Abstract

A pair of optical pulses traveling through two dispersive media will become broadened and, as a result, the degree of coincidence between the optical pulses will be reduced. For a pair of entangled photons, however, nonlocal dispersion cancellation in which the dispersion experienced by one photon cancels the dispersion experienced by the other photon is possible. In this paper, we report an experimental demonstration of nonlocal dispersion cancellation using entangled photons. The degree of two-photon coincidence is shown to increase beyond the limit attainable without entanglement. Our results have important applications in fiber-based quantum communication and quantum metrology.

© 2009 Optical Society of America

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  1. J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
    [CrossRef] [PubMed]
  2. 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]
  3. Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
    [CrossRef] [PubMed]
  4. P. P. Rohde and T. C. Ralph, "Optimal photons for quantum information processing," Phys. Rev. A 72, 052332 (2005).
    [CrossRef]
  5. T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
    [CrossRef]
  6. V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
    [CrossRef]
  7. M. J. Fitch and J. D. Franson, "Dispersion cancellation and nonclassical noise reduction for large-photon-number states," Phys. Rev. A 65, 053809 (2002).
    [CrossRef]
  8. J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
    [CrossRef]
  9. The demonstration in Ref. [8] is local in the sense that both photons propagate through the same optical fiber. Furthermore, actual reduction of a broadened wave packet is not experimentally demonstrated.
  10. 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]
  11. M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
    [CrossRef] [PubMed]
  12. Dispersion cancellation of Ref. [10, 11] is based on Hong-Ou-Mandel interference in which two photons meet again before getting detected. It, therefore, is not a nonlocal effect and there exists a classical analog. On the other hand, in the nonlocal dispersion cancellation of Ref. [1], dispersion experienced by one photon is nonlocally cancelled by dispersion experienced by it’s entangled pair photon which may be arbitrarily far apart. See Ref. [13, 14].
  13. J. D. Franson, Proceedings of the 9th Rochester Conference on Coherence and Quantum Optics, eds. N. P. Bigelow, J. H. Eberly, and C. R. Stroud, "Nonlocal Interferometry: Beyond Bell’s Inequality," Jr. (American Institute of Physics, 2008).
  14. J. D. Franson, "Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry," prreprint arXiv: 0907.5196 (2009).
  15. Y.-H. Kim and W. P. Grice, "Measurement of the spectral properties of the two-photon state generated via type II spontaneous parametric downconversion," Opt. Lett. 30, 908-910 (2005).
    [CrossRef] [PubMed]
  16. S.-Y. Baek and Y.-H. Kim, "Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion," Phys. Rev. A 77, 043807 (2008).
    [CrossRef]
  17. M. H. Rubin, "Transverse correlation in optical spontaneous parametric down-conversion," Phys. Rev. A 54, 5349-5360 (1996).
    [CrossRef] [PubMed]
  18. We have assumed © 2D4L4 (®1z1+®2z2)2. This condition holds in general as the crystal parameter DL is much smaller than the external parameters ®1z1 and ®2z2.
  19. A. Valencia, M. V. Chekhova, A. Trifonov, and Y. H. Shih, "Entangled two-photon wave packet in a dispersive medium," Phys. Rev. Lett. 88, 183601 (2002).
    [CrossRef] [PubMed]
  20. S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
    [CrossRef]
  21. S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
    [CrossRef]
  22. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley & Sons, Hoboken, New Jersey, 2007).
  23. E. B. Treacy, "Optical Pulse CompressionWith Diffraction Gratings," IEEE J. Quantum Electron. QE-5, 454-458 (1969).
    [CrossRef]
  24. R. L. Fork, O. E. Martinez, J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett. 9, 150-152 (1984).
    [CrossRef] [PubMed]
  25. The gratings G1 and G2 are Spectrogon model 715.701.990 and 715.701.350, respectively. Both gratings have the same line spacing (2400 grooves/mm) and blaze wavelength (800 nm) but different in size. The detailed specifications can be found at http://www.spectrogon.com/gratpulse.html.
  26. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, Burlington, MA, 2006).
  27. The measurement errors are mainly from measuring the distance G, ±1 mm, and the angle  _, ±2◦.
  28. G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
    [CrossRef]

2009 (1)

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

2008 (3)

S.-Y. Baek and Y.-H. Kim, "Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion," Phys. Rev. A 77, 043807 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
[CrossRef]

2005 (2)

2003 (1)

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

2002 (2)

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

M. J. Fitch and J. D. Franson, "Dispersion cancellation and nonclassical noise reduction for large-photon-number states," Phys. Rev. A 65, 053809 (2002).
[CrossRef]

2001 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
[CrossRef]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
[CrossRef] [PubMed]

1998 (2)

J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
[CrossRef]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

1996 (1)

M. H. Rubin, "Transverse correlation in optical spontaneous parametric down-conversion," Phys. Rev. A 54, 5349-5360 (1996).
[CrossRef] [PubMed]

1992 (2)

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]

J. D. Franson, "Nonlocal cancellation of dispersion," Phys. Rev. A 45, 3126-3132 (1992).
[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]

1984 (1)

1969 (1)

E. B. Treacy, "Optical Pulse CompressionWith Diffraction Gratings," IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

Aspelmeyer, M.

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

Baek, S.-Y.

S.-Y. Baek and Y.-H. Kim, "Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion," Phys. Rev. A 77, 043807 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
[CrossRef]

Brendel, J.

J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
[CrossRef]

Chekhova, M. V.

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

Chiao, R. Y.

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]

Fitch, M. J.

M. J. Fitch and J. D. Franson, "Dispersion cancellation and nonclassical noise reduction for large-photon-number states," Phys. Rev. A 65, 053809 (2002).
[CrossRef]

Fork, R. L.

Franson, J. D.

M. J. Fitch and J. D. Franson, "Dispersion cancellation and nonclassical noise reduction for large-photon-number states," Phys. Rev. A 65, 053809 (2002).
[CrossRef]

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

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
[CrossRef]

Gisin, N.

J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
[CrossRef]

Gordon, J. P.

Grice, W. P.

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]

Jennewein, T.

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

Kim, Y.-H.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
[CrossRef]

S.-Y. Baek and Y.-H. Kim, "Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion," Phys. Rev. A 77, 043807 (2008).
[CrossRef]

Y.-H. Kim and W. P. Grice, "Measurement of the spectral properties of the two-photon state generated via type II spontaneous parametric downconversion," Opt. Lett. 30, 908-910 (2005).
[CrossRef] [PubMed]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
[CrossRef] [PubMed]

Kulik, S. P.

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
[CrossRef] [PubMed]

Kwiat, P. G.

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]

Kwon, O.

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
[CrossRef]

Mandel, L.

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]

Martinez, O. E.

Nasr, M. B.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Ou, Z. Y.

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]

Ralph, T. C.

P. P. Rohde and T. C. Ralph, "Optimal photons for quantum information processing," Phys. Rev. A 72, 052332 (2005).
[CrossRef]

Rohde, P. P.

P. P. Rohde and T. C. Ralph, "Optimal photons for quantum information processing," Phys. Rev. A 72, 052332 (2005).
[CrossRef]

Rubin, M. H.

M. H. Rubin, "Transverse correlation in optical spontaneous parametric down-conversion," Phys. Rev. A 54, 5349-5360 (1996).
[CrossRef] [PubMed]

Saleh, B. E. A.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Sergienko, A. V.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Shih, Y. H.

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

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
[CrossRef] [PubMed]

Simon, C.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

Steinberg, A. M.

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]

Teich, M. C.

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

Treacy, E. B.

E. B. Treacy, "Optical Pulse CompressionWith Diffraction Gratings," IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

Trifonov, A.

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

Ursin, R.

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

Valencia, A.

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

Weihs, G.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

Weinfurter, H.

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

Zbinden, H.

J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
[CrossRef]

Zeilinger, A.

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. B. Treacy, "Optical Pulse CompressionWith Diffraction Gratings," IEEE J. Quantum Electron. QE-5, 454-458 (1969).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (1)

T. Jennewein, R. Ursin, M. Aspelmeyer, and A. Zeilinger, "Performing high-quality multi-photon experiments with parametric down-conversion," J. Phys. B: At. Mol. Opt. Phys. 42, 114008 (2009).
[CrossRef]

Nature (London) (1)

V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced positioning and clock synchronization," Nature (London) 412, 417-419 (2001).
[CrossRef]

Opt. Commun. (1)

J. Brendel, H. Zbinden, and N. Gisin, "Measurement of chromatic dispersion in optical fibers using pairs of correlated photons," Opt. Commun. 151, 35-39 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (7)

S.-Y. Baek and Y.-H. Kim, "Spectral properties of entangled photon pairs generated via frequency-degenerate type-I spontaneous parametric down-conversion," Phys. Rev. A 77, 043807 (2008).
[CrossRef]

M. H. Rubin, "Transverse correlation in optical spontaneous parametric down-conversion," Phys. Rev. A 54, 5349-5360 (1996).
[CrossRef] [PubMed]

P. P. Rohde and T. C. Ralph, "Optimal photons for quantum information processing," Phys. Rev. A 72, 052332 (2005).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Temporal shaping of a heralded single-photon wave packet," Phys. Rev. A 77, 013829 (2008).
[CrossRef]

S.-Y. Baek, O. Kwon, and Y.-H. Kim, "Nonlocal dispersion control of a single-photon waveform," Phys. Rev. A 78, 013816 (2008).
[CrossRef]

M. J. Fitch and J. D. Franson, "Dispersion cancellation and nonclassical noise reduction for large-photon-number states," Phys. Rev. A 65, 053809 (2002).
[CrossRef]

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

Phys. Rev. Lett. (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]

Y.-H. Kim, S. P. Kulik, and Y. H. Shih, "Quantum teleportation of a polarization state with a complete bell state measurement," Phys. Rev. Lett. 86, 1370-1373 (2001).
[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]

M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Demonstration of Dispersion-Canceled Quantum-Optical Coherence Tomography," Phys. Rev. Lett. 91, 083601 (2003).
[CrossRef] [PubMed]

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

G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger, "Violations of Bell’s Inequality under Strict Einstein Locality Conditions," Phys. Rev. Lett. 81, 5039-5043 (1998).
[CrossRef]

Other (9)

The gratings G1 and G2 are Spectrogon model 715.701.990 and 715.701.350, respectively. Both gratings have the same line spacing (2400 grooves/mm) and blaze wavelength (800 nm) but different in size. The detailed specifications can be found at http://www.spectrogon.com/gratpulse.html.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, Burlington, MA, 2006).

The measurement errors are mainly from measuring the distance G, ±1 mm, and the angle  _, ±2◦.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley & Sons, Hoboken, New Jersey, 2007).

We have assumed © 2D4L4 (®1z1+®2z2)2. This condition holds in general as the crystal parameter DL is much smaller than the external parameters ®1z1 and ®2z2.

The demonstration in Ref. [8] is local in the sense that both photons propagate through the same optical fiber. Furthermore, actual reduction of a broadened wave packet is not experimentally demonstrated.

Dispersion cancellation of Ref. [10, 11] is based on Hong-Ou-Mandel interference in which two photons meet again before getting detected. It, therefore, is not a nonlocal effect and there exists a classical analog. On the other hand, in the nonlocal dispersion cancellation of Ref. [1], dispersion experienced by one photon is nonlocally cancelled by dispersion experienced by it’s entangled pair photon which may be arbitrarily far apart. See Ref. [13, 14].

J. D. Franson, Proceedings of the 9th Rochester Conference on Coherence and Quantum Optics, eds. N. P. Bigelow, J. H. Eberly, and C. R. Stroud, "Nonlocal Interferometry: Beyond Bell’s Inequality," Jr. (American Institute of Physics, 2008).

J. D. Franson, "Nonclassical Nature of Dispersion Cancellation and Nonlocal Interferometry," prreprint arXiv: 0907.5196 (2009).

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Figures (5)

Fig. 1.
Fig. 1.

Each photon of the entangled photon pair is subject to different dispersion β 1 and β 2. The coincidence circuit measures G (2)(t 1t 2).

Fig. 2.
Fig. 2.

Schematic of the experiment. Positive dispersion β 1 is introduced by a 1.6 km long single-mode optical fiber and negative dispersion β 2 is introduced by using a pair of gratings (G 1 and G 2) and a mirror. FPC and M represent a fiber polarization controller and a monochromator, respectively.

Fig. 3.
Fig. 3.

Experimentally measured entangled photon wave packet. Monochromator was not used for this measurement. (a) With positive dispersion β 1 only, the wave packet has the FWHM width of 3.861 ns. (b) With both positive dispersion β 1 and negative dispersion β 2, the wave acket has the FWHM width of 2.436 ns. Solid lines are Gaussian fit to the data.

Fig. 4.
Fig. 4.

Spectrally-resolved entangled photon wave packet with the monochromator. (a) With positive dispersion β1 only. (b) With both positive dispersion β1 and negative dispersion β2. Solid lines are Gaussian fit to the data. The nonlocal dispersion cancellation effect is clear demonstrated.

Fig. 5.
Fig. 5.

The joint detection probability for a number of cases involving classical pulse pairs under group velocity dispersion. (a) Detection probabilities for pulse 1, P 1(t 1), and pulse 2, P 2(t 2), after they have propagated through +β and -β media, respectively. The joint detection probability Pc (t 1t 2) is always broader then the single detection probabilities. Note that (+β, -β) refers to the case in which pulse 1 (pulse 2) goes through the positive (the negative) dispersive medium. Figures (b), (c), and (d) show the joint detection probabilities for a frequency-anticorrelated mixture of classical pulse pairs. Note that (+β, 0) refers to the case in which pulse 1 goes through the positive dispersion medium while pulse 2 goes through a non-dispersive medium. (+β, +β), and (+β, -β) have similar meanings. If spectrally identical sources are used, the the overall joint detection probabilities cannot be smaller than the individual probabilities. See text for details.

Equations (22)

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ψ= d ω1 d ω2 (ω1,ω2) a (ω1) a (ω2) 0 ,
G(2)(t1,t2)=0E2(+)(t2)E1(+)(t1)ψ2,
ψ= d v (v)a(Ω1+v)a (Ω2v) 0 ,
G(2)(t1t2)= d v (v) eiv(t1t2) × ei(α1z1α1z2)v ei(β1z1+β2z2)v2 2 .
G(2)(t1t2)C e(t1t2τˉ)2 2 σ2 ,
Δ t 2 2ln2γD2L2 (β1z1+β2z2) .
Δ tNDC 2 2ln2γD2L2 β2 z2 .
β2 z2 = λ22πc2 (λ2d)Gcos(θ)3,
ρmixed dν f1 (ν)f2(ν)a(Ω1+ν)a(Ω2ν)00a(Ω1+ν)a(Ω2ν),
G(2) (t1,t2)=Tr[ρmixedE1()(t1)E2()(t2)E2(+)(t2)E1(+)(t1)],
G(2) (t1,t2)=1.
E1 (t1,z1)=1E02πeν122σ02ei(k1(Ω1)+α1ν1+β1ν12)z1ei(Ω1+ν1)t1,
I1 (z1,t1)=E024πa12e(α1z1t1)22σ12 ,
I2 (z2,t2)=E024πa22e(α2z2t2)22σ22,
P (τ)=dt1ηI1(z1,t1)I2(z2,t1+τ)=Ce(ττˉ)22(σ12+σ22),
σT2 = σ12 + σ22 = 2 σ02 (12σ04+β12z12+β22z22),
σT2 2 σ02 (β12z12+β22z22).
Δ t 4 ln2 σ0 β12z12+β22z22.
τm = z1ν1(Ω+) z2ν2(Ω) ,
Δ τ (+β,0)τ+1τ0=z1ν1(Ω+ν)z1ν1(Ω).
Δ τ (+β,+β)=τ+1τ0=Δτ(+β,0)+z2ν2(Ω)z2ν2(Ων),
Δ τ (+β,+β)>Δτ(+β,0)>Δτ(+β,β).

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