Abstract

We experimentally generate a non-classical correlated two-color photon pair at 780 and 1529.4 nm in a ladder-type configuration using a hot 85Rb atomic vapor with the production rate of ~107/s. The non-classical correlation between these two photons is demonstrated by strong violation of Cauchy-Schwarz inequality by the factor R = 48 ± 12. Besides, we experimentally investigate the relations between the correlation and some important experimental parameters such as the single-photon detuning, the powers of pumps. We also make a theoretical analysis in detail and the theoretical predictions are in reasonable agreement with our experimental results.

© 2012 OSA

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  1. J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
    [CrossRef] [PubMed]
  2. 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(5), R3429–R3432 (1995).
    [CrossRef] [PubMed]
  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(18), 3600–3603 (1995).
    [CrossRef] [PubMed]
  4. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [CrossRef] [PubMed]
  5. J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
    [CrossRef] [PubMed]
  6. B. S. Shi and A. Tomita, “Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,” Phys. Rev. A 69(1), 013803 (2004).
    [CrossRef]
  7. 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(13), 2556–2559 (1999).
    [CrossRef]
  8. F. Y. Wang, B. S. Shi, and G. C. Guo, “Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line,” Opt. Lett. 33(19), 2191–2193 (2008).
    [CrossRef] [PubMed]
  9. F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
    [CrossRef]
  10. M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
    [CrossRef]
  11. X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
    [CrossRef] [PubMed]
  12. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
    [CrossRef] [PubMed]
  13. D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science 306(5696), 663–666 (2004).
    [CrossRef] [PubMed]
  14. S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
    [CrossRef] [PubMed]
  15. 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(18), 183601 (2005).
    [CrossRef] [PubMed]
  16. S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
    [CrossRef] [PubMed]
  17. Q. F. Chen, B. S. Shi, M. Feng, Y. S. Zhang, and G. C. Guo, “Non-degenerated nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16(26), 21708–21713 (2008).
    [CrossRef] [PubMed]
  18. X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
    [CrossRef]
  19. R. T. Willis, “Photon pair production from a hot atomic ensemble in the diamond configuration,” Ph. D. thesis, University of Maryland, College Park, (2009).
  20. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
    [CrossRef] [PubMed]
  21. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
    [CrossRef]
  22. R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
    [CrossRef] [PubMed]
  23. 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(2), 023808 (2006).
    [CrossRef]
  24. C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
    [CrossRef]
  25. S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation nearatomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
    [CrossRef]
  26. R. W. Boyd, Nonlinear Optics 2nd ed (Academic Press, SanDiego, 1998).
  27. D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
    [CrossRef]

2012 (1)

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

2011 (1)

2010 (2)

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
[CrossRef]

2009 (2)

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[CrossRef]

2008 (5)

S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation nearatomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[CrossRef]

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[CrossRef] [PubMed]

Q. F. Chen, B. S. Shi, M. Feng, Y. S. Zhang, and G. C. Guo, “Non-degenerated nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16(26), 21708–21713 (2008).
[CrossRef] [PubMed]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line,” Opt. Lett. 33(19), 2191–2193 (2008).
[CrossRef] [PubMed]

2007 (1)

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[CrossRef]

2006 (3)

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(2), 023808 (2006).
[CrossRef]

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

2005 (1)

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(18), 183601 (2005).
[CrossRef] [PubMed]

2004 (2)

B. S. Shi and A. Tomita, “Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,” Phys. Rev. A 69(1), 013803 (2004).
[CrossRef]

D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science 306(5696), 663–666 (2004).
[CrossRef] [PubMed]

2003 (2)

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

2001 (1)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

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(13), 2556–2559 (1999).
[CrossRef]

1995 (2)

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(5), R3429–R3432 (1995).
[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(18), 3600–3603 (1995).
[CrossRef] [PubMed]

1989 (1)

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

Aspelmeyer, M.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

Balic, V.

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(18), 183601 (2005).
[CrossRef] [PubMed]

Bao, X. H.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Becerra, F. E.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[CrossRef] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[CrossRef]

Belthangady, C.

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[CrossRef] [PubMed]

Benson, O.

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Boozer, A. D.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

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(18), 183601 (2005).
[CrossRef] [PubMed]

Chanelière, T.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

Chapman, M. S.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

Chen, Q. F.

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[CrossRef]

Q. F. Chen, B. S. Shi, M. Feng, Y. S. Zhang, and G. C. Guo, “Non-degenerated nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16(26), 21708–21713 (2008).
[CrossRef] [PubMed]

Chen, S.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Chen, Y. A.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Chen, Z. B.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

Ding, D. S.

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

Du, S. W.

S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation nearatomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[CrossRef]

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[CrossRef] [PubMed]

Duan, L.-M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[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(6862), 413–418 (2001).
[CrossRef] [PubMed]

Feng, M.

Franson, J. D.

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

Gasparoni, S.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

Guo, G. C.

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
[CrossRef]

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line,” Opt. Lett. 33(19), 2191–2193 (2008).
[CrossRef] [PubMed]

Q. F. Chen, B. S. Shi, M. Feng, Y. S. Zhang, and G. C. Guo, “Non-degenerated nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16(26), 21708–21713 (2008).
[CrossRef] [PubMed]

Harris, S. E.

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[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(18), 183601 (2005).
[CrossRef] [PubMed]

Jenkins, S. D.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

Jennewein, T.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

Kennedy, T. A. B.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

Kimble, H. J.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

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(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Koch, L.

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

Kolchin, P.

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[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(18), 183601 (2005).
[CrossRef] [PubMed]

Kuzmich, A.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science 306(5696), 663–666 (2004).
[CrossRef] [PubMed]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[CrossRef] [PubMed]

Lu, X. S.

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[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(13), 2556–2559 (1999).
[CrossRef]

Lukin, M. D.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[CrossRef] [PubMed]

Matsukevich, D. N.

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[CrossRef] [PubMed]

D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science 306(5696), 663–666 (2004).
[CrossRef] [PubMed]

Orozco, L. A.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[CrossRef] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[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(13), 2556–2559 (1999).
[CrossRef]

Pan, J. W.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

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(5), R3429–R3432 (1995).
[CrossRef] [PubMed]

Qian, Y.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Raymond Ooi, C. H.

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[CrossRef]

Rolston, S. L.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[CrossRef] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[CrossRef]

Rubin, M. H.

S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation nearatomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[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(2), 023808 (2006).
[CrossRef]

Schmiedmayer, J.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Scholz, M.

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

Scully, M. O.

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[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(5), R3429–R3432 (1995).
[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(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Shi, B. S.

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
[CrossRef]

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line,” Opt. Lett. 33(19), 2191–2193 (2008).
[CrossRef] [PubMed]

Q. F. Chen, B. S. Shi, M. Feng, Y. S. Zhang, and G. C. Guo, “Non-degenerated nonclassical photon pairs in a hot atomic ensemble,” Opt. Express 16(26), 21708–21713 (2008).
[CrossRef] [PubMed]

B. S. Shi and A. Tomita, “Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,” Phys. Rev. A 69(1), 013803 (2004).
[CrossRef]

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(18), 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(5), R3429–R3432 (1995).
[CrossRef] [PubMed]

Strassel, T.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Strekalov, D. 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(5), R3429–R3432 (1995).
[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(18), 3600–3603 (1995).
[CrossRef] [PubMed]

Sun, Q.

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[CrossRef]

Tomita, A.

B. S. Shi and A. Tomita, “Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,” Phys. Rev. A 69(1), 013803 (2004).
[CrossRef]

Ullmann, R.

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

Wang, F. Y.

F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
[CrossRef]

F. Y. Wang, B. S. Shi, and G. C. Guo, “Observation of time correlation function of multimode two-photon pairs on a rubidium D2 line,” Opt. Lett. 33(19), 2191–2193 (2008).
[CrossRef] [PubMed]

Wen, J. M.

S. W. Du, J. M. Wen, and M. H. Rubin, “Narrowband biphoton generation nearatomic resonance,” J. Opt. Soc. Am. B 25(12), C98–C108 (2008).
[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(2), 023808 (2006).
[CrossRef]

Willis, R. T.

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Photon statistics and polarization correlations at telecommunications wavelengths from a warm atomic ensemble,” Opt. Express 19(15), 14632–14641 (2011).
[CrossRef] [PubMed]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[CrossRef]

Yang, J.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Yang, T.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Yin, G. Y.

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[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(18), 183601 (2005).
[CrossRef] [PubMed]

Yuan, Z. S.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Zeilinger, A.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

Zhang, H.

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Zhang, Y. S.

Zhao, B.

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (2006).
[CrossRef] [PubMed]

Zhou, Z. Y.

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

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(6862), 413–418 (2001).
[CrossRef] [PubMed]

Zou, X. B.

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

Zubairy, M. S.

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

M. Scholz, L. Koch, R. Ullmann, and O. Benson, “Single-mode operation of a high-brightness narrow-band single-photon source,” Appl. Phys. Lett. 94(20), 201105 (2009).
[CrossRef]

Chin. Phys. Lett. (2)

X. S. Lu, Q. F. Chen, B. S. Shi, and G. C. Guo, “Generation of a non-classical correlated photon pair via spontaneous four-wave mixing in a cold atomic ensemble,” Chin. Phys. Lett. 26(6), 064204 (2009).
[CrossRef]

D. S. Ding, Z. Y. Zhou, B. S. Shi, X. B. Zou, and G. C. Guo, “Two-photon atomic coherence effect of transition 5S1/2–5P3/2–4D5/2(4D3/2) of 85Rb atoms,” Chin. Phys. Lett. 29(2), 024202 (2012).
[CrossRef]

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

Nature (3)

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature 423(6941), 731–734 (2003).
[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(6862), 413–418 (2001).
[CrossRef] [PubMed]

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Experimental realization of freely propagating teleported qubits,” Nature 421(6924), 721–725 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

F. Y. Wang, B. S. Shi, and G. C. Guo, “Generation of narrow-band photon pairs for quantum memory,” Opt. Commun. 283(14), 2974–2977 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (5)

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(5), R3429–R3432 (1995).
[CrossRef] [PubMed]

B. S. Shi and A. Tomita, “Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer,” Phys. Rev. A 69(1), 013803 (2004).
[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(2), 023808 (2006).
[CrossRef]

C. H. Raymond Ooi, Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: generalized analytical quantum Langevin theory,” Phys. Rev. A 75(1), 013820 (2007).
[CrossRef]

R. T. Willis, F. E. Becerra, L. A. Orozco, and S. L. Rolston, “Correlated photon pairs generated from a warm atomic ensemble,” Phys. Rev. A 82(5), 053842 (2010).
[CrossRef]

Phys. Rev. Lett. (8)

T. Chanelière, D. N. Matsukevich, S. D. Jenkins, T. A. B. Kennedy, M. S. Chapman, and A. Kuzmich, “Quantum telecommunication based on atomic cascade transitions,” Phys. Rev. Lett. 96(9), 093604 (2006).
[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(13), 2556–2559 (1999).
[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(18), 3600–3603 (1995).
[CrossRef] [PubMed]

J. D. Franson, “Bell inequality for position and time,” Phys. Rev. Lett. 62(19), 2205–2208 (1989).
[CrossRef] [PubMed]

S. Chen, Y. A. Chen, T. Strassel, Z. S. Yuan, B. Zhao, J. Schmiedmayer, and J. W. Pan, “Deterministic and storable single-photon source based on a quantum memory,” Phys. Rev. Lett. 97(17), 173004 (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(18), 183601 (2005).
[CrossRef] [PubMed]

S. W. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100(18), 183603 (2008).
[CrossRef] [PubMed]

X. H. Bao, Y. Qian, J. Yang, H. Zhang, Z. B. Chen, T. Yang, and J. W. Pan, “Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories,” Phys. Rev. Lett. 101(19), 190501 (2008).
[CrossRef] [PubMed]

Science (1)

D. N. Matsukevich and A. Kuzmich, “Quantum state transfer between matter and light,” Science 306(5696), 663–666 (2004).
[CrossRef] [PubMed]

Other (2)

R. T. Willis, “Photon pair production from a hot atomic ensemble in the diamond configuration,” Ph. D. thesis, University of Maryland, College Park, (2009).

R. W. Boyd, Nonlinear Optics 2nd ed (Academic Press, SanDiego, 1998).

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Figures (7)

Fig. 1
Fig. 1

Energy levels diagram of the ladder-type configuration in our experiment. Δ1, Δ´1 is the detuning of the frequency of the Pump 1 and Pump 2 with the definitions Δ´1 = ωp231, Δ1 = ω43p1. Δ2, Δ´2 is the detuning of the frequency of the Signal 1 and Signal 2 with the definitions Δ´2 = ωs221, Δ2 = ω42s1.

Fig. 2
Fig. 2

Experimental setup. Signal 2 photons are collected by a multi-mode fiber, Signal 1 photons are delayed using a 200-m long single-mode fiber firstly, then are collected by a single-mode fiber.λ/2: half-wave plate;PBS: polarization beam splitter; DG535: delay generator; Detector 1: In-GaAs Photon Detector; Detector 2: Avalanche diode; α,β are the angles of the Pump 1 and Signal 2, and the Pump 2 and Signal 1, and α = β = 3.6°; Slit 1 and slit 2 are slits which are used to reduce noise.

Fig. 3
Fig. 3

(a) is the theoretical curve using the parameters γ1 = 3 × 2π × 106 (s−1), Γ1 = 1 × 2π × 106 (s−1), Ωp1 = 60 × 2π × 106 (s−1). Figure 3(b) is the theoretical curve describing the correlation function with large decay rates γ1 = 210 × 2π × 106 (s−1), Γ1 = 100 × 2π × 106 (s−1).

Fig. 4
Fig. 4

(a) is the theoretical curve describing the correlation of biphoton vs the detuning of Pump 2. Figure 4(b) is the theoretical curve describing the relation between the correlation function and the power of Pump 2.

Fig. 5
Fig. 5

(a) is the measurement of cross-correlation function of two signals. Black line is the theoretical fitted curve using Eq. (24). Figure 5(b) and Fig. 5(c) are the measurements of autocorrelation functions of Signal 2 and Signal 1 respectively.

Fig. 6
Fig. 6

(a) is the cross-correlation function vs the different detuningof Pump 2. Figure 6(b) is plot of the correlation gs1,s2(0) vs the detuning of Pump 2 from the data of Fig. 5(a) and Fig. 6(a). The solid line is the guide for eye.

Fig. 7
Fig. 7

(a) is the correlation gs1,s2(0) vs the power of Pump 2, and Fig. 7(b) is the correlation gs1,s2(0) vs the power of Pump 1. The solid line is the guide for eye.

Equations (26)

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

Ε ^ p1 (+) = ε p1 exp(i ω p1 t+i k p1 z), Ε ^ p2 (+) = ε p2 exp(i ω p2 ti k p2 z), Ε ^ s1 (+) = 1 2π dω 2 ω s1 c ε 0 A a ^ s1 exp(i ω s1 t+i k s1 z), Ε ^ s2 (+) = 1 2π dω 2 ω s2 c ε 0 A a ^ s2 exp(i ω s2 ti k s2 z).
Ω p1 = u 34 E ^ P1 (+) , Ω p2 = u 13 E ^ P2 (+) , Ω s1 = u 42 E ^ S1 (+) , Ω s2 = u 21 E ^ S2 (+) .
Η int = Δ 1 ' |33| Δ 2 ' |22|+( Δ 2 Δ 2 ' )|44| ( Ω s2 |21|+ Ω p2 |31|+ Ω p1 |43|+ Ω s1 |42|+H.c).
ρ ˙ ij = i k ( H ik ρ kj ρ ik H kj ) Γ ij ρ ij .
ρ ˙ 21 =i Ω s2 ( ρ 11 ρ 22 )+i Ω s1 * ρ 41 i Ω p2 ρ 23 ρ 21 Γ 21
ρ ˙ 31 =i Ω p2 ( ρ 11 ρ 33 )+i Ω p1 * ρ 41 i Ω s2 ρ 32 ρ 31 Γ 31
ρ ˙ 42 =i Ω s1 ( ρ 22 ρ 44 )+i Ω p1 ρ 32 i Ω s2 * ρ 41 ρ 42 Γ 42
ρ ˙ 43 =i Ω p1 ( ρ 33 ρ 44 )+i Ω s1 ρ 23 i Ω p2 * ρ 41 ρ 43 Γ 43
ρ ˙ 41 =i Ω s1 ρ 21 +i Ω p1 ρ 31 i Ω s2 ρ 42 i Ω p2 ρ 43 ρ 41 Γ 41
ρ ˙ 32 =i Ω s1 ρ 34 i Ω s2 * ρ 31 +i Ω p1 * ρ 42 +i Ω p2 ρ 12 ρ 32 Γ 32
P ^ s2 (1) = ε 0 iN u 21 2 ( Γ 14 +2 γ 1 ) ε 0 ( Γ 13 Γ 14 + Ω p1 2 ) E ^ S2 (+) .
P ^ s2 (3) = ε 0 iN u 21 u 13 u 34 u 42 3 ε 0 Γ 21 ( Γ 31 Γ 41 + Ω p1 2 ) E ^ P1 (+) E ^ P2 (+) E ^ S1 () .
χ s2 (1) = iN u 21 2 ( Γ 14 +2 γ 1 ) ε 0 ( Γ 13 Γ 14 + Ω p1 2 ) .
χ s2 (3) = iN u 21 u 13 u 34 u 42 3 ε 0 Γ 21 ( Γ 31 Γ 41 + Ω p1 2 ) .
|ψ=L d ω s1 d ω s2 κ( ω s1 , ω s2 )δ( ω p1 + ω p2 ω s2 ω s1 )sinc( δkL 2 ) a s1 ( ω s1 ) a s2 ( ω s2 )|0.
k p1 k p2 + k s1 k s2 =0, ω p1 + ω p2 ω s2 ω s1 =0,
|ψ=L d ω s2 κ( ω p1 + ω p2 ω s2 , ω s2 )sinc( δkL 2 ) a s1 + ( ω p1 + ω p2 ω s2 ) a s2 + ( ω s2 )|0.
G (2) (τ)= | L d τ ' κ ˜ ( τ ' ) Φ ˜ (τ τ ' ) e i( ω c + ω p ) t s1 | 2 .
k s1 = ω s1 c 1+ χ s1 (1) = ω s1 c + ω s1 2c χ s1 (1) k s2 = ω s2 c 1+ χ s2 (1) = ω s2 c + ω s2 2c χ s2 (1)
Φ ˜ (τ τ ' )= 1 2π d ω s2 Φ( ω s2 ) e i ω s2 (τ τ ' ) δ(τ τ ' ).
G (2) (τ)= | iL ε p1 ε p2 ω ¯ s1 ω ¯ s2 4πc d ω s2 χ s2 (3) ( ω s2 ) e i ω s2 τ | 2 .
G (2) (τ)= | NL u 21 u 13 u 34 u 42 ε p1 ε p2 ω ¯ s1 ω ¯ s2 4 3 ε 0 πc[i Δ 1D (2 Γ 1 γ 1 )+ Ω p1 2 ] e i ω ¯ s2 τ ( e γ 1 τ e 2 Γ 1 τ γ 1 Ω p1 2 Δ 1D 2 τ+i Ω p1 2 Δ 1D τ ) 1 u 2π e v 2 / u 2 dv | 2 Ξ(τ)
B | A ( Δ 1D i γ 1 ) 1 u 2π e v 2 / u 2 dv | 2
g s1s2 (2) (τ)= G (2) (τ)+B B
R= g s1,s2 (τ) 2 g s1,s1 g s2,s2 1
R= g s1,s2 (τ) 2 g s1,s1 g s2,s2 =48±12>1

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