 81(9), 1829–1832 (1998).
[Crossref]

Blanchet, J.-L.

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

Boyd, R. W.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Brambilla, E.

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

Bramdilla, E.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

Bromberg, Y.

O. Lib, G. Hasson, and Y. Bromberg, “Wavefront Shaping of Spatially Entangled Photons Scattered by Dynamic Random Media,” arXiv:1902.06653 [physics, physics:quant-ph] (2019).ArXiv:1902.06653.

Brustlein, S.

S. Brustlein, F. Devaux, and E. Lantz, “Limits of amplification of weaks images,” J. Mod. Opt. 53(5-6), 799–807 (2006).
[Crossref]

Buller, G. S.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Candé, M.

M. Candé, A. Goetschy, and S. E. Skipetrov, “Transmission of quantum entanglement through a random medium,” Euro. Phys. Lett. 107, 54004 (2014).
[Crossref]

M. Candé and S. E. Skipetrov, “Quantum versus classical effects in two-photon speckle patterns,” Phys. Rev. A 87(1), 013846 (2013).
[Crossref]

David Burnham, C.

C. David Burnham and L. Donald Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25(2), 84–87 (1970).
[Crossref]

Defienne, H.

H. Defienne and S. Gigan, “Spatially-entangled Photon-pairs Generation Using Partial Spatially Coherent Pump Beam,” Phys. Rev. A 99(5), 053831 (2019).
[Crossref]

H. Defienne, M. Reichert, and J. W. Fleischer, “Adaptive Quantum Optics with Spatially Entangled Photon Pairs,” Phys. Rev. Lett. 121(23), 233601 (2018).
[Crossref]

Denis, S.

Devaux, F.

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

E. Lantz, S. Denis, P.-A. Moreau, and F. Devaux, “Einstein-Podolsky-Rosen paradox in single pairs of images,” Opt. Express 23(20), 26472 (2015).
[Crossref]

P.-A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113(16), 160401 (2014).
[Crossref]

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

S. Brustlein, F. Devaux, and E. Lantz, “Limits of amplification of weaks images,” J. Mod. Opt. 53(5-6), 799–807 (2006).
[Crossref]

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

E. Lantz and F. Devaux, “Numerical simulation of spatial fluctuations in parametric image amplification,” Eur. Phys. J. D 17(1), 93–98 (2001).
[Crossref]

F. Devaux and E. Lantz, “Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal,” Eur. Phys. J. D 8(1), 117–124 (2000).
[Crossref]

Di. Trapani, P.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

Donald Weinberg, L.

C. David Burnham and L. Donald Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25(2), 84–87 (1970).
[Crossref]

Edgar, M. P.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Fabre, C.

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

Fanjoux, G.

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

Fleischer, J. W.

H. Defienne, M. Reichert, and J. W. Fleischer, “Adaptive Quantum Optics with Spatially Entangled Photon Pairs,” Phys. Rev. Lett. 121(23), 233601 (2018).
[Crossref]

Furfaro, L.

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

Gatti, A.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

Gigan, S.

H. Defienne and S. Gigan, “Spatially-entangled Photon-pairs Generation Using Partial Spatially Coherent Pump Beam,” Phys. Rev. A 99(5), 053831 (2019).
[Crossref]

Goetschy, A.

M. Candé, A. Goetschy, and S. E. Skipetrov, “Transmission of quantum entanglement through a random medium,” Euro. Phys. Lett. 107, 54004 (2014).
[Crossref]

Goodman, J. W.

J. W. Goodman, “Statistical Optis,” (Wiley classics library, 2000).

Hasson, G.

O. Lib, G. Hasson, and Y. Bromberg, “Wavefront Shaping of Spatially Entangled Photons Scattered by Dynamic Random Media,” arXiv:1902.06653 [physics, physics:quant-ph] (2019).ArXiv:1902.06653.

Huck, A.

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

Izdebski, F.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Jaeger, G.

D. S. Simon, G. Jaeger, and A. V. Sergienko, “Quantum Metrology, Imaging, and Communication,” (Springer, 2016).

Jedrkiewicz, O.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

Lagendijk, A.

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

Lantz, E.

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

E. Lantz, S. Denis, P.-A. Moreau, and F. Devaux, “Einstein-Podolsky-Rosen paradox in single pairs of images,” Opt. Express 23(20), 26472 (2015).
[Crossref]

P.-A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113(16), 160401 (2014).
[Crossref]

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

S. Brustlein, F. Devaux, and E. Lantz, “Limits of amplification of weaks images,” J. Mod. Opt. 53(5-6), 799–807 (2006).
[Crossref]

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

E. Lantz and F. Devaux, “Numerical simulation of spatial fluctuations in parametric image amplification,” Eur. Phys. J. D 17(1), 93–98 (2001).
[Crossref]

F. Devaux and E. Lantz, “Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal,” Eur. Phys. J. D 8(1), 117–124 (2000).
[Crossref]

Leach, J.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Li, D.

D. Li, Y. Yao, and M. Li, “Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium,” Opt. Commun. 446, 106–112 (2019).
[Crossref]

Li, M.

D. Li, Y. Yao, and M. Li, “Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium,” Opt. Commun. 446, 106–112 (2019).
[Crossref]

Lib, O.

O. Lib, G. Hasson, and Y. Bromberg, “Wavefront Shaping of Spatially Entangled Photons Scattered by Dynamic Random Media,” arXiv:1902.06653 [physics, physics:quant-ph] (2019).ArXiv:1902.06653.

Lodahl, P.

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

Lugiato, L. A.

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

M.-Sisini, J.

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

M.-Sissini, J.

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

Moerman, J. J. D.

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of Two-Photon Speckle Patterns,” Phys. Rev. Lett. 104(17), 173601 (2010).
[Crossref]

Moken, C. H.

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

Moreau, P.-A.

E. Lantz, S. Denis, P.-A. Moreau, and F. Devaux, “Einstein-Podolsky-Rosen paradox in single pairs of images,” Opt. Express 23(20), 26472 (2015).
[Crossref]

P.-A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113(16), 160401 (2014).
[Crossref]

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

P.-A. Moreau, “Aspect spatiaux de l’intrication en amplification paramétrique: paradox EPR dans les images jumelles et expérience de Hong-Ou-Mandel,” PhD thesis, 191 (2015).

Mosset, A.

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

Padgett, M. J.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Pádua, S.

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

Peeters, W. H.

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of Two-Photon Speckle Patterns,” Phys. Rev. Lett. 104(17), 173601 (2010).
[Crossref]

Pires, H. D.

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Statistical properties of two-photon speckles,” Phys. Rev. A 85(3), 033807 (2012).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Reichert, M.

H. Defienne, M. Reichert, and J. W. Fleischer, “Adaptive Quantum Optics with Spatially Entangled Photon Pairs,” Phys. Rev. Lett. 121(23), 233601 (2018).
[Crossref]

Saleh, B. E. A.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19(5), 1174 (2002).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

Sergienko, A. V.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19(5), 1174 (2002).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

D. S. Simon, G. Jaeger, and A. V. Sergienko, “Quantum Metrology, Imaging, and Communication,” (Springer, 2016).

Shih, Y. H.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Simon, D. S.

D. S. Simon, G. Jaeger, and A. V. Sergienko, “Quantum Metrology, Imaging, and Communication,” (Springer, 2016).

Skipetrov, S. E.

M. Candé, A. Goetschy, and S. E. Skipetrov, “Transmission of quantum entanglement through a random medium,” Euro. Phys. Lett. 107, 54004 (2014).
[Crossref]

M. Candé and S. E. Skipetrov, “Quantum versus classical effects in two-photon speckle patterns,” Phys. Rev. A 87(1), 013846 (2013).
[Crossref]

S. E. Skipetrov, “Quantum theory of dynamic multiple light scattering,” Phys. Rev. A 75(5), 053808 (2007).
[Crossref]

Smolka, S.

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

Souto Ribeiro, P. H.

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Tasca, D. S.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Teich, M. C.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Entangled-photon Fourier optics,” J. Opt. Soc. Am. B 19(5), 1174 (2002).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

Treps, N.

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

van Exter, M. P.

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Statistical properties of two-photon speckles,” Phys. Rev. A 85(3), 033807 (2012).
[Crossref]

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of Two-Photon Speckle Patterns,” Phys. Rev. Lett. 104(17), 173601 (2010).
[Crossref]

C. W. J. Beenakker, J. W. F. Venderbos, and M. P. van Exter, “Two-photon speckle as a probe of multi-dimensional entanglement,” Phys. Rev. Lett. 102(19), 193601 (2009).
[Crossref]

Venderbos, J. W. F.

C. W. J. Beenakker, J. W. F. Venderbos, and M. P. van Exter, “Two-photon speckle as a probe of multi-dimensional entanglement,” Phys. Rev. Lett. 102(19), 193601 (2009).
[Crossref]

Walborn, S. P.

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

Warburton, R. E.

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Woudenberg, J.

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Statistical properties of two-photon speckles,” Phys. Rev. A 85(3), 033807 (2012).
[Crossref]

Yao, Y.

D. Li, Y. Yao, and M. Li, “Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium,” Opt. Commun. 446, 106–112 (2019).
[Crossref]

Eur. Phys. J. D (5)

F. Devaux and E. Lantz, “Spatial and temporal properties of parametric fluorescence around degeneracy in a type I LBO crystal,” Eur. Phys. J. D 8(1), 117–124 (2000).
[Crossref]

E. Lantz and F. Devaux, “Numerical simulation of spatial fluctuations in parametric image amplification,” Eur. Phys. J. D 17(1), 93–98 (2001).
[Crossref]

E. Lantz, N. Treps, C. Fabre, and E. Brambilla, “Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations,” Eur. Phys. J. D 29(3), 437–444 (2004).
[Crossref]

F. Devaux, J. M.-Sisini, P.-A. Moreau, and E. Lantz, “Towards the evidence of a purely spatial Einstein-Podolsky-Rosen paradox in images: measurement scheme and first experimental results,” Eur. Phys. J. D 66(7), 192 (2012).
[Crossref]

A. Mosset, F. Devaux, G. Fanjoux, and E. Lantz, “Direct experimental characterization of the Bose-Einstein distribution of spatial fluctuations of spontaneous parametric down-conversion,” Eur. Phys. J. D 28(3), 447–451 (2004).
[Crossref]

Euro. Phys. Lett. (1)

M. Candé, A. Goetschy, and S. E. Skipetrov, “Transmission of quantum entanglement through a random medium,” Euro. Phys. Lett. 107, 54004 (2014).
[Crossref]

J. Mod. Opt. (2)

O. Jedrkiewicz, E. Bramdilla, M. Bache, A. Gatti, L. A. Lugiato, and P. Di. Trapani, “Quantum spatial correlations in high-gain parametric down-conversion measured by means of a CCD camera,” J. Mod. Opt. 53(5-6), 575–595 (2006).
[Crossref]

S. Brustlein, F. Devaux, and E. Lantz, “Limits of amplification of weaks images,” J. Mod. Opt. 53(5-6), 799–807 (2006).
[Crossref]

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

Mon. Not. R. Astron. Soc. (1)

E. Lantz, J.-L. Blanchet, L. Furfaro, and F. Devaux, “Multi-imaging and Bayesian estimation for photon counting with EMCCDs,” Mon. Not. R. Astron. Soc. 386(4), 2262–2270 (2008).
[Crossref]

Nat. Commun. (1)

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3(1), 984 (2012).
[Crossref]

Opt. Commun. (1)

D. Li, Y. Yao, and M. Li, “Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium,” Opt. Commun. 446, 106–112 (2019).
[Crossref]

Opt. Express (1)

Phys. Rep. (1)

S. P. Walborn, C. H. Moken, S. Pádua, and P. H. Souto Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495(4-5), 87–139 (2010).
[Crossref]

Phys. Rev. A (9)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

E. Bramdilla, A. Gatti, M. Bache, and L. A. Lugiato, “Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion,” Phys. Rev. A 69(2), 023802 (2004).
[Crossref]

F. Devaux, A. Mosset, F. Bassignot, and E. Lantz, “Quantum holography with biphotons of high Schmidt number,” Phys. Rev. A 99(3), 033854 (2019).
[Crossref]

P.-A. Moreau, J. M.-Sissini, F. Devaux, and E. Lantz, “Realization of the purely spatial Einstein-Podolsky-Rosen paradox in full-field images of spontaneous parametric down-conversion,” Phys. Rev. A 86(1), 010101 (2012).
[Crossref]

S. E. Skipetrov, “Quantum theory of dynamic multiple light scattering,” Phys. Rev. A 75(5), 053808 (2007).
[Crossref]

M. Candé and S. E. Skipetrov, “Quantum versus classical effects in two-photon speckle patterns,” Phys. Rev. A 87(1), 013846 (2013).
[Crossref]

H. Defienne and S. Gigan, “Spatially-entangled Photon-pairs Generation Using Partial Spatially Coherent Pump Beam,” Phys. Rev. A 99(5), 053831 (2019).
[Crossref]

H. D. Pires, J. Woudenberg, and M. P. van Exter, “Statistical properties of two-photon speckles,” Phys. Rev. A 85(3), 033807 (2012).
[Crossref]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62(4), 043816 (2000).
[Crossref]

Phys. Rev. Lett. (7)

H. Defienne, M. Reichert, and J. W. Fleischer, “Adaptive Quantum Optics with Spatially Entangled Photon Pairs,” Phys. Rev. Lett. 121(23), 233601 (2018).
[Crossref]

P.-A. Moreau, F. Devaux, and E. Lantz, “Einstein-Podolsky-Rosen paradox in twin images,” Phys. Rev. Lett. 113(16), 160401 (2014).
[Crossref]

C. David Burnham and L. Donald Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25(2), 84–87 (1970).
[Crossref]

C. W. J. Beenakker, J. W. F. Venderbos, and M. P. van Exter, “Two-photon speckle as a probe of multi-dimensional entanglement,” Phys. Rev. Lett. 102(19), 193601 (2009).
[Crossref]

S. Smolka, A. Huck, U. L. Andersen, A. Lagendijk, and P. Lodahl, “Observation of Spatial Quantum Correlations Induced by Multiple Scattering of Nonclassical Light,” Phys. Rev. Lett. 102(19), 193901 (2009).
[Crossref]

W. H. Peeters, J. J. D. Moerman, and M. P. van Exter, “Observation of Two-Photon Speckle Patterns,” Phys. Rev. Lett. 104(17), 173601 (2010).
[Crossref]

C. W. J. Beenakker, “Thermal Radiation and Amplified Spontaneous Emission from a Random Medium,” Phys. Rev. Lett. 81(9), 1829–1832 (1998).
[Crossref]

Other (4)

O. Lib, G. Hasson, and Y. Bromberg, “Wavefront Shaping of Spatially Entangled Photons Scattered by Dynamic Random Media,” arXiv:1902.06653 [physics, physics:quant-ph] (2019).ArXiv:1902.06653.

D. S. Simon, G. Jaeger, and A. V. Sergienko, “Quantum Metrology, Imaging, and Communication,” (Springer, 2016).

P.-A. Moreau, “Aspect spatiaux de l’intrication en amplification paramétrique: paradox EPR dans les images jumelles et expérience de Hong-Ou-Mandel,” PhD thesis, 191 (2015).

J. W. Goodman, “Statistical Optis,” (Wiley classics library, 2000).

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Figures (5)

Fig. 1.
Fig. 1. Two photon speckle generation with entangled photon pairs. The two configurations (a) and (b) are related to the far-field and near-field correlations, respectively. The $\chi ^{(2)}$ nonlinear crystal is pumped by laser pulses at the angular frequency $\omega _p$. The entangled photons (signal and idler) are generated at $\omega _s$ and $\omega _i=\omega _p-\omega _s$. Two separated optical systems with the transfer functions $h_1$ and $h_2$ are used to focus the signal and idler beams onto a thin complex medium that transmits the two beams with the transmissions $t_s$ and $t_i$ for the signal and idler beams respectively. Then, another two separated optical systems with the transfer functions $h_{1}'$ and $h_{2}'$ are used to image the transmitted beams on the $EMCCD1$ and $EMCCD2$ cameras.
Fig. 2.
Fig. 2. (a) Experimental setup: Entangled photon pairs at 710 $nm$ are generated via SPDC in a type-II BBO using a 330 $ps$ pump pulse at 355 $nm$. The crystal is imaged onto the thin diffuser with a $4-f$ optical system. The entangled photon pairs (signal and idler) transmitted by the diffuser are detected and resolved spatially in the far-field on two EMCCD cameras. (b): 3D-profile of the diffuser and (c): Far-field intensity of the coherent scattered light (in a.u). $\rvert V\rangle$ and $\rvert H\rangle$: the vertical and horizontal polarizations. $(P_1)$ and $(P_2)$: the Fourier plane and $(P')$ the image plane. D: dichroic mirror, $F_3$ and $F_4$: the interferential filters.
Fig. 3.
Fig. 3. Without diffuser,(a) average photon number in single far-field images (signal or idler) of SPDC and (b) measured correlation function in dB between 100 twin images. With diffuser, (c) average photon number in single far-field images (signal or idler) of SPDC and (d) measured correlation function in dB over 40 000 twin images. With stochastic simulations, (e) average photon number in single far-field images (signal or idler) of SPDC and (f) correlation function issued from 10 000 stochastic simulations with diffuser.
Fig. 4.
Fig. 4. Experimental setup:Entangled photon pairs at 710 $nm$ are generated via SPDC in a type-II BBO using 330 $ps$ pump pulse at 355 $nm$. Lens $L_1$ ($f_1$=150 $mm$) is used to image the far field of the crystal onto the diffuser placed in the Fourier plane. The entangled photon pairs (signal and idler) transmitted by the diffuser are detected in the near field on the EMCCD1 and EMCCD2 cameras using lenses $L_2$ ($f_2$=150 $mm$) and $L_3$ ($f_3$=150 $mm$) respectively. $\rvert V\rangle$ and $\rvert H\rangle$: the vertical and horizontal polarizations. $(P_1)$ and $(P_2)$: the image plane and $(P')$ the Fourier plane. D: a dichroic mirror, $F_1$ and $F_2$: interferential filters.
Fig. 5.
Fig. 5. Without diffuser, (a) average photon number in single near-field images(signal or idler) of SPDC and (b) measured correlation function in dB between 100 twin images. With diffuser, (c) average photon number in single near-field images (signal or idler)of SPDC and (d) measured correlation function in dB over 70 000 twin images. With stochastic simulations, (e) average photon number in single near-field images (signal or idler) of SPDC and (f) correlation issued from 10 000 stochastic simulations with diffuser.

Equations (11)

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{ h s ( r 1 , r , ω s ) = d r s h 1 ( r s , r , ω s ) t s ( r s , ω s ) h 1 ( r 1 , r s , ω s ) h i ( r 2 , r , ω p ω s ) = d r i h 2 ( r i , r , ω p ω s ) t i ( r i , ω p ω s ) h 2 ( r 2 , r i , ω p ω s ) ,
ψ ( r 1 , r 2 ) E p ( r ) h s ( r 1 , r ) h i ( r 2 , r ) d r
{ h 1 ( r 1 , r ) = e 2 i k f i λ f e i k f r 1 . r h 2 ( r 2 , r ) = e 2 i k f i λ f e i k f r 2 . r
{ h s ( r 1 , r ) = t ( r ) e 2 i k f i λ f e i k f r 1 . r h i ( r 2 , r ) = t ( r ) e 2 i k f i λ f e i k f r 2 . r
ψ ( r 1 , r 2 ) E p ( r ) t 2 ( r ) e i k f ( r 1 + r 2 ) . r d r
G ( 2 ) ( r 1 , r 2 ) = | ψ ( r 1 , r 2 ) | 2 | E ~ p ( 2 π r 1 + r 2 λ f ) t 2 ~ ( 2 π r 1 + r 2 λ f ) | 2
{ h s ( r 1 , r ) = e 4 i k f i λ f t ~ s ( 2 π r r 1 λ f ) h i ( r 2 , r ) = e 4 i k f i λ f t ~ i ( 2 π r r 2 λ f )
ψ ( r 1 , r 2 ) E p ( r ) t ~ s ( 2 π r r 1 λ f ) t ~ i ( 2 π r r 2 λ f ) d r
G ( 2 ) ( r 1 , r 2 ) = | ψ ( r 1 , r 2 ) | 2 | E p ( r ) t ~ s ( 2 π r r 1 λ f ) t ~ i ( 2 π r r 2 λ f ) d r | 2
V x , y = 0 , 25 2 σ ν x , y 2 σ x , y 2
V = V x V y = 100