Abstract

We propose a method to generate a narrowband triphoton W state entangled in time (or energy) via two four-wave mixing processes in cold atomic gas media. The calculation of such a triphoton W state is performed with second-order perturbation theory. To characterize the optical properties of the state, we analyze the two-photon and three-photon temporal correlations in the photon coincidence counting measurement. Considering the role of determining the time coherence of triphotons between the nonlinear susceptibilities and phase matchings, we concentrate on two regimes, damped Rabi oscillation and group delay, to look at the temporal correlations. To further enhance the nonlinear interactions, it may be promising to consider cold atoms confined within hollow fibers or loaded into a high-Q cavity.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).
  2. A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).
  3. W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
    [CrossRef]
  4. A. Cabello, “Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states,” Phys. Rev. A 65, 032108 (2002).
    [CrossRef]
  5. D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
    [CrossRef]
  6. J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
    [CrossRef] [PubMed]
  7. M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
    [CrossRef] [PubMed]
  8. C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
    [CrossRef] [PubMed]
  9. H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
    [CrossRef] [PubMed]
  10. Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
    [CrossRef] [PubMed]
  11. L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
    [CrossRef] [PubMed]
  12. J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
    [CrossRef]
  13. P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000).
    [CrossRef] [PubMed]
  14. P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001).
    [CrossRef]
  15. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
    [CrossRef]
  16. J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009).
    [CrossRef]
  17. J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
    [CrossRef]
  18. J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.
  19. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
    [CrossRef] [PubMed]
  20. Y.-H. Shih, “Entangled biphoton source—property and preparation,” Rep. Prog. Phys. 66, 1009-1044 (2003).
    [CrossRef]
  21. 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]
  22. H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
    [CrossRef]
  23. C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
    [CrossRef] [PubMed]
  24. J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, “High purity bright single photon source,” Opt. Express 15, 7940-7949 (2007).
    [CrossRef] [PubMed]
  25. J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006).
    [CrossRef]
  26. J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
    [CrossRef]
  27. J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
    [CrossRef]
  28. J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
    [CrossRef]
  29. J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
    [CrossRef]
  30. P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75, 033814 (2007).
    [CrossRef]
  31. C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007).
    [CrossRef]
  32. S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008).
    [CrossRef]
  33. C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
    [CrossRef]
  34. Y. P. Huang and M. G. Moore, “Ultra-bright biphoton emission from an atomic vapor based on Doppler-free four-wave-mixing and collective emission,” arXiv:0901.4789.
  35. V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
    [CrossRef] [PubMed]
  36. P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
    [CrossRef] [PubMed]
  37. S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
    [CrossRef] [PubMed]
  38. S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
    [CrossRef] [PubMed]
  39. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
    [CrossRef]
  40. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-41 (1997).
    [CrossRef]
  41. M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
    [CrossRef]
  42. M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
    [CrossRef]
  43. T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
    [CrossRef]
  44. M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
    [CrossRef] [PubMed]
  45. J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
    [CrossRef] [PubMed]
  46. 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]
  47. D. N. Klyshko, Photons and Nonlinear Optics (Gordon and Breach, 1988).
  48. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  49. M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.
  50. M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349-5360 (1996).
    [CrossRef] [PubMed]
  51. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  52. S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
    [CrossRef] [PubMed]
  53. J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
    [CrossRef]
  54. Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
    [CrossRef] [PubMed]
  55. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
    [CrossRef] [PubMed]

2009 (5)

L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
[CrossRef] [PubMed]

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009).
[CrossRef]

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

2008 (5)

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008).
[CrossRef]

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

2007 (9)

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75, 033814 (2007).
[CrossRef]

C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
[CrossRef]

J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, “High purity bright single photon source,” Opt. Express 15, 7940-7949 (2007).
[CrossRef] [PubMed]

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

2006 (6)

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
[CrossRef]

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

2005 (4)

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

2004 (3)

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
[CrossRef]

2003 (1)

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

2002 (1)

A. Cabello, “Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states,” Phys. Rev. A 65, 032108 (2002).
[CrossRef]

2001 (3)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001).
[CrossRef]

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

2000 (3)

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

1999 (2)

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

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]

1998 (1)

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-41 (1997).
[CrossRef]

1996 (1)

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

1994 (1)

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]

Adamson, R. B.

L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
[CrossRef] [PubMed]

Anderson, B.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Bajcsy, M.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Balic, V.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

Bao, X.-H.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Barreiro, S.

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

Becher, C.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Belthangady, C.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Benhelm, J.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Berardi, V.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

Blatt, R.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Bourennane, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Bouwmeester, D.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Braje, D. A.

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

Braunstein, S. L.

P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001).
[CrossRef]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Brown, A. W.

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Cabello, A.

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

A. Cabello, “Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states,” Phys. Rev. A 65, 032108 (2002).
[CrossRef]

Chekhova, M. V.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

Chen, S.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Chen, Y.-A.

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

Chen, Z.-B.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Cirac, J. I.

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Daniell, M.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Du, S.

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008).
[CrossRef]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
[CrossRef]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

Dür, W.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Eibl, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Fukuoka, K.

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

Garuccio, A.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

Giedke, G.

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

Greenberger, D. M.

A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).

Hafezi, M.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Hänsel, H.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Harris, S. E.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-41 (1997).
[CrossRef]

Hemmer, P. R.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.

Hofferberth, S.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Horikiri, T.

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
[CrossRef]

Horne, M. A.

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).

A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).

Huang, Y. P.

Y. P. Huang and M. G. Moore, “Ultra-bright biphoton emission from an atomic vapor based on Doppler-free four-wave-mixing and collective emission,” arXiv:0901.4789.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Ivanova, O. A.

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

Keller, T. E.

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[CrossRef]

Khadka, U.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

Kiesel, N.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

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]

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

Kobayashi, T.

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
[CrossRef]

Kolchin, P.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75, 033814 (2007).
[CrossRef]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

Kraus, B.

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

Kuklewicz, C. E.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Kurtsiefer, C.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Lancaster, G. P. T.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Lewenstein, M.

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

Li, Y.

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

Loh, H.

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

Loock, P. Van

P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001).
[CrossRef]

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]

Lukin, M. D.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Marangos, J.

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Metcalf, H. J.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
[CrossRef]

Mikami, H.

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

Mitchell, M. W.

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

Moore, M. G.

Y. P. Huang and M. G. Moore, “Ultra-bright biphoton emission from an atomic vapor based on Doppler-free four-wave-mixing and collective emission,” arXiv:0901.4789.

Neergaard-Nielsen, J. S.

Nielsen, B. M.

Ooi, C. H. R.

C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007).
[CrossRef]

Osorio, C. I.

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

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]

Pan, J.-W.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Peng, C.-Z.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Peyronel, T.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Polzik, E. S.

Riebe, M.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Roos, C. F.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Rubin, M. H.

J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009).
[CrossRef]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008).
[CrossRef]

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
[CrossRef]

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006).
[CrossRef]

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[CrossRef]

M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349-5360 (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]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.

Schmidt-Kaler, F.

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Scully, M. O.

C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007).
[CrossRef]

M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.

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]

Shalm, L. K.

L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
[CrossRef] [PubMed]

Shapiro, J. H.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Shih, Y.-H.

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
[CrossRef]

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

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[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]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.

Simon, J.

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

Steinberg, A. M.

L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
[CrossRef] [PubMed]

Takahashi, H.

Thompson, J. K.

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

Torres, J. P.

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

van der Straten, P.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
[CrossRef]

van Loock, P.

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

Vidal, G.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Vistnes, A. I.

Vuletic, V.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

Wang, H.

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
[CrossRef]

Weinfurter, H.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

Wen, J.-M.

J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009).
[CrossRef]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

S. Du, J.-M. Wen, and M. H. Rubin, “Narrowband biphoton generation near atomic resonance,” J. Opt. Soc. Am. B 25, C98-C108 (2008).
[CrossRef]

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
[CrossRef]

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006).
[CrossRef]

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

Wong, F. N. C.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Wu, L.-A.

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[CrossRef]

Xiao, M.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Xu, P.

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

Yang, J.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Yang, T.

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

Yin, G. Y.

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149-2151 (2008).
[CrossRef] [PubMed]

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

Zeilinger, A.

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).

A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).

Zhang, A.-N.

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

Zhang, H.

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

Zhang, Y. P.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Zhao, Z.

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

Zibrov, A. S.

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

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

Nature (3)

J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature 403, 515-519 (2000).
[CrossRef] [PubMed]

L. K. Shalm, R. B. Adamson, and A. M. Steinberg, “Squeezing and over-squeezing of triphotons,” Nature 457, 67-70 (2009).
[CrossRef] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413-418 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (21)

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in multiphoton entanglement,” Phys. Rev. A 76, 045802 (2007).
[CrossRef]

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

M. V. Chekhova, O. A. Ivanova, V. Berardi, and A. Garuccio, “Spectral properties of three-photon entangled states generated via three-photon parametric down-conversion in a χ(3) medium,” Phys. Rev. A 72, 023818 (2005).
[CrossRef]

T. E. Keller, M. H. Rubin, Y.-H. Shih, and L.-A. Wu, “Theory of the three-photon entangled state,” Phys. Rev. A 57, 2076-2079 (1998).
[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]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. I. Perturbation theory,” Phys. Rev. A 74, 023808 (2006).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Transverse effects in paired-photon generation via an electromagnetically induced transparency medium. II. Beyond perturbation theory,” Phys. Rev. A 74, 023809 (2006).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Biphoton generation in a two-level atomic ensemble,” Phys. Rev. A 75, 033809 (2007).
[CrossRef]

J.-M. Wen, S. Du, and M. H. Rubin, “Spontaneous parametric down-conversion in a three-level system,” Phys. Rev. A 76, 013825 (2007).
[CrossRef]

J.-M. Wen, S. Du, Y. P. Zhang, M. Xiao, and M. H. Rubin, “Nonclassical light generation via a four-level inverted-Y system,” Phys. Rev. A 77, 033816 (2008).
[CrossRef]

P. Kolchin, “Electromagnetically-induced-transparency-based paired photon generation,” Phys. Rev. A 75, 033814 (2007).
[CrossRef]

C. H. R. Ooi and M. O. Scully, “Two-photon correlation in a cascade amplifier: Propagation effects via a simple model, nonclassical regimes, and validity of neglecting Langevin noise,” Phys. Rev. A 76, 043822 (2007).
[CrossRef]

C. I. Osorio, S. Barreiro, M. W. Mitchell, and J. P. Torres, “Spatial entanglement of paired photons generated in cold atomic ensembles,” Phys. Rev. A 78, 052301 (2008).
[CrossRef]

H. Wang, T. Horikiri, and T. Kobayashi, “Polarization-entangled mode-locked photons from cavity-enhanced spontaneous parametric down-conversion,” Phys. Rev. A 70, 043804 (2004).
[CrossRef]

J. Yang, X.-H. Bao, H. Zhang, S. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, “Experimental quantum teleportation and multiphoton entanglement via interfering narrowband photon sources,” Phys. Rev. A 80, 042321 (2009).
[CrossRef]

P. Van Loock and S. L. Braunstein, “Greenberger-Horne-Zeilinger nonlocality in phase space,” Phys. Rev. A 63, 022106 (2001).
[CrossRef]

G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, “Separability properties of three-mode Gaussian states,” Phys. Rev. A 64, 052303 (2001).
[CrossRef]

J.-M. Wen and M. H. Rubin, “Distinction of tripartite Greenberger-Horne-Zeilinger and W states entangled in time (or energy) and space,” Phys. Rev. A 79, 025802 (2009).
[CrossRef]

J.-M. Wen, P. Xu, M. H. Rubin, and Y.-H. Shih, “Transverse correlations in tripartite entanglement: Geometrical and physical optics,” Phys. Rev. A 76, 023828 (2007).
[CrossRef]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

A. Cabello, “Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states,” Phys. Rev. A 65, 032108 (2002).
[CrossRef]

Phys. Rev. Lett. (14)

D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345-1349 (1999).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, “New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography,” Phys. Rev. Lett. 95, 150404 (2005).
[CrossRef] [PubMed]

Y.-A. Chen, T. Yang, A.-N. Zhang, Z. Zhao, A. Cabello, and J.-W. Pan, “Experimental violation of Bell's inequality beyond Tsirelson's bound,” Phys. Rev. Lett. 97, 170408 (2006).
[CrossRef] [PubMed]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84, 3482-3485 (2000).
[CrossRef] [PubMed]

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Time-bin-modulated biphotons from cavity-enhanced down-conversion,” Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

V. Balić, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, “Generation of paired photons with controllable waveforms,” Phys. Rev. Lett. 94, 183601 (2005).
[CrossRef] [PubMed]

P. Kolchin, S. Du, C. Belthangady, G. Y. Yin, and S. E. Harris, “Generation of narrow-bandwidth paired photons: Use of a single driving laser,” Phys. Rev. Lett. 97, 113602 (2006).
[CrossRef] [PubMed]

S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98, 053601 (2007).
[CrossRef] [PubMed]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef] [PubMed]

M. Bajcsy, S. Hofferberth, V. Balić, T. Peyronel, M. Hafezi, A. S. Zibrov, V. Vuletic, and M. D. Lukin, “Efficient all-optical switching using slow light within a hollow fiber,” Phys. Rev. Lett. 102, 203902 (2009).
[CrossRef] [PubMed]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99, 123603 (2007).
[CrossRef] [PubMed]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four-wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102, 013601 (2009).
[CrossRef] [PubMed]

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]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36-41 (1997).
[CrossRef]

Rep. Prog. Phys. (1)

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

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
[CrossRef]

Science (2)

J. K. Thompson, J. Simon, H. Loh, and V. Vuletic, “A high-brightness source of narrowband, identical-photon pairs,” Science 313, 74-77 (2006).
[CrossRef] [PubMed]

C. F. Roos, M. Riebe, H. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478-1480 (2004).
[CrossRef] [PubMed]

Other (9)

D. M. Greenberger, M. A. Horne, and A. Zeilinger, “Going beyond Bell's theorem,” in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, M.Kafatos, ed. (Kluwer, 1989).

A. Zeilinger, M. A. Horne, and D. M. Greenberger, NASA Conf. Publ. No. 3135 (National Aeronautics and Space Administration, Code NTT, Washington D.C., 1997).

J.-M. Wen, M. H. Rubin, and Y.-H. Shih, “Spatial resolution enhancement in quantum imaging beyond the diffraction limit using entangled photon-number state,” ArXiv:0812.2032.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).
[CrossRef]

Y. P. Huang and M. G. Moore, “Ultra-bright biphoton emission from an atomic vapor based on Doppler-free four-wave-mixing and collective emission,” arXiv:0901.4789.

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

M. D. Lukin, P. R. Hemmer, and M. O. Scully, “Resonant nonlinear optics in phase-coherent media,” in Adv. At., Mol., Opt. Phys. Vol. 42, B.Bederson and H.Walther, eds. (Elsevier, 2000), pp. 347-386.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Generation of a triphoton W state entangled in time-energy (and space). (a) Schematic of triphoton W state generation and detection in the backward geometry. Two counterpropagating weak pump field ( ω p ) and strong control field ( ω c 1 ) induce spontaneous emission of paired Stokes ( ω s 1 ) and anti-Stokes ( ω a s 1 ) photons in the first atomic ensemble. By sending the ω s 1 photon with another strong control laser ( ω c 2 ) into the second ensemble, another paired Stokes ( ω s 2 ) and anti-Stokes ( ω a s 2 ) photons are created. This completes the three-photon state formation. (b) Four-level double-Λ EIT configurations for triphoton generation.

Fig. 2
Fig. 2

Two-photon coincidences in the damped (a) and overdamped Rabi oscillation regions. The parameters are chosen as in (a) γ 31 = 6 π MHz, γ 21 = 0.6 γ 31 , Ω c 1 = 23 γ 31 ; and (b) Ω c 1 = 7 γ 31 .

Fig. 3
Fig. 3

Triphoton coincidences in the damped (a) and overdamped Rabi oscillation regions. The same parameters are chosen as in Figs. 2b and 2b plus Ω c 2 = 28 γ 31 .

Equations (39)

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

H 1 ( t 1 ) = V 1 d 3 r ε 0 χ 1 ( 3 ) E p ( + ) E c 1 ( + ) E s 1 ( ) E a s 1 ( ) + H.c. ,
H 2 ( t 2 ) = V 2 d 3 r ε 0 χ 2 ( 3 ) E s 1 ( + ) E c 2 ( + ) E s 2 ( ) E a s 2 ( ) + H.c. ,
E j ( + ) = k E j a ( k j ) e i ( k j r ω j t ) ,
E j = i ω j 2 ε 0 n j 2 V q ,
[ a ( k j ) , a ( k l ) ] = δ k j k l .
E p ( + ) = E p e i ( k p z ω p t 1 ) , E c j ( + ) = E c j e i ( k c j z + ω c j t j ) ,
| Ψ = ( i ) 2 d t 2 d t 1 T [ H 2 ( t 2 ) H 1 ( t 1 ) ] | 0 ,
| Ψ = k a s 1 k s 2 k a s 2 F ( k a s 1 , k s 2 , k a s 2 ) a ( k a s 1 ) a ( k s 2 ) a ( k a s 2 ) | 0 ,
F ( k a s 1 , k s 2 , k a s 2 ) = k s 1 β χ 1 ( 3 ) χ 2 ( 3 ) Φ 1 ( Δ k 1 L 1 ) Φ 2 ( Δ k 2 L 2 ) H tr 1 ( α s 1 + α a s 1 ) H tr 2 ( α s 1 α a s 2 α s 2 ) × δ ( ω p + ω c 1 ω s 1 ω a s 1 ) δ ( ω s 1 + ω c 2 ω s 2 ω a s 2 ) .
Φ j ( Δ k j L j ) = 1 e i Δ k j L j i Δ k j L j = sinc ( Δ k j L j 2 ) e i Δ k j L j 2 ,
H tr 1 ( α s 1 + α a s 1 ) = 1 A 1 A 1 d 2 ρ e i ( α s 1 + α a s 1 ) ρ ,
H tr 2 ( α s 1 α s 2 α a s 2 ) = 1 A 2 A 2 d 2 ρ e i ( α s 1 α s 2 α a s 2 ) ρ .
β = i π 2 E c 1 E c 2 E p ϖ s 1 ϖ s 2 ϖ a s 2 n s 1 2 n s 2 n a s 2 ϖ a s 1 2 ε 0 n a s 1 2 V q .
ω p + ω c 1 = ω s 1 + ω a s 1 , ω s 1 + ω c 2 = ω s 2 + ω a s 2 ,
k p k c 1 = k s 1 k a s 1 , k s 1 k c 2 = k s 2 k a s 2 .
K s 1 K a s 1 = k p k c 1 , K s 2 K a s 2 = K s 1 k c 2 ,
ϖ s 1 + ϖ a s 1 = ω p + ω c 1 , ϖ s 2 + ϖ a s 2 = ϖ s 1 + ω c 2 .
Δ k 1 = ν 1 ( 1 v s 1 ( 1 ) + 1 v a s 1 ) ,
Δ k 2 = ν 1 ( 1 v s 2 1 v s 1 ( 2 ) ) + ν 2 ( 1 v s 2 + 1 v a s 2 ) ,
Δ k 1 = ν 1 v a s 1 , Δ k 2 = ν 2 v a s 2 .
R 3 = lim T 1 T 0 T d t 1 0 T d t 2 0 T d t 3 Ψ | E 1 ( ) ( τ 1 ) E 2 ( ) ( τ 2 ) E 3 ( ) ( τ 3 ) E 3 ( + ) ( τ 3 ) E 2 ( + ) ( τ 2 ) E 1 ( + ) ( τ 1 ) | Ψ ,
R 2 = lim T 1 T 0 T d t 1 0 T d t 2 Ψ | E 1 ( ) ( τ 1 ) E 2 ( ) ( τ 2 ) E 2 ( + ) ( τ 2 ) E 1 ( + ) ( τ 1 ) | Ψ ,
R 1 = lim T 1 T 0 T d t 1 Ψ | E 1 ( ) ( τ 1 ) E 1 ( + ) ( τ 1 ) | Ψ .
R 3 = | 0 | E 3 ( + ) ( τ 3 ) E 2 ( + ) ( τ 2 ) E 1 ( + ) ( τ 1 ) | Ψ | 2 = | A 3 ( τ 1 , τ 2 , τ 3 ) | 2 .
R 2 = k 3 | 0 | a ( k 3 ) E 2 ( + ) ( τ 2 ) E 1 ( + ) ( τ 1 ) | Ψ | 2 = k 3 | A 2 ( τ 1 , τ 2 ) | 2 .
R 1 = k 2 k 3 | 0 | a ( k 3 ) a ( k 2 ) E 1 ( + ) | Ψ | 2 = k 2 k 3 | A 1 | 2 .
A 3 ( τ 1 , τ 2 , τ 3 ) = A 30 k a s 1 k a s 2 k s 2 e i ( ω a s 1 τ 1 + ω a s 2 τ 2 + ω s 2 τ 3 ) F ( k a s 1 , k s 2 , k a s 2 ) ,
A 2 ( τ 2 , τ 3 ) = A 20 k s 2 k a s 2 e i ( ω a s 2 τ 2 + ω s 2 τ 3 ) F ( k a s 1 , k a s 2 , k s 2 ) ,
k j V q 1 3 2 π d ω j d k j d ω j = V q 1 3 2 π d ω j v j .
R 2 ( τ 23 ) = R 20 d ν 1 | χ 1 ( 3 ) ( ν 1 ) sinc ( ν 1 L 1 2 v a s 1 ) | 2 | d ν 2 χ 2 ( 3 ) ( ν 1 , ν 2 ) sinc ( ν 2 L 2 2 v a s 2 ) e i ν 2 ( τ 23 + L 2 2 v a s 2 ) | 2 ,
R 2 ( τ 23 ) = R 20 d ν 1 | χ 1 ( 3 ) ( ν 1 ) | 2 | d ν 2 χ 2 ( 3 ) ( ν 1 , ν 2 ) e i ν 2 τ 23 | 2 .
χ 1 ( 3 ) ( ν 1 ) = N 1 μ 13 μ 32 μ 24 μ 41 4 3 ε 0 ( Δ p + i γ 14 ) ( ν 1 Ω e 1 2 + i γ e 1 ) ( ν 1 + Ω e 1 2 + i γ e 1 ) ,
χ 2 ( 3 ) ( ν 1 , ν 2 ) = N 2 ξ 31 ξ 23 ξ 42 ξ 14 4 3 ε 0 ( Δ s i ζ 14 ) ( ν 2 Ω e 2 2 + i γ e 2 ) ( ν 2 + Ω e 2 2 + i γ e 2 ) .
R 2 ( τ 23 ) = R 20 e 2 γ e 2 τ 23 [ 1 cos ( Ω e 2 τ 23 ) ] Θ ( τ 23 ) .
R 2 ( τ 23 ) = R 20 d ν 1 | sinc ( ν 1 L 1 2 v a s 1 ) | 2 | d ν 2 sinc ( ν 2 L 2 2 v a s 2 ) e i ν 2 ( τ 23 + L 2 2 v a s 2 ) | 2 .
A 3 ( τ 13 , τ 23 ) = A 30 d ν 1 χ 1 ( 3 ) ( ν 1 ) sinc ( ν 1 L 1 2 v a s 1 ) e i ν 1 ( τ 13 + L 1 2 v a s 1 ) d ν 2 χ 2 ( 3 ) ( ν 1 , ν 2 ) sinc ( ν 2 L 2 2 v a s 2 ) e i ν 2 ( τ 23 + L 2 2 v a s 2 ) ,
A 3 ( τ 13 , τ 23 ) = A 30 d ν 1 χ 1 ( 3 ) ( ν 1 ) e i ν 1 τ 13 d ν 2 χ 2 ( 3 ) ( ν 1 , ν 2 ) e i ν 2 τ 23 ,
R 3 ( τ 13 , τ 23 ) = R 30 j = 1 2 e 2 γ e j τ j 3 [ 1 cos ( Ω e j τ j 3 ) ] Θ ( τ j 3 ) ,
A 3 ( τ 13 , τ 23 ) = A 30 d ν 1 sinc ( ν 1 L 1 2 v a s 1 ) e i ν 1 ( τ 13 + L 1 2 v a s 1 ) d ν 2 sinc ( ν 2 L 2 2 v a s 2 ) e i ν 2 ( τ 23 + L 2 2 v a s 2 ) .

Metrics