Abstract

We investigate entanglement in the above-threshold optical parametric oscillator, both theoretically and experimentally, and discuss its potential applications to quantum information. The fluctuations measured in the subtraction of signal and idler amplitude quadratures are Δ2p̂=0.50(1), or 3.01(9) dB, and in the sum of phase quadratures they are Δ2q̂+=0.73(1), or 1.37(6) dB. A detailed experimental study of the noise behavior as a function of pump power is presented, and the discrepancies with theory are discussed.

© 2007 Optical Society of America

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  1. R. H. Kingston, "Parametric amplification and oscillation of optical frequencies," Proc. IRE 50, 472-474 (1962).
  2. R. Graham and H. Haken, "The quantum fluctuations of the optical parametric oscillator," Z. Phys. 210, 276-302 (1968).
    [CrossRef]
  3. L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
    [CrossRef] [PubMed]
  4. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
    [CrossRef] [PubMed]
  5. M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988).
    [CrossRef] [PubMed]
  6. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
    [CrossRef] [PubMed]
  7. S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
    [CrossRef]
  8. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
    [CrossRef] [PubMed]
  9. C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
    [CrossRef]
  10. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
    [CrossRef] [PubMed]
  11. X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
    [CrossRef]
  12. A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
    [CrossRef] [PubMed]
  13. X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
    [CrossRef] [PubMed]
  14. J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.
  15. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
    [CrossRef] [PubMed]
  16. R. Simon, "Peres-Horodecki separability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2726-2729 (2000).
    [CrossRef] [PubMed]
  17. A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
    [CrossRef]
  18. J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, "Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation," Opt. Lett. 30, 1177-1179 (2005).
    [CrossRef] [PubMed]
  19. M. D. Reid and P. D. Drummond, "Correlations in nondegenerate parametric oscillation--squeezing in the presence of phase diffusion," Phys. Rev. A 40, 4493-4506 (1989).
    [CrossRef] [PubMed]
  20. P. D. Drummond and M. D. Reid, "Correlations in nondegenerate parametric oscillation. 2. Below threshold results," Phys. Rev. A 41, 3930-3949 (1990).
    [CrossRef] [PubMed]
  21. S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
    [CrossRef]
  22. P. D. Drummond and C. W. Gardiner, "Generalized P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980).
    [CrossRef]
  23. K. V. Kheruntsyan and K. G. Petrosyan, "Exact steady-state Wigner function for a nondegenerate parametric oscillator," Phys. Rev. A 62, 015801 (2000).
    [CrossRef]
  24. B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
    [CrossRef]
  25. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 1999).
  26. C. W. Gardiner, Quantum Noise (Springer-Verlag, 1991).
  27. K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
    [CrossRef]
  28. R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
    [CrossRef]
  29. E. C. G. Sudarshan, "Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams," Phys. Rev. Lett. 10, 277-279 (1963).
    [CrossRef]
  30. P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
    [CrossRef]
  31. Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
    [CrossRef] [PubMed]

2006 (1)

2005 (4)

J. Laurat, L. Longchambon, C. Fabre, and T. Coudreau, "Experimental investigation of amplitude and phase quantum correlations in a type II optical parametric oscillator above threshold: from nondegenerate to degenerate operation," Opt. Lett. 30, 1177-1179 (2005).
[CrossRef] [PubMed]

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

2004 (3)

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
[CrossRef]

2003 (1)

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

2002 (2)

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

2000 (3)

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

R. Simon, "Peres-Horodecki separability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2726-2729 (2000).
[CrossRef] [PubMed]

K. V. Kheruntsyan and K. G. Petrosyan, "Exact steady-state Wigner function for a nondegenerate parametric oscillator," Phys. Rev. A 62, 015801 (2000).
[CrossRef]

1998 (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

1992 (1)

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

1991 (1)

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

1990 (1)

P. D. Drummond and M. D. Reid, "Correlations in nondegenerate parametric oscillation. 2. Below threshold results," Phys. Rev. A 41, 3930-3949 (1990).
[CrossRef] [PubMed]

1989 (1)

M. D. Reid and P. D. Drummond, "Correlations in nondegenerate parametric oscillation--squeezing in the presence of phase diffusion," Phys. Rev. A 40, 4493-4506 (1989).
[CrossRef] [PubMed]

1988 (1)

M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988).
[CrossRef] [PubMed]

1987 (1)

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

1986 (1)

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

1980 (1)

P. D. Drummond and C. W. Gardiner, "Generalized P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980).
[CrossRef]

1977 (1)

S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
[CrossRef]

1968 (1)

R. Graham and H. Haken, "The quantum fluctuations of the optical parametric oscillator," Z. Phys. 210, 276-302 (1968).
[CrossRef]

1963 (2)

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

E. C. G. Sudarshan, "Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams," Phys. Rev. Lett. 10, 277-279 (1963).
[CrossRef]

1962 (1)

R. H. Kingston, "Parametric amplification and oscillation of optical frequencies," Proc. IRE 50, 472-474 (1962).

Bloomer, R.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.

Bowen, W. P.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Camy, G.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

Carmichael, H. J.

H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 1999).

Cassemiro, K. N.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

Chaturvedi, S.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
[CrossRef]

Cirac, J. I.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Coudreau, T.

Coutinho dos Santos, B.

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

Cruz, L. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

da Silva, L. F.

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

Dechoum, K.

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

Drummond, P. D.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

P. D. Drummond and M. D. Reid, "Correlations in nondegenerate parametric oscillation. 2. Below threshold results," Phys. Rev. A 41, 3930-3949 (1990).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, "Correlations in nondegenerate parametric oscillation--squeezing in the presence of phase diffusion," Phys. Rev. A 40, 4493-4506 (1989).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988).
[CrossRef] [PubMed]

P. D. Drummond and C. W. Gardiner, "Generalized P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980).
[CrossRef]

S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
[CrossRef]

Duan, L. M.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Fabre, C.

Feng, S.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.

Fuchs, C. A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Furusawa, A.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Galatola, P.

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

Gao, J. G.

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Gardiner, C. W.

P. D. Drummond and C. W. Gardiner, "Generalized P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980).
[CrossRef]

C. W. Gardiner, Quantum Noise (Springer-Verlag, 1991).

Giacobino, E.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

Giedke, G.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

Glauber, R. J.

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

Graham, R.

R. Graham and H. Haken, "The quantum fluctuations of the optical parametric oscillator," Z. Phys. 210, 276-302 (1968).
[CrossRef]

Haken, H.

R. Graham and H. Haken, "The quantum fluctuations of the optical parametric oscillator," Z. Phys. 210, 276-302 (1968).
[CrossRef]

Hall, J. L.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Heidmann, A.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

Horowicz, R. J.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

Jia, X. J.

X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Jing, J.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.

Kheruntsyan, K. V.

K. V. Kheruntsyan and K. G. Petrosyan, "Exact steady-state Wigner function for a nondegenerate parametric oscillator," Phys. Rev. A 62, 015801 (2000).
[CrossRef]

Khoury, A. Z.

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

Kimble, H. J.

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Kingston, R. H.

R. H. Kingston, "Parametric amplification and oscillation of optical frequencies," Proc. IRE 50, 472-474 (1962).

Korolkova, N.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

Lam, P. K.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

Laurat, J.

Leuchs, G.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

Longchambon, L.

Lugiato, L. A.

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

Martinelli, M.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
[CrossRef]

Nussenzveig, P.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
[CrossRef]

Olsen, M. K.

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Pan, Q.

X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Peng, K. C.

X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Pereira, S. F.

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

Petrosyan, K. G.

K. V. Kheruntsyan and K. G. Petrosyan, "Exact steady-state Wigner function for a nondegenerate parametric oscillator," Phys. Rev. A 62, 015801 (2000).
[CrossRef]

Pfister, O.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.

Polzik, E. S.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Porreca, M. G.

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

Ralph, T. C.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

Reid, M. D.

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

P. D. Drummond and M. D. Reid, "Correlations in nondegenerate parametric oscillation. 2. Below threshold results," Phys. Rev. A 41, 3930-3949 (1990).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, "Correlations in nondegenerate parametric oscillation--squeezing in the presence of phase diffusion," Phys. Rev. A 40, 4493-4506 (1989).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988).
[CrossRef] [PubMed]

Reynaud, S.

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

Schnabel, R.

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

Schori, C.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

Silberhorn, Ch.

Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

Simon, R.

R. Simon, "Peres-Horodecki separability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2726-2729 (2000).
[CrossRef] [PubMed]

Sorensen, J. L.

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

Su, X. L.

X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Sudarshan, E. C. G.

E. C. G. Sudarshan, "Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams," Phys. Rev. Lett. 10, 277-279 (1963).
[CrossRef]

Tan, A.

Tombesi, P.

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

van Loock, P.

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Villar, A. S.

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
[CrossRef]

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S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
[CrossRef]

Wu, H.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Wu, L.-A.

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

Xie, C. D.

X. L. Su, A. Tan, X. J. Jia, Q. Pan, C. D. Xie, and K. C. Peng, "Experimental demonstration of quantum entanglement between frequency-nondegenerate optical twin beams," Opt. Lett. 31, 1133-1135 (2006).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

Zoller, P.

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

J. Phys. A (2)

S. Chaturvedi, P. D. Drummond, and D. F. Walls, "2 photon absorption with coherent and partially coherent driving fields," J. Phys. A 10, L187-L192 (1977).
[CrossRef]

P. D. Drummond and C. W. Gardiner, "Generalized P-representations in quantum optics," J. Phys. A 13, 2353-2368 (1980).
[CrossRef]

Opt. Commun. (2)

P. Galatola, L. A. Lugiato, M. G. Porreca, P. Tombesi, and G. Leuchs, "System control by variation of the squeezing phase," Opt. Commun. 85, 95-103 (1991).
[CrossRef]

A. S. Villar, M. Martinelli, and P. Nussenzveig, "Testing the entanglement of intense beams produced by a nondegenerate optical parametric oscillator," Opt. Commun. 242, 551-563 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

R. J. Glauber, "Coherent and incoherent states of the radiation field," Phys. Rev. 131, 2766-2788 (1963).
[CrossRef]

Phys. Rev. A (6)

K. Dechoum, P. D. Drummond, S. Chaturvedi, and M. D. Reid, "Critical fluctuations and entanglement in the nondegenerate parametric oscillator," Phys. Rev. A 70, 053807 (2004).
[CrossRef]

K. V. Kheruntsyan and K. G. Petrosyan, "Exact steady-state Wigner function for a nondegenerate parametric oscillator," Phys. Rev. A 62, 015801 (2000).
[CrossRef]

B. Coutinho dos Santos, K. Dechoum, A. Z. Khoury, L. F. da Silva, and M. K. Olsen, "Quantum analysis of the nondegenerate optical parametric oscillator with injected signal," Phys. Rev. A 72, 033820 (2005).
[CrossRef]

M. D. Reid and P. D. Drummond, "Correlations in nondegenerate parametric oscillation--squeezing in the presence of phase diffusion," Phys. Rev. A 40, 4493-4506 (1989).
[CrossRef] [PubMed]

P. D. Drummond and M. D. Reid, "Correlations in nondegenerate parametric oscillation. 2. Below threshold results," Phys. Rev. A 41, 3930-3949 (1990).
[CrossRef] [PubMed]

C. Schori, J. L. Sorensen, and E. S. Polzik, "Narrow-band frequency tunable light source of continuous quadrature entanglement," Phys. Rev. A 66, 033802 (2002).
[CrossRef]

Phys. Rev. Lett. (11)

L.-A. Wu, H. J. Kimble, J. L. Hall, and H. Wu, "Generation of squeezed states by parametric down conversion," Phys. Rev. Lett. 57, 2520-2523 (1986).
[CrossRef] [PubMed]

A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, and G. Camy, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987).
[CrossRef] [PubMed]

M. D. Reid and P. D. Drummond, "Quantum correlations of phase in nondegenerate parametric oscillation," Phys. Rev. Lett. 60, 2731-2733 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, "Realization of the Einstein-Podolsky-Rosen paradox for continuous variables," Phys. Rev. Lett. 68, 3663-3666 (1992).
[CrossRef] [PubMed]

X. J. Jia, X. L. Su, Q. Pan, J. G. Gao, C. D. Xie, and K. C. Peng, "Experimental demonstration of unconditional entanglement swapping for continuous variables," Phys. Rev. Lett. 93, 250503 (2004).
[CrossRef]

A. S. Villar, L. S. Cruz, K. N. Cassemiro, M. Martinelli, and P. Nussenzveig, "Generation of bright two-color continuous variable entanglement," Phys. Rev. Lett. 95, 243603 (2005).
[CrossRef] [PubMed]

W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, "Experimental investigation of criteria for continuous variable entanglement," Phys. Rev. Lett. 90, 043601 (2003).
[CrossRef] [PubMed]

E. C. G. Sudarshan, "Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams," Phys. Rev. Lett. 10, 277-279 (1963).
[CrossRef]

Ch. Silberhorn, N. Korolkova, and G. Leuchs, "Quantum key distribution with bright entangled beams," Phys. Rev. Lett. 88, 167902 (2002).
[CrossRef] [PubMed]

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
[CrossRef] [PubMed]

R. Simon, "Peres-Horodecki separability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2726-2729 (2000).
[CrossRef] [PubMed]

Proc. IRE (1)

R. H. Kingston, "Parametric amplification and oscillation of optical frequencies," Proc. IRE 50, 472-474 (1962).

Rev. Mod. Phys. (1)

S. L. Braunstein and P. van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005).
[CrossRef]

Science (1)

A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, "Unconditional quantum teleportation," Science 282, 706-709 (1998).
[CrossRef] [PubMed]

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R. Graham and H. Haken, "The quantum fluctuations of the optical parametric oscillator," Z. Phys. 210, 276-302 (1968).
[CrossRef]

Other (3)

H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, 1999).

C. W. Gardiner, Quantum Noise (Springer-Verlag, 1991).

J. Jing, S. Feng, R. Bloomer, and O. Pfister, "Experimental continuous-variable entanglement of phase-locked bright optical beams," arXiv.org archive, e-Print quant-ph/0604134http://arxiv.org/abs/quantph/0604134.

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Figures (6)

Fig. 1
Fig. 1

Prediction of the linearized theory for fluctuation in the sum–subtraction of field quadratures as a function of σ for a shot-noise limited pump beam. Solid line, S q + ; dashed curve, S p + ; line with crosses, S p ; line with circles, S q .

Fig. 2
Fig. 2

Sketch of the experimental setup.

Fig. 3
Fig. 3

Measurement of the pump noise as a function of the analysis frequency. Open circles, unfiltered laser noise; full circles, laser noise at the output of the filter cavity. In view of the large excess noise at 12 MHz and its second harmonic, we suppressed those frequencies from the data.

Fig. 4
Fig. 4

Intensity noise of the reflected pump beam, as a function of the detuning of the OPO cavity. The excess noise observed is peaked for Δ 0 , close to one-half the OPO cavity bandwidth. The asymmetry in the mean-field signal is attributable to the thermal bistability. The analysis frequency is 27 MHz . Circles, reflected pump noise; full curve, reflected average intensity.

Fig. 5
Fig. 5

Noise behavior as a function of σ. (a) Predictions of the linearized model for an input pump beam with S p 0 = 1.5 and S q 0 = 5.5 ; dashed curve, S p + ; solid line with open circles, S q , solid curve, S q + ; solid line with crosses, S p ; SQL = 1.0 is indicated by a dashed line. (b) Experimental result for σ ranging from 1.06 to 2.2. Full circles, S p + ; triangles, S q ; open circles, S q + ; squares, S p ; SQL = 1.0 is indicated by a dashed line.

Fig. 6
Fig. 6

Sum (full circles) and difference (open circles) of the quadrature noise measured as a function of the detuning of the analysis cavities. Squeezed-state entanglement can be directly observed, with Δ 2 p ̂ = 0.50 ( 1 ) , or 3.01 ( 9 ) dB, and Δ 2 q ̂ + = 0.73 ( 1 ) , or 1.37 ( 6 ) dB.

Equations (35)

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Δ 2 p ̂ + Δ 2 q ̂ + 2 ,
τ d d t α 0 = γ 0 ( 1 i Δ 0 ) α 0 2 χ * α 1 α 2 + 2 γ 0 α 0 in + 2 μ 0 δ v 0 ,
τ d d t α 1 = γ ( 1 i Δ ) α 1 + 2 χ α 0 α 2 * + 2 γ δ u 1 + 2 μ δ v 1 ,
τ d d t α 2 = γ ( 1 i Δ ) α 2 + 2 χ α 0 α 1 * + 2 γ δ u 2 + 2 μ δ v 2 ,
τ d d t δ p = 2 γ δ p + 2 γ δ u p + 2 μ δ v p ,
τ d d t δ q = 2 Δ γ δ p + 2 γ δ u q + 2 μ δ v q ,
τ d d t δ p + = 2 Δ γ δ q + + 2 γ β δ p 0 + 2 Δ γ β δ q 0 + 2 γ δ u p + + 2 μ δ v p + ,
τ d d t δ q + = 2 γ δ q + 2 Δ γ β δ p 0 + 2 γ β δ q 0 + 2 γ δ u q + + 2 μ δ v q + ,
τ d d t δ p 0 = 2 γ β δ p + + 2 Δ γ β δ q + γ 0 δ p 0 Δ 0 γ 0 δ q 0 + 2 γ 0 δ p 0 i n + 2 μ 0 δ v p 0 ,
τ d d t δ q 0 = 2 Δ γ β δ p + 2 γ β δ q + + Δ 0 γ 0 δ p 0 γ 0 δ q 0 + 2 γ 0 δ q 0 i n + 2 μ 0 δ v q 0 ,
g = χ γ D 2 γ r ,
x 0 = g 2 γ r p 0 , q 0 = g 2 γ r q 0 , x + = g p + , y + = g q + , x = g p , y = g q ,
d x 0 d T = γ r [ x 0 2 σ + 1 2 ( x + 2 x 2 y + 2 + y 2 ) ] ,
d y 0 d T = γ r [ y 0 + x + y + x y ] ,
d x d T = x 1 2 [ x 0 x + y 0 y ] + g 2 [ x 0 + i y 0 ξ + x 0 i y 0 ξ + ] ,
d y + d T = y + + 1 2 [ y 0 x + x 0 y + ] i g 2 [ x 0 + i y 0 ξ + x 0 i y 0 ξ + + ] ,
d x + d T = x + + 1 2 [ x 0 x + + y 0 y + ] + g 2 [ x 0 + i y 0 ξ + + x 0 i y 0 ξ + + ] ,
d y d T = y + 1 2 [ x 0 y y 0 x ] i g 2 [ x 0 + i y 0 ξ x 0 i y 0 ξ + ] ,
ξ + ( T ) ξ + ( T ) = ξ + + ( T ) ξ + + ( T ) = δ ( T T ) ,
ξ ( T ) ξ ( T ) = ξ + ( T ) ξ + ( T T ) = δ ( T T ) .
x k = n = 0 g n x k ( n ) ,
y k = n = 0 g n y k ( n ) .
x 0 s = 2 ,
x + s = 2 ( σ 1 ) 1 2 ,
x s = 0 ,
y 0 s = y + s = y s = 0 .
d x 0 ( 1 ) d T = γ r [ x 0 ( 1 ) + 2 ( σ 1 ) 1 2 x + ( 1 ) ] ,
d y 0 ( 1 ) d T = γ r [ y 0 ( 1 ) + 2 ( σ 1 ) 1 2 y + ( 1 ) ] ,
d x + ( 1 ) d T = ( σ 1 ) 1 2 x 0 ( 1 ) + ( ξ + + ξ + + ) ,
d x ( 1 ) d T = 2 x ( 1 ) + ( ξ + ξ + ) ,
d y + ( 1 ) d T = 2 y + ( 1 ) + ( σ 1 ) 1 2 y 0 ( 1 ) i ( ξ + ξ + + ) ,
d y ( 1 ) d T = i ( ξ ξ + ) .
S p ( Ω ) = 1 1 Ω 2 + 1 ,
S q + ( Ω ) = 1 ( 4 Ω 2 + γ r 2 ) 2 Ω 2 [ 4 Ω 2 + γ r 2 2 γ r ( σ 1 ) ] 2 + [ 4 Ω 2 + γ r 2 σ ] 2 ,
Δ 2 p ̂ + Δ 2 q ̂ + = 1.23 ( 2 ) < 2 ,

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