Abstract

One-photon and two-photon wave packets of entangled two-photon states in spontaneous parametric downconversion (SPDC) fields are calculated and measured experimentally. For type II SPDC, measured one-photon and two-photon wave packets agree well with theory. For type I SPDC, the measured one-photon wave packet agrees with the theory. However, the two-photon wave packet is much bigger than the expected value, and the visibility of interference is low. We identify the sources of this discrepancy as the spatial filtering of the two-photon bandwidth and nonpair detection events caused by the detector apertures and the tuning-curve characteristics of the type I SPDC.

© 2003 Optical Society of America

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References

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  1. D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, New York, 1988).
  2. C. K. Hong and L. Mandel, “Theory of frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
    [CrossRef] [PubMed]
  3. 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]
  4. Y. H. Shih and C. O. Alley, in Proceedings of the Second International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1986, M. Namiki, ed. (Physical Society of Japan, Tokyo, 1987).
  5. 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]
  6. 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).
    [CrossRef] [PubMed]
  7. Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
    [CrossRef] [PubMed]
  8. P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
    [CrossRef] [PubMed]
  9. Y. H. Shih and A. V. Sergienko, “Two-photon anti-correlation in a Hanbury-Brown-Twiss type experiment,” Phys. Lett. A 186, 29–34 (1994).
    [CrossRef]
  10. Y. H. Shih and A. V. Sergienko, “A two-photon interference experiment using type II optical parametric down conversion,” Phys. Lett. A 191, 201–207 (1994).
    [CrossRef]
  11. A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
    [CrossRef]
  12. A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
    [CrossRef] [PubMed]
  13. D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
    [CrossRef]
  14. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
  15. It is possible to completely remove the group-velocity dispersion effect from G(2)(τ) if the positive dispersion introduced in E1(+)(t) is matched with a negative dispersion introduced in E2(+)(t); see Ref. 19.
  16. Dispersion cancellation experiment based on this effect is reported in Ref. 20 and Ref. 21. This is, however, different from Franson’s nonlocal cancellation of dispersion in G(2)(τ) described in Ref. 19.
  17. Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
    [CrossRef]
  18. Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
    [CrossRef]
  19. J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
    [CrossRef] [PubMed]
  20. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
    [CrossRef] [PubMed]
  21. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
    [CrossRef] [PubMed]

2003 (1)

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

2002 (2)

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[CrossRef]

2001 (1)

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

1999 (1)

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
[CrossRef]

1994 (3)

Y. H. Shih and A. V. Sergienko, “Two-photon anti-correlation in a Hanbury-Brown-Twiss type experiment,” Phys. Lett. A 186, 29–34 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, “A two-photon interference experiment using type II optical parametric down conversion,” Phys. Lett. A 191, 201–207 (1994).
[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]

1992 (4)

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef] [PubMed]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

1988 (2)

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]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

1987 (1)

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).
[CrossRef] [PubMed]

1985 (1)

C. K. Hong and L. Mandel, “Theory of frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[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]

Burlakov, A. V.

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

Chekhova, M. V.

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

Chiao, R. Y.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

Franson, J. D.

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

Grice, W. P.

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[CrossRef]

Hong, C. K.

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).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, “Theory of frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

Karabutova, O. A.

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

Kim, Y.-H.

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[CrossRef]

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
[CrossRef]

Klyshko, D. N.

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]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

Mandel, L.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

C. K. Hong and L. Mandel, “Theory of frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[CrossRef] [PubMed]

Ou, Z. Y.

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Rubin, M. H.

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]

Sergienko, A. V.

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 A. V. Sergienko, “Two-photon anti-correlation in a Hanbury-Brown-Twiss type experiment,” Phys. Lett. A 186, 29–34 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, “A two-photon interference experiment using type II optical parametric down conversion,” Phys. Lett. A 191, 201–207 (1994).
[CrossRef]

Shih, Y.

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
[CrossRef]

Shih, Y. H.

Y. H. Shih and A. V. Sergienko, “A two-photon interference experiment using type II optical parametric down conversion,” Phys. Lett. A 191, 201–207 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, “Two-photon anti-correlation in a Hanbury-Brown-Twiss type experiment,” Phys. Lett. A 186, 29–34 (1994).
[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, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
[CrossRef] [PubMed]

Strekalov, D. V.

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
[CrossRef]

Trifonov, A.

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

Valencia, A.

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

Y.-H. Kim and W. P. Grice, “Generation of pulsed polarization-entangled two-photon state via temporal and spectral engineering,” J. Mod. Opt. 49, 2309–2323 (2002).
[CrossRef]

Phys. Lett. A (2)

Y. H. Shih and A. V. Sergienko, “Two-photon anti-correlation in a Hanbury-Brown-Twiss type experiment,” Phys. Lett. A 186, 29–34 (1994).
[CrossRef]

Y. H. Shih and A. V. Sergienko, “A two-photon interference experiment using type II optical parametric down conversion,” Phys. Lett. A 191, 201–207 (1994).
[CrossRef]

Phys. Rev. A (8)

A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, and S. P. Kulik, “Collinear two-photon state with spectral properties of type-I and polarization properties of type-II spontaneous parametric down-conversion: preparation and testing,” Phys. Rev. A 64, 041803(R) (2001).
[CrossRef]

C. K. Hong and L. Mandel, “Theory of frequency down conversion of light,” Phys. Rev. A 31, 2409–2418 (1985).
[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]

Y.-H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003).
[CrossRef]

J. D. Franson, “Nonlocal cancellation of dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer,” Phys. Rev. A 45, 6659–6665 (1992).
[CrossRef] [PubMed]

D. V. Strekalov, Y.-H. Kim, and Y. Shih, “Experimental study of a subsystem in an entangled two-photon state,” Phys. Rev. A 60, 2685–2688 (1999).
[CrossRef]

P. G. Kwiat, A. M. Steinberg, and R. Y. Chiao, “Observation of a quantum eraser: a revival of coherence in a two-photon interference experiment,” Phys. Rev. A 45, 7729–7739 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[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]

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).
[CrossRef] [PubMed]

Z. Y. Ou and L. Mandel, “Violation of Bell’s inequality and classical probability in a two-photon correlation experiment,” Phys. Rev. Lett. 61, 50–53 (1988).
[CrossRef] [PubMed]

A. Valencia, M. V. Chekhova, A. Trifonov, and Y. Shih, “Entangled two-photon wave packet in a dispersive medium,” Phys. Rev. Lett. 88, 183601 (2002).
[CrossRef] [PubMed]

Other (5)

Y. H. Shih and C. O. Alley, in Proceedings of the Second International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1986, M. Namiki, ed. (Physical Society of Japan, Tokyo, 1987).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).

It is possible to completely remove the group-velocity dispersion effect from G(2)(τ) if the positive dispersion introduced in E1(+)(t) is matched with a negative dispersion introduced in E2(+)(t); see Ref. 19.

Dispersion cancellation experiment based on this effect is reported in Ref. 20 and Ref. 21. This is, however, different from Franson’s nonlocal cancellation of dispersion in G(2)(τ) described in Ref. 19.

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

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Figures (6)

Fig. 1
Fig. 1

Experiment using collinear type II SPDC. λ/2 plate is oriented at 22.5°, and λ/4 plates are oriented at 45°. The polarizer (PBS) and λ/2 plate set, shown in the inset, is inserted only when first-order interference is measured. The shaded area containing PBS, λ/4 plates, and mirrors is equivalent to commonly used quartz polarization delay.

Fig. 2
Fig. 2

Experimental setup using noncollinear type I SPDC. λ/2 plate rotates the polarization of the signal photon from horizontal to vertical. FM is a flipper mirror.

Fig. 3
Fig. 3

Experimental data for type II SPDC. (a) First-order interference. (b) Second-order interference. Solid circles are for θ1=θ2=45°, and empty circles are for θ1=-θ2=45°, where θ1 and θ2 are analyzer (A1 and A2) angles. Peak-dip visibility is ∼84%. Coincidence peak or dip occurs when the e-polarized photons are delayed by D×L/2247 fs with respect to the o-polarized photons before reaching the beam splitter BS.

Fig. 4
Fig. 4

Calculated first- and second-order interference patterns for (a) and (b) type II SPDC and (c) and (d) type I SPDC. Only the fringe envelopes are shown for the first-order interference Rs. It is clear that Rs and Rc have the same envelope shapes. However, the width of the coincidence envelope is half that of first-order interference (Rs). The plots are calculated for the following parameters: BBO crystal with 2-mm thickness, 351.1-nm pump wavelength, and 702.2-nm SPDC central wavelength. For (b), the delay is shifted by D×L/2247 fs for easy comparison with (a).

Fig. 5
Fig. 5

Experimental data for type I SPDC experiment. (a) First-order interference. Only UV cutoff filter (cutoff at 550 nm) is used to suppress the pump noise. The visibility is ∼92%. (b), (c), and (d) show second-order interference measurements. Diamond data points show the level of accidental coincidence. Solid data points are for θ1=-θ2=45°, and empty circles are for θ1=θ2=45°. Spectral filters used for (b), (c), and (d) are 3-nm FWHM, 20-nm FWHM, and 80-nm FWHM, respectively.

Fig. 6
Fig. 6

Tuning curve for noncollinear type I SPDC used in this experiment. Two vertical bars located at ±3° represent the angles defined by the apertures. Left (right) curve shows the angle–spectrum distribution of the signal (idler) photons. See text for details.

Equations (21)

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

|Ψ=s,iδ(ωs+ωi-ωp)δ(ks+ki-kp)×as(ω(ks))ai(ωi(ki))|0,
|ψ=-i-dtH|0.
H=0χ(2)Vd3rEp(+)Es(-)Ei(-)+h.c.,
|ψ=dωsdωisincΔL2exp-i ΔL2as(ωs)ai(ωi)|0,
|ψ=-dνT(ν)as(Ω+ν)ai(Ω-ν)|0,
S(ν)=sincνDL2,
S(ν)=sincν2DL2,
ρ^s=tri[ρˆ]=-dν|S(ν)|2as(Ω+ν)|00|as(Ω+ν).
G(1)(τ)=tr[ρ^sEs(-)(t)Es(+)(t+τ)],
G(1)(τ)=0dω|S(ω-Ω)|2exp(-iωτ),
G(2)(τ)=|0|E2(+)(t+τ)E1(+)(t)|ψ|2,
G(2)(τ)=-S(ν)exp(-iντ)2.
Rs=tr[ρ^sE(-)(t)E(+)(t)],
Rs=0|S(ω-Ω)|2{1+cos(ωτ)},
Rs=12 {1+g(1)(τ)cos(Ωτ)},
Rc=|0|E2(+)(t2)E1(+)(t1)|ψ|2dt1dt2.
E2(+)(t2)=-i sin θ2dνas(Ω+ν)exp[-i(Ω+ν)t2]+cos θ2dνai(Ω-ν)×exp[-i(Ω-ν)(t2+τ)],
E1(+)(t1)=-sin θ1dνas(Ω+ν)exp[-i(Ω+ν)t1]+i cos θ1dνai(Ω-ν)×exp[-i(Ω-ν)(t1+τ)],
Rc=dt+dt-dνdνS(ν)S(ν)exp[i(ν-ν)τ]×sin(νt-)sin(νt-),
dν|S(ν)|2-dν|S(ν)|2exp(-i2ντ),=1-g(1)(2τ),
Rc=12 {1±g(1)(2τ)},

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