Abstract

The quantum entanglement of amplitude and phase quadratures between two intense optical beams with a total intensity of 22mW and a frequency difference of 1nm, which are produced from an optical parametric oscillator operating above threshold, is experimentally demonstrated with two sets of unbalanced Mach–Zehnder interferometers. The measured quantum correlations of intensity and phase are in reasonable agreement with the results calculated based on a semiclassical analysis of the noise characteristics given by Fabre et al. [J. Phys. (France) 50, 1209 (1989)] .

© 2006 Optical Society of America

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  1. S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
    [CrossRef]
  2. M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
    [CrossRef] [PubMed]
  3. M. D. Reid and P. D. Drummond, Phys. Rev. A 40, 4493 (1989).
    [CrossRef] [PubMed]
  4. C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
    [CrossRef]
  5. J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
    [CrossRef]
  6. A. S. Villar, M. Martinelli, and P. Nussenzveig, Opt. Commun. 242, 551 (2004).
    [CrossRef]
  7. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
    [CrossRef] [PubMed]
  8. P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, Opt. Lett. 22, 1893 (1997).
    [CrossRef]
  9. H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
    [CrossRef]
  10. J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, Opt. Lett. 23, 870 (1998).
    [CrossRef]
  11. J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
    [CrossRef] [PubMed]
  12. Y. Zhang, K. Kasai, and M. Watanabe, Opt. Express 11, 14 (2003).
    [CrossRef] [PubMed]
  13. J. Laurat, L. Longchambon, and C. Fabre, Opt. Lett. 30, 1177 (2005).
    [CrossRef] [PubMed]
  14. A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
    [CrossRef] [PubMed]
  15. O. Glöckl, U. L. Andersen, S. Lorenz, Ch. Silberhorn, N. Korolkova, and G. Leuchs, Opt. Lett. 29, 1936 (2004).
    [CrossRef] [PubMed]
  16. Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
    [CrossRef] [PubMed]
  17. X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
    [CrossRef]
  18. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
    [CrossRef] [PubMed]
  19. X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
    [CrossRef]

2005 (4)

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

J. Laurat, L. Longchambon, and C. Fabre, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

2004 (2)

2003 (2)

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

Y. Zhang, K. Kasai, and M. Watanabe, Opt. Express 11, 14 (2003).
[CrossRef] [PubMed]

2001 (2)

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

2000 (1)

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

1999 (1)

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

1998 (1)

1997 (1)

1991 (1)

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

1989 (2)

M. D. Reid and P. D. Drummond, Phys. Rev. A 40, 4493 (1989).
[CrossRef] [PubMed]

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

1988 (1)

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef] [PubMed]

1987 (1)

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Andersen, U. L.

Braunstein, S. L.

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Camy, G.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Cassemiro, K. N.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Cirac, J. I.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Coudreau, T.

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

Courtois, J. Y.

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

Cruz, L. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Cui, F. Y.

Drummond, P. D.

M. D. Reid and P. D. Drummond, Phys. Rev. A 40, 4493 (1989).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Fabre, C.

J. Laurat, L. Longchambon, and C. Fabre, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, Opt. Lett. 22, 1893 (1997).
[CrossRef]

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Gao, J. R.

Giacobino, E.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Giedke, G.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

Glöckl, O.

Heidmann, A.

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Horowicz, R. J.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Jia, X. J.

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

Jing, J. T.

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

Kasai, K.

König, F.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Korolkova, N.

O. Glöckl, U. L. Andersen, S. Lorenz, Ch. Silberhorn, N. Korolkova, and G. Leuchs, Opt. Lett. 29, 1936 (2004).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Lam, P. K.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Laurat, J.

J. Laurat, L. Longchambon, and C. Fabre, Opt. Lett. 30, 1177 (2005).
[CrossRef] [PubMed]

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

Leuchs, G.

O. Glöckl, U. L. Andersen, S. Lorenz, Ch. Silberhorn, N. Korolkova, and G. Leuchs, Opt. Lett. 29, 1936 (2004).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Li, X. Y.

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

Longchambon, L.

Lorenz, S.

Maître, A.

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

P. H. Souto Ribeiro, C. Schwob, A. Maître, and C. Fabre, Opt. Lett. 22, 1893 (1997).
[CrossRef]

Martinelli, M.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, Opt. Commun. 242, 551 (2004).
[CrossRef]

Nussenzveig, P.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, Opt. Commun. 242, 551 (2004).
[CrossRef]

Pan, Q.

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

Peng, K. C.

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, Opt. Lett. 23, 870 (1998).
[CrossRef]

Porzio, A.

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

Reid, M. D.

M. D. Reid and P. D. Drummond, Phys. Rev. A 40, 4493 (1989).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef] [PubMed]

Reynaud, S.

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

Schwob, C.

Silberhorn, Ch.

O. Glöckl, U. L. Andersen, S. Lorenz, Ch. Silberhorn, N. Korolkova, and G. Leuchs, Opt. Lett. 29, 1936 (2004).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Smith, A.

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

Souto Ribeiro, P. H.

Su, H.

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

Su, X. L.

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

Treps, N.

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

van Loock, P.

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

Villar, A. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, Opt. Commun. 242, 551 (2004).
[CrossRef]

Wang, H.

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

Watanabe, M.

Weiss, O.

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

Xie, C. D.

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

J. R. Gao, F. Y. Cui, C. Y. Xue, C. D. Xie, and K. C. Peng, Opt. Lett. 23, 870 (1998).
[CrossRef]

Xue, C. Y.

Zhang, Y.

Y. Zhang, K. Kasai, and M. Watanabe, Opt. Express 11, 14 (2003).
[CrossRef] [PubMed]

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

Zoller, P.

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

J. Y. Courtois, A. Smith, C. Fabre, and S. Reynaud, J. Mod. Opt. 38, 177 (1991).
[CrossRef]

J. Opt. B. (1)

X. J. Jia, X. L. Su, Q. Pan, C. D. Xie, and K. C. Peng, J. Opt. B. 7, 189 (2005).
[CrossRef]

J. Phys. (France) (1)

C. Fabre, E. Giacobino, A. Heidmann, and S. Reynaud, J. Phys. (France) 50, 1209 (1989).
[CrossRef]

Opt. Commun. (2)

A. S. Villar, M. Martinelli, and P. Nussenzveig, Opt. Commun. 242, 551 (2004).
[CrossRef]

X. Y. Li, Q. Pan, J. T. Jing, C. D. Xie, and K. C. Peng, Opt. Commun. 201, 165 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

M. D. Reid and P. D. Drummond, Phys. Rev. A 40, 4493 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (7)

M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).
[CrossRef] [PubMed]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, Phys. Rev. Lett. 59, 2555 (1987).
[CrossRef] [PubMed]

H. Wang, Y. Zhang, Q. Pan, H. Su, A. Porzio, C. D. Xie, and K. C. Peng, Phys. Rev. Lett. 82, 1414 (1999).
[CrossRef]

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, Phys. Rev. Lett. 91, 213601 (2003).
[CrossRef] [PubMed]

Ch. Silberhorn, P. K. Lam, O. Weiss, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
[CrossRef] [PubMed]

L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
[CrossRef] [PubMed]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup: Nd : YAP KTP , laser source; + , positive–negative power combiner; D1–D4 ETX500 InGaAs photodiode detectors; SA’s, spectrum analyzers, other abbreviations defined in text.

Fig. 2
Fig. 2

(a) Amplitude and (b) phase correlation noise powers of twin beams at 20 MHz . i, SNL; ii, correlation noise; iii, electronics noise limit. Measurement parameters of the spectrum analyzer: resolution bandwidth, 10 kHz ; video bandwidth, 30 Hz .

Fig. 3
Fig. 3

Normalized noise power spectra of i, amplitude difference and ii, phase sum calculated from theoretical analysis. Star and filled circle, experimental values for amplitude (0.55, corresponding to 2.58 dB below the SNL) and phase (0.78, corresponding to 1.05 dB below the SNL) correlation, respectively.

Equations (3)

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

S I ( f ) = S 0 [ 1 η ξ 1 + ( f B ) 2 ] ,
S P ( f ) = S 0 [ 1 η ξ σ 2 + ( f B ) 2 ] ,
δ ( X 1 X 2 2 ) 2 + δ ( Y 1 + Y 2 2 ) 2 = 1.332 ,

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