Abstract

We experimentally demonstrate amplitude and phase modulation of a time-energy entangled two-photon wave function. The entangled photons are produced by spontaneous parametric down-conversion, spectrally dispersed in an prism compressor, modulated in amplitude and/or phase, and detected in coincidence by sum-frequency generation. First, we present a Fourier optical analysis of the optical setup yielding an analytic expression for the resulting field distribution at the exit plane of the shaping apparatus. We then introduce amplitude and/or phase shaping and present results which can only be obtained through a combination of the two. Specifically, we use a shaper-based interferometer to measure the two-photon interference of an almost bandwidth-limited two-photon wave function.

©2008 Optical Society of America

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  1. E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).
    [Crossref]
  2. S. Popescu and D. Rohrlich, “The joy of entanglement,” in Introduction to quantum computation and information, H.-K. Lo, S. Popescu, and T. Spiller eds. (World Scientific, 1998), pp. 29–48.
    [Crossref]
  3. N. Gisin and R. Thew, “Quantum communication,” Nature Phot. 1, 165–171 (2007).
    [Crossref]
  4. D. Bouwmeester, A. Ekert, and A. ZeilingerThe Physics of Quantum Information (Springer, 2000).
  5. 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]
  6. 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]
  7. 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]
  8. A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a biphotonic field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).
  9. 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, 867–870 (1993).
    [Crossref]
  10. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
    [Crossref] [PubMed]
  11. P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
    [Crossref] [PubMed]
  12. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [Crossref] [PubMed]
  13. T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
    [Crossref]
  14. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
    [Crossref] [PubMed]
  15. 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]
  16. 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]
  17. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
    [Crossref] [PubMed]
  18. Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83, 2556–2559 (1999).
    [Crossref]
  19. M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
    [Crossref] [PubMed]
  20. S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
    [Crossref]
  21. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
    [Crossref] [PubMed]
  22. B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
    [Crossref] [PubMed]
  23. G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597–3639 (1968).
    [Crossref]
  24. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
    [Crossref]
  25. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 1996).
  26. 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]
  27. B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
    [Crossref]

2007 (2)

N. Gisin and R. Thew, “Quantum communication,” Nature Phot. 1, 165–171 (2007).
[Crossref]

B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
[Crossref]

2005 (2)

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
[Crossref] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
[Crossref] [PubMed]

2004 (1)

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
[Crossref]

2003 (1)

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
[Crossref] [PubMed]

2000 (2)

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]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[Crossref]

1999 (1)

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83, 2556–2559 (1999).
[Crossref]

1997 (1)

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]

1995 (3)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
[Crossref]

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[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, 867–870 (1993).
[Crossref]

1990 (1)

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[Crossref] [PubMed]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[Crossref] [PubMed]

1988 (2)

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]

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 (2)

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[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]

1981 (1)

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a biphotonic field,” Sov. Phys. 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)

G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

1935 (1)

E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).
[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]

Afek, I.

B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
[Crossref]

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]

Arecchi, F. T.

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
[Crossref] [PubMed]

Bellini, M.

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
[Crossref]

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
[Crossref] [PubMed]

Björk, G.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (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]

Bouwmeester, D.

D. Bouwmeester, A. Ekert, and A. ZeilingerThe Physics of Quantum Information (Springer, 2000).

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

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]

Bromberg, Y.

B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
[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]

Chiao, R. Y.

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, 867–870 (1993).
[Crossref]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[Crossref] [PubMed]

Chuang, I.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref] [PubMed]

Dayan, B.

B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
[Crossref]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
[Crossref] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
[Crossref] [PubMed]

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 1996).

Dowling, J. 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]

Eberhard, P. H.

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, 867–870 (1993).
[Crossref]

Ekert, A.

D. Bouwmeester, A. Ekert, and A. ZeilingerThe Physics of Quantum Information (Springer, 2000).

Franson, J. D.

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62, 2205–2208 (1989).
[Crossref] [PubMed]

Friesem, A. A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
[Crossref] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
[Crossref] [PubMed]

Ghosh, R.

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[Crossref] [PubMed]

Gisin, N.

N. Gisin and R. Thew, “Quantum communication,” Nature Phot. 1, 165–171 (2007).
[Crossref]

Hong, C. K.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[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]

Jacobson, J.

J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref] [PubMed]

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.

G. D. Boyd and D. A. Kleinman, “Parametric Interaction of Focused Gaussian Light Beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

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]

Kwiat, P. G.

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, 867–870 (1993).
[Crossref]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[Crossref] [PubMed]

Lu, Y. J.

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83, 2556–2559 (1999).
[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,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

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]

R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987).
[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]

Marin, F.

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
[Crossref] [PubMed]

Nathel, H.

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[Crossref] [PubMed]

Ou, Z. Y.

Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric down-conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett. 83, 2556–2559 (1999).
[Crossref]

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]

Pe’er, A.

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
[Crossref] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
[Crossref] [PubMed]

Penin, A. N.

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a biphotonic field,” Sov. Phys. 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, “High-efficiency single-photon detectors,” Phys. Rev. A 48, 867–870 (1993).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
[Crossref]

Popescu, S.

S. Popescu and D. Rohrlich, “The joy of entanglement,” in Introduction to quantum computation and information, H.-K. Lo, S. Popescu, and T. Spiller eds. (World Scientific, 1998), pp. 29–48.
[Crossref]

Rohrlich, D.

S. Popescu and D. Rohrlich, “The joy of entanglement,” in Introduction to quantum computation and information, H.-K. Lo, S. Popescu, and T. Spiller eds. (World Scientific, 1998), pp. 29–48.
[Crossref]

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]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic Press, 1996).

Schrödinger, E.

E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik,” Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).
[Crossref]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
[Crossref]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

A. A. Malygin, A. N. Penin, and A. V. Sergienko, “Absolute calibration of the sensitivity of photodetectors using a biphotonic field,” Sov. Phys. JETP Lett. 33, 477–480 (1981).

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
[Crossref]

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]

Silberberg, Y.

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[Crossref]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,” Phys. Rev. Lett. 94, 043602 (2005).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Steinberg, A. M.

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, 867–870 (1993).
[Crossref]

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D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
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S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
[Crossref]

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
[Crossref] [PubMed]

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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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A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[Crossref]

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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).
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J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref] [PubMed]

Zavatta, A.

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
[Crossref]

M. Bellini, F. Marin, S. Viciani, A. Zavatta, and F. T. Arecchi, “Nonlocal Pulse Shaping with Entangled Photon Pairs,” Phys. Rev. Lett. 90, 043602 (2003).
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[Crossref]

Phys. Rev. A (6)

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, 867–870 (1993).
[Crossref]

P. G. Kwiat, W. A. Vareka, C. K. Hong, H. Nathel, and R. Y. Chiao, “Correlated two-photon interference in a dual-beam Michelson interferometer,” Phys. Rev. A 41, 2910–2913 (1990).
[Crossref] [PubMed]

T. B. Pittman, Y. H. Shih, D.V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3432 (1995).
[Crossref]

S. Viciani, A. Zavatta, and M. Bellini, “Nonlocal modulations of the temporal and spectral profiles of an entangled photon pair,” Phys. Rev. A 69, 053801 (2004).
[Crossref]

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]

B. Dayan, Y. Bromberg, I. Afek, and Y. Silberberg, “Spectral polarization and spectral phase control of time-energy entangled photons,” Phys. Rev. A 75, 043804 (2007).
[Crossref]

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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).
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J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995).
[Crossref] [PubMed]

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).
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[Crossref] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of Two-Photon “Ghost” Interference and Diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
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[Crossref] [PubMed]

B. Dayan, A. Pe’er, A. A. Friesem, and Y. Silberberg, “Temporal Shaping of Entangled Photons,” Phys. Rev. Lett. 94, 073601 (2005).
[Crossref] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1. Optical setup and schematic for Fourier optical analysis.

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Fig. 2.
Fig. 2. Coincidence signal as a function of the position of (a) a spectral edge, (b) a spectral slice, and (c) of an amplitude grating. The insets show the shape of the different amplitude filters which are scanned across the spectrum.

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Fig. 3.
Fig. 3. Coincidence signal as a function of (a) the magnitude of the quadratic spectral phase and (b) the slope of a V-shaped linear phase. The insets show the shape of the two types of phase modulations.

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Fig. 4.
Fig. 4. Two-photon interference with (a) γ=1 and ϕ=0,π, and (b) γ=0 and ϕ=0,π. The inset in (a) shows a small section of the two-photon interference for ϕ=0 and π, respectively.

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Equations (8)

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E ˜ 1 + ( x , ω ) ∝ E ˜ 0 + ( x , ω ) M ( − mx − f ( m + 1 ) k c γ ( ω − ω c ) ) exp [ − i k c m f x 2 + i f ( m + 1 ) k c γ 2 ( ω − ω c ) 2 ] ,
E ˜ 1 ( ω ) = E ˜ 0 ( ω ) M ( ω ) ,
M ( ω ) ∝ ∫ d x F ( x ) M ( − mx − f ( m + 1 ) k c γ ( ω − ω c ) ) exp ( − i k c m f x 2 ) .
∣ Ψ 〉 =| 0 〉 + ∫ d ω s ξ ( ω s ) a ̂ s † ( ω s ) a ̂ i † ( ω pc − ω s ) ∣ 0 〉 ,
ξ ( ω s ) ≐ α E ˜ p sin c ( Δ k L 2 ) e − i Δ k L 2 .
G ( 2 ) ( 0 , 0 ) = ∣ 〈 0 ∣ E ̂ s + ( 0 ) E ̂ i + ( 0 ) ∣ Ψ 〉 ∣ 2 = ∣ ∫ d ω s M s ( ω s ) M i ( ω pc − ω s ) ξ ( ω s ) ∣ 2 .
M s , i ( ω ) = rt ( 1 + e − i ω τ ) ,
M s , i ( ω ) = 1 2 [ 1 + exp ( − i ω τ + i ( 1 − γ ) ω pc 2 τ − i ϕ ) ] .

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