Abstract

Correlations between photons are interesting for a number of applications and concepts in metrology, in particular for resolution improvements in different methods of quantum imaging. We demonstrate the application of a blazed grating for the characterization of the degree of spatial correlation of biphotons. The biphotons are generated by type II parametric downconversion. Compared to an ordinary transmission grating, a blazed grating shows a high diffraction efficiency only for a single order of diffraction. Thus, higher intensities in the Fraunhofer far field behind the grating, and easier photon counting, can be achieved. The distribution of the two-photon rate in the Fraunhofer far field of the blazed grating can show one additional order of diffraction with a visibility related to the degree of correlation of the biphotons. The number of spatial modes that are populated by the biphoton beam can be directly altered in our experiments. The relation of the spatial mode order of the photon propagation to the observable degree of spatial correlation of the biphotons is investigated and related to the Schmidt number of spatially entangled modes.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2009 (1)

W. H. Peeters, J. I. Renema, and M. O. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

2008 (1)

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

2007 (2)

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

2006 (3)

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

2004 (3)

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontanous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[CrossRef] [PubMed]

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009-1044 (2003).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down conversion,” Phys. Rev. A 67, 041805(R) (2003).
[CrossRef]

2002 (1)

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic deBroglie wavelength of entangled photon pairs generated by spontanous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

2001 (3)

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

M. D'Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High efficiency entangled photon pair collection in type II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[CrossRef]

2000 (5)

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

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

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

1999 (1)

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

1998 (1)

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[CrossRef]

1997 (2)

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

1995 (3)

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

A. Eckert and P. L. Knight, “Entangled quantum systems and the Schmidt decomposition,” Am. J. Phys. 5, 415-423 (1995).
[CrossRef]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

1987 (1)

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Abouraddy, A.

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

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

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Aiello, A.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Aspelmeyer, M.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

Bennink, R. S.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontanous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[CrossRef] [PubMed]

Bentley, S. J.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontanous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[CrossRef] [PubMed]

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Boyd, R. W.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontanous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[CrossRef] [PubMed]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Brida, G.

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Burlakov, A. V.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Cable, H.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Caricato, V.

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Chang, H. J.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Chekhova, M. V.

M. D'Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Cirac, J. I.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

D'Angelo, M.

M. D'Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

De Martini, F.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Dowling, J. P.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Duan, L. M.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Eberly, J. H.

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Eckert, A.

A. Eckert and P. L. Knight, “Entangled quantum systems and the Schmidt decomposition,” Am. J. Phys. 5, 415-423 (1995).
[CrossRef]

Edamatsu, K.

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down conversion,” Phys. Rev. A 67, 041805(R) (2003).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic deBroglie wavelength of entangled photon pairs generated by spontanous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Efremov, M. A.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

Eisert, J.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt., DOI:10.1080/09500340903359962.

Fedorov, M. V.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Fei, H. B.

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

Fonseca, E. J. S.

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

Gasparoni, S.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

Genovese, M.

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Giedke, G.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Giovannetti, V.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

Glasser, R.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Gramegna, M.

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Hecht, E.

E. Hecht, Chapter 10.2 in Optics, 4th Ed. (Addison Wesley, 2002).

Henkel, C.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt., DOI:10.1080/09500340903359962.

Hong, C. K.

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Howell, J. C.

J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontanous parametric down conversion,” Phys. Rev. Lett. 92, 210403 (2004).
[CrossRef] [PubMed]

Itoh, T.

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down conversion,” Phys. Rev. A 67, 041805(R) (2003).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic deBroglie wavelength of entangled photon pairs generated by spontanous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Jost, B. M.

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

Klyshko, D. N.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Knight, P. L.

A. Eckert and P. L. Knight, “Entangled quantum systems and the Schmidt decomposition,” Am. J. Phys. 5, 415-423 (1995).
[CrossRef]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Korn, D.

M. Ostermeyer, D. Korn, and D. Puhlmann, “Two dimensional characterization of space momentum entangled photon pairs,” arXiv:0905.4830.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt., DOI:10.1080/09500340903359962.

Kulik, S. P.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

G. Brida, V. Caricato, M. Genovese, M. Gramegna, M. V. Fedorov, and S. P. Kulik, “Characterization of spectral entanglement of spontaneous parametric-down conversion biphotons,” arXiv:0904.3009.

Kurtsiefer, C.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High efficiency entangled photon pair collection in type II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Law, C. K.

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Mancini, S.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

Mandel, L.

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Monken, C. H.

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

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Moreva, E. V.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

Nienhuis, G.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Oberparleiter, M.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High efficiency entangled photon pair collection in type II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[CrossRef]

Oemrawsingh, S. S. R.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Ostermeyer, M.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt., DOI:10.1080/09500340903359962.

M. Ostermeyer, D. Korn, and D. Puhlmann, “Two dimensional characterization of space momentum entangled photon pairs,” arXiv:0905.4830.

O'Sullivan-Hale, M. N.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Ou, Z. Y.

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Padua, S.

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

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Pan, J. W.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

Peeters, W. H.

W. H. Peeters, J. I. Renema, and M. O. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

Penin, A. N.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Popescu, S.

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

Puhlmann, D.

M. Ostermeyer, D. Korn, and D. Puhlmann, “Two dimensional characterization of space momentum entangled photon pairs,” arXiv:0905.4830.

M. Ostermeyer, D. Korn, D. Puhlmann, C. Henkel, and J. Eisert, “Two-dimensional characterization of spatially entangled photon pairs,” J. Mod. Opt., DOI:10.1080/09500340903359962.

Renema, J. I.

W. H. Peeters, J. I. Renema, and M. O. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

Saleh, B. E. A.

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

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

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

Sciarrino, F.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Sergienko, A. V.

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

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

Shih, Y.

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

Y. Shih, “Entangled biphoton source-property and preparation,” Rep. Prog. Phys. 66, 1009-1044 (2003).
[CrossRef]

M. D'Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef] [PubMed]

Shih, Y. H.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Shimizu, R.

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down conversion,” Phys. Rev. A 67, 041805(R) (2003).
[CrossRef]

K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic deBroglie wavelength of entangled photon pairs generated by spontanous parametric down-conversion,” Phys. Rev. Lett. 89, 213601 (2002).
[CrossRef] [PubMed]

Shin, H.

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Souto Ribeiro, P. H.

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[CrossRef]

Straupe, S. S.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

Strekalov, D. V.

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

Teich, M. C.

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

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

H. B. Fei, B. M. Jost, S. Popescu, B. E. A. Saleh, and M. C. Teich, “Entanglement-induced two-photon transparency,” Phys. Rev. Lett. 78, 1679-1682 (1997).
[CrossRef]

Tombesi, P.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

Ursin, R.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

van Exter, M. O.

W. H. Peeters, J. I. Renema, and M. O. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

van Exter, M. P.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Vitali, D.

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

Vitelli, C.

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

Volov, P. A.

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Walther, P.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

Weinfurter, H.

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High efficiency entangled photon pair collection in type II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733-2736 (2000).
[CrossRef] [PubMed]

Woerdman, J. P.

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Yamamoto, Y.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835 (1995).
[CrossRef] [PubMed]

Zeilinger, A.

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

Zoller, P.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Acoust. Hologr. (1)

A. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Double slit interference of biphotons generated in spontaneous parametric down conversion from a thick crystal,” Acoust. Hologr. 3, 50 (2001).

Am. J. Phys. (1)

A. Eckert and P. L. Knight, “Entangled quantum systems and the Schmidt decomposition,” Am. J. Phys. 5, 415-423 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. Shih, “Quantum imaging,” IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

J. Mod. Opt. (1)

H. J. Chang, H. Shin, M. N. O'Sullivan-Hale, and R. W. Boyd, “Implementation of sub-Rayleigh lithography using an N-photon absorber,” J. Mod. Opt. 53, 2271-2277 (2006).
[CrossRef]

Nature (1)

P. Walther, J. W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, “De Broglie wavelength of a non-local four-photon state,” Nature 429, 158-161 (2004).
[CrossRef] [PubMed]

Phys. Rev. A (9)

A. V. Burlakov, M. V. Chekhova, D. N. Klyshko, S. P. Kulik, A. N. Penin, Y. H. Shih, and D. V. Strekalov, “Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions,” Phys. Rev. A 56, 3214-3225 (1997).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs generated by spontaneous parametric down conversion,” Phys. Rev. A 67, 041805(R) (2003).
[CrossRef]

F. Sciarrino, C. Vitelli, F. De Martini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008).
[CrossRef]

R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006).
[CrossRef]

C. H. Monken, P. H. Souto Ribeiro, and S. Padua, “Transfer of angular spectrum and parametric down-conversion,” Phys. Rev. A 57, 3123 (1998).
[CrossRef]

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

W. H. Peeters, J. I. Renema, and M. O. van Exter, “Engineering of two-photon spatial quantum correlations behind a double slit,” Phys. Rev. A 79, 043817 (2009).
[CrossRef]

C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High efficiency entangled photon pair collection in type II parametric fluorescence,” Phys. Rev. A 64, 023802 (2001).
[CrossRef]

M. P. van Exter, A. Aiello, S. S. R. Oemrawsingh, G. Nienhuis, and J. P. Woerdman, “Effect of spatial filtering on the Schmidt decomposition of entangled photons,” Phys. Rev. A 74, 012309 (2006).
[CrossRef]

Phys. Rev. Lett. (14)

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92, 127903 (2004).
[CrossRef] [PubMed]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, “Entangling macroscopic oscillators exploting radition pressure,” Phys. Rev. Lett. 88, 120401 (2000).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, “New high intensity source of polarization entangled photon pairs,” Phys. Rev. Lett. 75, 337 (1995).
[CrossRef]

See C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044-2046 (1987) for Hong-Ou-Mandel (HOM) interference. In our setup HOM interference for photons from type II parametric downconversion is used in an analogous way as used in K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76, 4656 (1996).
[CrossRef] [PubMed]

M. V. Fedorov, M. A. Efremov, P. A. Volov, E. V. Moreva, S. S. Straupe, and S. P. Kulik, “Anisotropically and high entanglement of biphoton states generated in spontaneous parametric downconversion,” Phys. Rev. Lett. 99, 063901 (2007).
[CrossRef] [PubMed]

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Rep. Prog. Phys. (1)

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M. Ostermeyer, D. Korn, and D. Puhlmann, “Two dimensional characterization of space momentum entangled photon pairs,” arXiv:0905.4830.

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Figures (8)

Fig. 1
Fig. 1

Diffraction efficiency for the first order of diffraction in dependence of the wavelengths for the blazed grating used in the experiments (Blaze wavelength 500 nm , grating period 25 μ m ).

Fig. 2
Fig. 2

Calculated photon rates for Fraunhofer diffraction behind the blazed grating in near field illumination with a spot diameter of 100 μ m on the grating for a spatial correlation factor of the biphotons of top: r = 3 , middle: r = 0.85 , bottom: r = 0.01 .

Fig. 3
Fig. 3

Calculated photon rates for Fraunhofer diffraction behind the blazed grating in near field illumination with a spot diameter of 29 μ m for a correlation factor of the biphotons of r = 0.85 . Top: angular resolution 0.5 mrad , bottom: angular resolution 10 mrad .

Fig. 4
Fig. 4

Calculated photon rates for Fraunhofer diffraction behind the blazed grating in far field illumination for different spatial correlation factors of the biphoton of top; r = 3 ; middle, r = 0.85 ; bottom, r = 0.01 .

Fig. 5
Fig. 5

Setup to generate a biphoton beam by Hong–Ou–Mandel interference of photons produced from type II noncollinear parametric downconversion (left) and the setup of our grating experiment (right).

Fig. 6
Fig. 6

Single- and two-photon rate measured in the Fraunhofer far field behind the blazed grating (circles) and calculated theoretical expectation (straight line) in case of a correlation factor of r = 0.85 .

Fig. 7
Fig. 7

Two-photon count rate measured in the Fraunhofer far field behind blazed grating (circles) and calculated theoretical expectation (straight line) for increasing correlation factor achieved by moving the image plane of crystal near field away from the grating plane.

Fig. 8
Fig. 8

Two photon and single-photon count rate measured in the Fraunhofer far field behind blazed grating (circles) for decreasing number of illuminating higher-order spatial modes restricted by an aperture of varying diameter and calculated theoretical expectation (straight line) for decreasing correlation width as given. Top; aperture d = 4.0 mm ; middle; d = 2.5 mm ; bottom; d = 1.5 mm .

Equations (29)

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| ψ = d x 1 d x 2 F ( x 1 , x 2 ) a ̂ ( x 1 ) a ̂ ( x 2 ) | 0 .
F ( x 1 , x 2 ) = A ( x 1 ) A ( x 2 ) C ( x 1 x 2 ) .
R ( 2 ) ( x 1 , x 2 ) = ψ | a ̂ ( x 2 ) a ̂ ( x 1 ) a ̂ ( x 1 ) a ̂ ( x 2 ) | ψ = | 0 | a ̂ ( x 1 ) a ̂ ( x 2 ) | ψ | 2 = | F ( x 1 , x 2 ) | 2 .
R ( 2 ) ( k x 1 , k x 2 ) = | F ̃ ( k x 1 , k x 2 ) | 2 .
F ̃ ( k x 1 , k x 2 ) = 1 2 π d x 1 d x 2 A ( x 1 ) A ( x 2 ) C ( x 1 x 2 ) e i ( k x 1 x 1 + k x 2 x 2 ) .
R ( 1 ) ( k x 1 ) = d k x 2 R ( 2 ) ( k x 1 , k x 2 ) .
C ( x 1 , x 2 ) = exp [ ( x 1 ± x 2 ) 2 ( r d ) 2 ( 4 ln 2 ) ] .
R ( 2 ) ( k x , k x ) | F [ A ] ( k x ) | 4 ,
R ( 1 ) ( k x ) = | F [ A ] ( k x ) | 2 .
R ( 2 ) ( k x , k x ) | F [ A ] ( 2 k x ) | 4 ,
R ( 1 ) ( k x ) = const .
F ̃ PDC ( k 1 , k 2 ) E ̃ p ( k 1 + k 2 ) ξ ̃ ( k 1 , k 2 ) .
ξ ̃ ( k 1 , k 2 ) = sinc [ 1 2 L Δ k z ( k 1 , k 2 ) ] .
Δ k z ( k 1 , k 2 ) ϕ 0 + | k 1 k 2 | 2 4 n ω c + 1 2 k 2 y δ .
F ̃ PDC ( k 1 x , k 2 x ) E ̃ p ( k 1 + k 2 ) ξ ̃ ( k 1 k 2 ) .
ξ ̃ ( k 1 k 2 ) exp [ | k 1 k 2 | 2 8 n ω ( L c ) ] .
F PDC ( x 1 , x 2 ) E p ( k 1 + k 2 ) ξ ̃ ( k 1 k 2 ) e i k 1 x 1 e i k 2 x 2 d k 1 d k 2 .
F PDC ( x 1 , x 2 ) E p ( K 1 ) ξ ̃ ( K 2 ) e i K 1 X 1 e i K 2 X 2 d K 1 d K 2 ,
K 1 = k 1 + k 2 2 , K 2 = k 1 k 2 2 , X 1 = x 1 + x 2 2 ,
X 2 = x 1 x 2 2 .
F PDC ( x 1 , x 2 ) E p ( x 1 + x 2 ) ξ ( x 1 x 2 ) ,
E p ( x 1 + x 2 ) exp [ 1 2 ( x 1 + x 2 ) 2 2 σ k p 2 ] ,
ξ ( x 1 x 2 ) exp [ ( x 1 x 2 ) 2 L c ( n ω ) ] .
F PDC ( x 1 , x 2 ) exp [ 1 2 ( x 1 + x 2 ) 2 σ + 2 ] exp [ 1 2 ( x 1 x 2 ) 2 σ 2 ] .
ρ x = σ 2 σ + 2 σ 2 + σ + 2 .
A ( x 1 ) = E 1 ( x 1 ) T bl ( x 1 ) ,
F ( x 1 , x 2 ) E 1 ( x 1 ) E 2 ( x 2 ) C ( x 1 x 2 ) .
F ( x 1 , x 2 ) E 1 , 2 ( x 1 + x 2 ) C ( x 1 x 2 ) .
ρ x = σ g r 2 σ g r 2 + r 2 d 2 ( 8 ln 2 ) .

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