Abstract

We show that, with proper modification of the pump field description from plane-wave to spherical-like, which serves to incorporate geometric effects that were discarded in the plane-wave model, the efficiency of the spontaneous parametric down conversion process exhibits dependence on pump intensity, contrary to previous theoretical predictions. Experimental investigations of this behavior are carried out under focused pumping conditions, where pump divergence is kept constant, and pairs of photons are collected behind an aperture that is large compared to the overall down-conversion profile. The resulting photon yield is found to exhibit a strong dependence on pump intensity, and an enhancement of the down-conversion efficiency is observed. The modified pump field description is also modeled numerically and calculations are presented, which are found to display good accordance with experimental observations. The enhanced yield of spontaneous parametrically down-converted photons will prove beneficial for many practical applications of entangled photon pairs where a high flux is desired.

©2008 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  37. This approximation limits the crystal thickness to the order of 10-4 m. See Appendix A in [22] for details.
  38. M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
    [Crossref] [PubMed]
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    [Crossref]

2006 (2)

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

D. I. Lee and T. Goodson, “Entangled photon absorption in an organic porphyrin dendrimer,” J. Phys. Chem. B 110, 25582–25585 (2006).
[Crossref] [PubMed]

2005 (2)

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

2004 (1)

W. T. M. Irvine, A. L. Linares, M. J. A. de Dood, and D. Bouwmeester, “Optimal quantum cloning on a beam splitter,” Phys. Rev. Lett. 92, 047902 (2004).
[Crossref] [PubMed]

2003 (1)

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

2002 (1)

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Single photons on pseudodemand from stored parametric down-conversion,” Phys. Rev. A 66, 042303 (2002).
[Crossref]

2001 (2)

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quant. Inf. Comput. 1, 3–56 (2001).

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]

1998 (1)

C. H. Monken, P. H. S. Ribeiro, and S. Padua, “Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment,” Phys. Rev. A 57, R2267–R2269 (1998).
[Crossref]

1997 (4)

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[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]

1996 (2)

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

1995 (3)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental Evaluation of a 2-Photon Wave-Packet in Type-II Parametric Downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[Crossref]

1994 (4)

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of 2nd-Order Nonlinear-Optical Coefficients from the Spectral Brightness of Parametric Fluorescence,” Opt. Lett. 19, 168–170 (1994).
[Crossref] [PubMed]

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal Coherence Properties of Entangled Light-Beams Generated by Parametric Down-Conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[Crossref] [PubMed]

1993 (1)

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

1991 (1)

1988 (2)

Z. Y. Ou and L. Mandel, “Violation of Bells-Inequality and Classical Probability in a 2-Photon Correlation Experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[Crossref] [PubMed]

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric Down Conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

1987 (1)

1986 (1)

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct Observation of the 2nd-Order Coherence of Parametrically Generated Light,” Phys. Rev. Lett. 57, 2516–2519 (1986).
[Crossref] [PubMed]

1985 (1)

S. Friberg, C. K. Hong, and L. Mandel, “Measurement of Time Delays in the Parametric Production of Photon Pairs,” Phys. Rev. Lett. 54, 2011–2013 (1985).
[Crossref] [PubMed]

1981 (1)

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute Calibration of the Sensitivity of Photodetectors Using a Biphotonic Field,” JETP Lett. 33, 477–480 (1981).

1970 (1)

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

1968 (1)

D. A. Kleinman, “Theory of Optical Parametric Noise,” Phys. Rev. 174, 1027–1041 (1968).
[Crossref]

1963 (1)

R. J. Glauber, “Quantum Theory of Optical Coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

Abram, I.

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct Observation of the 2nd-Order Coherence of Parametrically Generated Light,” Phys. Rev. Lett. 57, 2516–2519 (1986).
[Crossref] [PubMed]

Alley, C. O.

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric Down Conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

Aspelmeyer, M.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Bennink, R. S.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Bouwmeester, D.

W. T. M. Irvine, A. L. Linares, M. J. A. de Dood, and D. Bouwmeester, “Optimal quantum cloning on a beam splitter,” Phys. Rev. Lett. 92, 047902 (2004).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Bovino, F. A.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Burnham, D. C.

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

Castagnoli, G.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Chakmakjian, S. H.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

Cheung, E. C.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of 2nd-Order Nonlinear-Optical Coefficients from the Spectral Brightness of Parametric Fluorescence,” Opt. Lett. 19, 168–170 (1994).
[Crossref] [PubMed]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

Colla, A. M.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

de Dood, M. J. A.

W. T. M. Irvine, A. L. Linares, M. J. A. de Dood, and D. Bouwmeester, “Optimal quantum cloning on a beam splitter,” Phys. Rev. Lett. 92, 047902 (2004).
[Crossref] [PubMed]

Di Giuseppe, G.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Dolique, G.

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct Observation of the 2nd-Order Coherence of Parametrically Generated Light,” Phys. Rev. Lett. 57, 2516–2519 (1986).
[Crossref] [PubMed]

Earl, D. D.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Eberhard, P. H.

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (John Wiley and Sons, New York, 1988).

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

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]

Franson, J. D.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Single photons on pseudodemand from stored parametric down-conversion,” Phys. Rev. A 66, 042303 (2002).
[Crossref]

Friberg, S.

S. Friberg, C. K. Hong, and L. Mandel, “Measurement of Time Delays in the Parametric Production of Photon Pairs,” Phys. Rev. Lett. 54, 2011–2013 (1985).
[Crossref] [PubMed]

Glauber, R. J.

R. J. Glauber, “Quantum Theory of Optical Coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

Goodson, T.

D. I. Lee and T. Goodson, “Entangled photon absorption in an organic porphyrin dendrimer,” J. Phys. Chem. B 110, 25582–25585 (2006).
[Crossref] [PubMed]

Grice, W. P.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley Pub. Co., Reading, MA, 1990).

Hong, C. K.

S. Friberg, C. K. Hong, and L. Mandel, “Measurement of Time Delays in the Parametric Production of Photon Pairs,” Phys. Rev. Lett. 54, 2011–2013 (1985).
[Crossref] [PubMed]

Irvine, W. T. M.

W. T. M. Irvine, A. L. Linares, M. J. A. de Dood, and D. Bouwmeester, “Optimal quantum cloning on a beam splitter,” Phys. Rev. Lett. 92, 047902 (2004).
[Crossref] [PubMed]

Jacobs, B. C.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Single photons on pseudodemand from stored parametric down-conversion,” Phys. Rev. A 66, 042303 (2002).
[Crossref]

Joobeur, A.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal Coherence Properties of Entangled Light-Beams Generated by Parametric Down-Conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[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]

Keller, T. E.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

Kleinman, D. A.

D. A. Kleinman, “Theory of Optical Parametric Noise,” Phys. Rev. 174, 1027–1041 (1968).
[Crossref]

Klyshko, D. N.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach Science Publishers, New York, 1988).

Koch, K.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of 2nd-Order Nonlinear-Optical Coefficients from the Spectral Brightness of Parametric Fluorescence,” Opt. Lett. 19, 168–170 (1994).
[Crossref] [PubMed]

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, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

Larchuk, T. S.

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

Lee, D. I.

D. I. Lee and T. Goodson, “Entangled photon absorption in an organic porphyrin dendrimer,” J. Phys. Chem. B 110, 25582–25585 (2006).
[Crossref] [PubMed]

Lee, P. S. K.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005).
[Crossref]

Linares, A. L.

W. T. M. Irvine, A. L. Linares, M. J. A. de Dood, and D. Bouwmeester, “Optimal quantum cloning on a beam splitter,” Phys. Rev. Lett. 92, 047902 (2004).
[Crossref] [PubMed]

Liu, J. M.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of 2nd-Order Nonlinear-Optical Coefficients from the Spectral Brightness of Parametric Fluorescence,” Opt. Lett. 19, 168–170 (1994).
[Crossref] [PubMed]

Liu, Y.

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

Malygin, A. A.

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute Calibration of the Sensitivity of Photodetectors Using a Biphotonic Field,” JETP Lett. 33, 477–480 (1981).

Mandel, L.

Z. Y. Ou and L. Mandel, “Violation of Bells-Inequality and Classical Probability in a 2-Photon Correlation Experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[Crossref] [PubMed]

S. Friberg, C. K. Hong, and L. Mandel, “Measurement of Time Delays in the Parametric Production of Photon Pairs,” Phys. Rev. Lett. 54, 2011–2013 (1985).
[Crossref] [PubMed]

Mattle, K.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (John Wiley and Sons, New York, 1988).

Monken, C. H.

C. H. Monken, P. H. S. Ribeiro, and S. Padua, “Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment,” Phys. Rev. A 57, R2267–R2269 (1998).
[Crossref]

Moore, G. T.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

E. C. Cheung, K. Koch, G. T. Moore, and J. M. Liu, “Measurements of 2nd-Order Nonlinear-Optical Coefficients from the Spectral Brightness of Parametric Fluorescence,” Opt. Lett. 19, 168–170 (1994).
[Crossref] [PubMed]

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]

Ou, Z. Y.

Z. Y. Ou and L. Mandel, “Violation of Bells-Inequality and Classical Probability in a 2-Photon Correlation Experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[Crossref] [PubMed]

Oudar, J. L.

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct Observation of the 2nd-Order Coherence of Parametrically Generated Light,” Phys. Rev. Lett. 57, 2516–2519 (1986).
[Crossref] [PubMed]

Padua, S.

C. H. Monken, P. H. S. Ribeiro, and S. Padua, “Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment,” Phys. Rev. A 57, R2267–R2269 (1998).
[Crossref]

Pan, J. W.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

Penin, A. N.

A. N. Penin and A. V. Sergienko, “Absolute Standardless Calibration of Photodetectors Based on Quantum 2-Photon Fields,” Appl. Opt. 30, 3582–3588 (1991).
[Crossref] [PubMed]

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute Calibration of the Sensitivity of Photodetectors Using a Biphotonic Field,” JETP Lett. 33, 477–480 (1981).

Petroff, M. D.

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

Pittman, T. B.

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Single photons on pseudodemand from stored parametric down-conversion,” Phys. Rev. A 66, 042303 (2002).
[Crossref]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

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]

Raj, R. K.

I. Abram, R. K. Raj, J. L. Oudar, and G. Dolique, “Direct Observation of the 2nd-Order Coherence of Parametrically Generated Light,” Phys. Rev. Lett. 57, 2516–2519 (1986).
[Crossref] [PubMed]

Rarity, J. G.

Resch, K. J.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Ribeiro, P. H. S.

C. H. Monken, P. H. S. Ribeiro, and S. Padua, “Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment,” Phys. Rev. A 57, R2267–R2269 (1998).
[Crossref]

Ridley, K. D.

Rubin, M. H.

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental Evaluation of a 2-Photon Wave-Packet in Type-II Parametric Downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[Crossref]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Rudolph, T.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Saleh, B. E. A.

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. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal Coherence Properties of Entangled Light-Beams Generated by Parametric Down-Conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[Crossref] [PubMed]

Schenck, E.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Sergienko, A. V.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental Evaluation of a 2-Photon Wave-Packet in Type-II Parametric Downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[Crossref]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

A. N. Penin and A. V. Sergienko, “Absolute Standardless Calibration of Photodetectors Based on Quantum 2-Photon Fields,” Appl. Opt. 30, 3582–3588 (1991).
[Crossref] [PubMed]

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute Calibration of the Sensitivity of Photodetectors Using a Biphotonic Field,” JETP Lett. 33, 477–480 (1981).

Shih, Y.

Y. Shih, “Two-Photon Entanglement and Quantum Reality,” in Advances in Atomic, Molecular, and Optical Physics, B. Bederson and H. Walther, eds. (Academic Press, Cambridge, 1999), pp. 1–42.
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Shih, Y. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

A. V. Sergienko, Y. H. Shih, and M. H. Rubin, “Experimental Evaluation of a 2-Photon Wave-Packet in Type-II Parametric Downconversion,” J. Opt. Soc. Am. B 12, 859–862 (1995).
[Crossref]

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

Y. H. Shih and C. O. Alley, “New Type of Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Optical Parametric Down Conversion,” Phys. Rev. Lett. 61, 2921–2924 (1988).
[Crossref] [PubMed]

Steinberg, A. M.

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute Efficiency and Time-Response Measurement of Single-Photon Detectors,” Appl. Opt. 33, 1844–1853 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

Tapster, P. R.

Teich, M. C.

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. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal Coherence Properties of Entangled Light-Beams Generated by Parametric Down-Conversion,” Phys. Rev. A 50, 3349–3361 (1994).
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Tittel, W.

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quant. Inf. Comput. 1, 3–56 (2001).

van Exter, M. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005).
[Crossref]

Varisco, P.

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Vedral, V.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Walmsley, I. A.

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

Walther, P.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Weihs, G.

W. Tittel and G. Weihs, “Photonic entanglement for fundamental tests and quantum communication,” Quant. Inf. Comput. 1, 3–56 (2001).

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett. 25, 84–87 (1970).
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Weinfurter, H.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[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]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Woerdman, J. P.

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005).
[Crossref]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley Pub. Co., Reading, MA, 1990).

Zeilinger, A.

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. H. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
[Crossref] [PubMed]

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, “Hot-Spots in Parametric Fluorescence with a Pump Beam of Finite Cross-Section,” IEEE J. Quantum Electron. 31, 769–781 (1995).
[Crossref]

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

J. Phys. Chem. B (1)

D. I. Lee and T. Goodson, “Entangled photon absorption in an organic porphyrin dendrimer,” J. Phys. Chem. B 110, 25582–25585 (2006).
[Crossref] [PubMed]

JETP Lett. (1)

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute Calibration of the Sensitivity of Photodetectors Using a Biphotonic Field,” JETP Lett. 33, 477–480 (1981).

Nature (2)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390, 575–579 (1997).
[Crossref]

P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, “Experimental one-way quantum computing,” Nature 434, 169–176 (2005).
[Crossref] [PubMed]

Opt. Commun. (1)

F. A. Bovino, P. Varisco, A. M. Colla, G. Castagnoli, G. Di Giuseppe, and A. V. Sergienko, “Effective fiber-coupling of entangled photons for quantum communication,” Opt. Commun. 227, 343–348 (2003).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (2)

R. J. Glauber, “Quantum Theory of Optical Coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

D. A. Kleinman, “Theory of Optical Parametric Noise,” Phys. Rev. 174, 1027–1041 (1968).
[Crossref]

Phys. Rev. A (12)

M. H. Rubin, D. N. Klyshko, Y. H. Shih, and A. V. Sergienko, “Theory of two-photon entanglement in type-II optical parametric down-conversion,” Phys. Rev. A 50, 5122–5133 (1994).
[Crossref] [PubMed]

P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “High-Efficiency Single-Photon Detectors,” Phys. Rev. A 48, R867–R870 (1993).
[Crossref] [PubMed]

P. S. K. Lee, M. P. van Exter, and J. P. Woerdman, “How focused pumping affects type-II spontaneous parametric down-conversion,” Phys. Rev. A 72, 033803 (2005).
[Crossref]

R. S. Bennink, Y. Liu, D. D. Earl, and W. P. Grice, “Spatial distinguishability of photons produced by spontaneous parametric down-conversion with a focused pump,” Phys. Rev. A 74, 023802 (2006).
[Crossref]

A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, “Coherence properties of entangled light beams generated by parametric down-conversion: Theory and experiment,” Phys. Rev. A 53, 4360–4371 (1996).
[Crossref] [PubMed]

T. B. Pittman, B. C. Jacobs, and J. D. Franson, “Single photons on pseudodemand from stored parametric down-conversion,” Phys. Rev. A 66, 042303 (2002).
[Crossref]

A. Joobeur, B. E. A. Saleh, and M. C. Teich, “Spatiotemporal Coherence Properties of Entangled Light-Beams Generated by Parametric Down-Conversion,” Phys. Rev. A 50, 3349–3361 (1994).
[Crossref] [PubMed]

T. E. Keller and M. H. Rubin, “Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse,” Phys. Rev. A 56, 1534–1541 (1997).
[Crossref]

W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997).
[Crossref]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[Crossref] [PubMed]

C. H. Monken, P. H. S. Ribeiro, and S. Padua, “Optimizing the photon pair collection efficiency: A step toward a loophole-free Bell’s inequalities experiment,” Phys. Rev. A 57, R2267–R2269 (1998).
[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).
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This approximation limits the crystal thickness to the order of 10-4 m. See Appendix A in [22] for details.

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Figures (4)

Fig. 1.
Fig. 1. Schematic representation of our experimental set-up. PD are photodetectors used to monitor fundamental and second harmonic pump power, DM denote dichroic mirrors utilized for spectral selection, PBS is a Glan-laser polarization beam splitter, and IF is a narrow-band interference filter.
Fig. 2.
Fig. 2. Image of the SPDC spatial profile in our experimental configuration under (a) sharpest focusing of pump beam (d=f=80mm), and (b) loose focusing (d=10mm) condition, generated by measuring transmitted flux through a 1-mm pinhole that is scanned across an image plane normal to the beam path after the collimating lens. Both axes denote position of the pinhole in millimeters. The poor resolution of the image is due to the relatively wide pinhole aperture that was used.
Fig. 3.
Fig. 3. Normalized coincidence-count rate data from (a) 0.5-mm thick, and (b) 2.0-mm thick BBO crystals measured as a function of percent peak pump power for three focusing conditions of the pump: d=80mm (squares), d=38mm (dots), and d=15mm (triangles). Solid lines represent numerical calculations of each case, and dashed lines show the theoretical prediction for the plane-wave (f→∞) limit.
Fig. 4.
Fig. 4. Intensity dependence of signal and idler single-count rates as a function of focusing lens-BBO separation for (a) 0.5-mm thick, and (b) 2.0-mm thick nonlinear crystals. Note that the scale for the thick crystal is ca. 3 times larger. Solid lines for each trace are fits to a parametrized exponential of a form matching that of the spherical-like envelope of the pump field. The mismatch in signals from the two detectors is due to the presence of extra optical loss along APD2 path which is not present in APD1. The insets illustrate progression from small separations between focusing lens and BBO to where the separation is equal to one focal-length of the pump focusing lens. The distance between the BBO and collimating lens is fixed at L=60mm. Because pump-beam divergence is constant throughout this translation, the angular spread of the SPDC spatial profile does not change. However, due to the wider cross-sectional area of interaction at small distances, the size of the profile at a constant distance from the BBO output surface gets narrower as one approaches d=f=80mm limit. A wide aperture is utilized to compensate for this change and ensure collection of the whole down-conversion profile at all d values.

Equations (9)

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E p ( r ; t ) = e ̂ E p ( r ) 0 d ω p A ( ω p ) e i k p ( ω p ) · r e i ω p t ,
E p ( r ) = E p e r 2 2 σ p 2 ,
E p ( r , z ; t ) = E p 0 d ω p A ( ω p ) e i ( ω p t K p z ) d 2 k e i ( k · r + k 2 σ p 2 2 ) .
H I = ε 0 V d 3 r χ E p ( + ) E s ( ) E i ( )
= A 1 d ω p A ( ω p ) d 3 k s d 3 k i V d 3 r a ̂ k s a ̂ k i e i ( ω s + ω i ω p ) t
× e i ( k p k s z k i z ) z e i ( k s k i ) · r e i 2 σ p 2 r 2 + H . C .
ψ = A 2 d ω p A ( ω p ) d 3 k s d 3 k i δ ( ω s + ω i ω p )
× 0 L dz e i ( k p k s z k i z ) z e i · r e ( σ p 2 2 ) ( k s + k i ) 2 a ̂ k s a ̂ k i 0
ψ E 1 ( ) E 2 ( ) E 2 ( + ) E 1 ( + ) ψ 2 = 0 E 2 ( + ) E 1 ( + ) ψ 2 ,

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