Abstract

We report on the generation of a type-I multimode two-photon state on a rubidium D2 line (780nm) using periodically poled KTiOPO4 crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function; the cross correlation between two photons shows a cavity bandwidth of about 7.8MHz. We also use a Fabry–Perot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retrieval of narrow-band photons in Rb atomic ensembles, which is important for long-distance quantum communication.

© 2008 Optical Society of America

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  1. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
    [CrossRef] [PubMed]
  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
    [CrossRef] [PubMed]
  3. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
    [CrossRef]
  4. D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
    [CrossRef]
  5. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
    [CrossRef] [PubMed]
  6. C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
    [CrossRef] [PubMed]
  7. B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
    [CrossRef] [PubMed]
  8. V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
    [CrossRef] [PubMed]
  9. C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
    [CrossRef] [PubMed]
  10. Z. Y. Ou and Y. J. Lu, Phys. Rev. Lett. 83, 2556 (1999).
    [CrossRef]
  11. H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
    [CrossRef]
  12. C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
    [CrossRef] [PubMed]
  13. M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
    [CrossRef]
  14. Y. J. Lu and Z. Y. Ou, Phys. Rev. A 62, 033804 (2000).
    [CrossRef]
  15. H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
    [CrossRef]
  16. R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
    [CrossRef]
  17. F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
    [CrossRef]

2008 (1)

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

2007 (2)

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

2006 (1)

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

2004 (1)

H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
[CrossRef]

2003 (3)

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

2002 (1)

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

2000 (2)

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Y. J. Lu and Z. Y. Ou, Phys. Rev. A 62, 033804 (2000).
[CrossRef]

1999 (1)

Z. Y. Ou and Y. J. Lu, Phys. Rev. Lett. 83, 2556 (1999).
[CrossRef]

1997 (1)

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

1991 (1)

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1970 (1)

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[CrossRef]

Andre, A.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Aspect, A.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Benson, O.

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

Boca, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (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, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Bouwmeester, D.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Bowen, W. P.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Burnham, D. C.

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[CrossRef]

Chen, Q.-F.

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Chou, C. W.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Duan, L.-M.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Eibl, M.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Eisaman, M. D.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Ekert, A. K.

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

Fattal, D.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Goto, H.

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

Grangier, P.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Grosshans, F.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Guo, G.-C.

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Herzog, U.

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

Horikiri, T.

H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
[CrossRef]

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Jacques, V.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[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, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Kobayashi, T.

H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
[CrossRef]

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

Kowaiski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Kuklewicz, C. E.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Kuzmich, A.

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

Lounis, B.

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Lu, Y. J.

Y. J. Lu and Z. Y. Ou, Phys. Rev. A 62, 033804 (2000).
[CrossRef]

Z. Y. Ou and Y. J. Lu, Phys. Rev. Lett. 83, 2556 (1999).
[CrossRef]

Lukin, M. D.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Mattle, K.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Moerner, W. E.

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Ou, Z. Y.

Y. J. Lu and Z. Y. Ou, Phys. Rev. A 62, 033804 (2000).
[CrossRef]

Z. Y. Ou and Y. J. Lu, Phys. Rev. Lett. 83, 2556 (1999).
[CrossRef]

Pan, J.-W.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Phillips, D. F.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Roch, J.-F.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Santori, C.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

Scholz, M.

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

Shapiro, J. H.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Shi, B.-S.

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Solomon, G. S.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

Treussart, F.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

van der Wal, C. H.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Vuckovic, J.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

Walsworth, R. L.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Wang, F.-Y.

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Wang, H.

H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
[CrossRef]

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Weinberg, D. L.

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[CrossRef]

Weinfurter, A.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Wolfgramm, F.

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

Wong, F. N. C.

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Wootters, W. K.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Wu, E.

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

Yamamoto, Y.

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

Yanagihara, Y.

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

Zeilinger, H.

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

Zhai, C.

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Zibrov, A. S.

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowaiski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

M. Scholz, F. Wolfgramm, U. Herzog, and O. Benson, Appl. Phys. Lett. 91, 191104 (2007).
[CrossRef]

Nature (4)

C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, Nature 419, 594 (2002).
[CrossRef] [PubMed]

D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, A. Weinfurter, and H. Zeilinger, Nature 390, 575 (1997).
[CrossRef]

A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, Nature 423, 731 (2003).
[CrossRef] [PubMed]

B. Lounis and W. E. Moerner, Nature 407, 491 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

F.-Y. Wang, B.-S. Shi, Q.-F. Chen, C. Zhai, and G.-C. Guo, Opt. Commun. 281, 4114 (2008).
[CrossRef]

Phys. Rev. A (3)

Y. J. Lu and Z. Y. Ou, Phys. Rev. A 62, 033804 (2000).
[CrossRef]

H. Goto, Y. Yanagihara, H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 68, 015803 (2003).
[CrossRef]

H. Wang, T. Horikiri, and T. Kobayashi, Phys. Rev. A 70, 043804 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, Phys. Rev. Lett. 97, 223601 (2006).
[CrossRef] [PubMed]

Z. Y. Ou and Y. J. Lu, Phys. Rev. Lett. 83, 2556 (1999).
[CrossRef]

D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
[CrossRef]

A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
[CrossRef] [PubMed]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
[CrossRef] [PubMed]

Science (2)

V. Jacques, E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J.-F. Roch, Science 315, 966 (2007).
[CrossRef] [PubMed]

C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, Science 301, 196 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Experiment setup: DL100̱780, ECDL operated at 780 nm ; ISO, optical isolator; EOM, electro-optic modulator; SAR, saturated absorption resonator; PD1 and PD2, fast photodetectors for cavity locking; PD3 and PD4, avalanche photodetectors; CFD, constant-fraction discriminator; pTA, picosecond time analyzer.

Fig. 2
Fig. 2

Oscillatory correlation function of multimode two-photon pairs. The coincidence counts are accumulated in 70   s . The pump power is about 15 μ W . The fitted parameters of the curve are C 1 = 93 , C 2 = 0 , Δ ω opo 2 π = 7.8 MHz , τ 0 = 59 ns , τ opo = 1.63 ns , and τ D = 220 ps .

Fig. 3
Fig. 3

Data shown were accumulated in 30   min . The solid curve is fitted by the function exp ( Δ ω opo τ τ 0 ) . The pump power is about 90 μ W . There is no obvious or regular oscillatory time correlation function.

Equations (5)

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

a o u t ( ω + ω m ) = G 1 ( ω ) a in ( ω m + ω ) + g 1 ( ω ) a in ( ω m ω ) + G 2 ( ω ) b in ( ω m + ω ) + g 2 ( ω ) b in ( ω m ω ) .
Γ ( 2 ) ( τ ) = E ̂ ( ) ( t ) E ̂ ( ) ( t + τ ) E ̂ ( + ) ( t + τ ) E ̂ ( + ) ( t ) ,
E ̂ ( + ) ( t ) = [ E ̂ ( ) ( t ) ] = 1 2 π d ω a ̂ ( ω ) e i ω t .
Γ ( 2 ) ( τ ) = ε 2 ( F F 0 ) 2 [ ( 2 ε ( 2 N + 1 ) Δ ω opo ) 2 + e Δ ω opo τ sin 2 [ ( 2 N + 1 ) Δ Ω opo τ 2 ] sin 2 ( Δ Ω opo τ 2 ) ] .
Γ c ( 2 ) ( τ ) = C 1 [ C 2 + e Δ ω opo τ τ 0 n ( 1 + 2 τ n τ opo τ 0 ln 2 τ D ) exp ( 2 τ n τ opo τ 0 ln 2 τ D ) ] .

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