Abstract

We experimentally investigate quadrature correlations between pump, signal, and idler fields in an above-threshold optical parametric oscillator. We observe new quantum correlations among the pump and signal or idler beams, as well as among the pump and a combined quadrature of signal and idler beams. A further investigation of unforeseen classical noise observed in this system is presented, which hinders the observation of the recently predicted tripartite entanglement. In spite of this noise, current results approach the limit required to demonstrate three-color entanglement.

©2007 Optical Society of America

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Entanglement in the above-threshold optical parametric oscillator

Alessandro S. Villar, Katiúscia N. Cassemiro, Kaled Dechoum, Antonio Z. Khoury, Marcelo Martinelli, and Paulo Nussenzveig
J. Opt. Soc. Am. B 24(2) 249-256 (2007)

Experimental observation of three-color optical quantum correlations

Katiúscia N. Cassemiro, Alessandro S. Villar, Paulo Valente, Marcelo Martinelli, and Paulo Nussenzveig
Opt. Lett. 32(6) 695-697 (2007)

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  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]
  2. 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]
  3. M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988)
    [Crossref] [PubMed]
  4. 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]
  5. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706–709 (1998).
    [Crossref] [PubMed]
  6. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
    [Crossref] [PubMed]
  7. H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
    [Crossref] [PubMed]
  8. 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]
  9. 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]
  10. J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
    [Crossref]
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    [Crossref]
  12. K. Kasai, G. Jiangrui, and C. Fabre, “Observation of squeezing using cascaded nonlinearity,” Europhys. Lett. 40, 25–30 (1997).
    [Crossref]
  13. A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
    [Crossref] [PubMed]
  14. K. N. Cassemiro, A. S. Villar, P. Valente, M. Martinelli, and P. Nussenzveig, “Experimental observation of three-color optical quantum correlations,” Opt. Lett. 32, 695–697 (2007).
    [Crossref] [PubMed]
  15. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [Crossref]
  16. P. Hyllus and J. Eisert, “Optimal entanglement witnesses for continuous-variable systems,” New J. Phys. 8, 51 (2006).
    [Crossref]
  17. S. J. van Enk, N. Lütkenhaus, and H. J. Kimble, “Experimental procedures for entanglement verification,” Phys. Rev. A 75, 052318 (2007).
    [Crossref]
  18. 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]
  19. R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
    [Crossref] [PubMed]
  20. B. Willke, N. Uehara, E. K. Gustafson, R. L. Byer, P. J. King, S. U. Seel, and R. L. Savage, “Spatial and temporal filtering of a 10-W Nd:YAG laser with a Fabry-Perot ring-cavity premode cleaner,” Opt. Lett. 23, 1704–1706 (1998).
    [Crossref]
  21. 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]
  22. 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]
  23. D. Wang, Y. Shang, X. J. Jia, C. D. Xie, and K. C. Peng, “Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator,” http://arxiv.org/abs/0709.4520.

2007 (3)

2006 (4)

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]

P. Hyllus and J. Eisert, “Optimal entanglement witnesses for continuous-variable systems,” New J. Phys. 8, 51 (2006).
[Crossref]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
[Crossref] [PubMed]

J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
[Crossref]

2005 (2)

2004 (2)

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]

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

2003 (1)

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

2002 (1)

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

2000 (2)

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]

1998 (2)

1997 (1)

K. Kasai, G. Jiangrui, and C. Fabre, “Observation of squeezing using cascaded nonlinearity,” Europhys. Lett. 40, 25–30 (1997).
[Crossref]

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]

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]

Aoki, T.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

Bloomer, R.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
[Crossref]

Braunstein, S. L.

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science 282, 706–709 (1998).
[Crossref] [PubMed]

Byer, R. L.

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]

Cassemiro, K. N.

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.

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]

Dechoum, K.

Drummond, P. D.

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

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]

Eisert, J.

P. Hyllus and J. Eisert, “Optimal entanglement witnesses for continuous-variable systems,” New J. Phys. 8, 51 (2006).
[Crossref]

Fabre, C.

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
[Crossref] [PubMed]

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]

K. Kasai, G. Jiangrui, and C. Fabre, “Observation of squeezing using cascaded nonlinearity,” Europhys. Lett. 40, 25–30 (1997).
[Crossref]

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]

Feng, S.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
[Crossref]

Fuchs, C. A.

A. Furusawa, J. L. Sørensen, 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.

H. Yonezawa, T. Aoki, and A. Furusawa, “Demonstration of a quantum teleportation network for continuous variables,” Nature 431, 430–433 (2004).
[Crossref] [PubMed]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

A. Furusawa, J. L. Sørensen, 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]

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]

Gustafson, E. K.

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]

Hyllus, P.

P. Hyllus and J. Eisert, “Optimal entanglement witnesses for continuous-variable systems,” New J. Phys. 8, 51 (2006).
[Crossref]

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]

D. Wang, Y. Shang, X. J. Jia, C. D. Xie, and K. C. Peng, “Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator,” http://arxiv.org/abs/0709.4520.

Jiangrui, G.

K. Kasai, G. Jiangrui, and C. Fabre, “Observation of squeezing using cascaded nonlinearity,” Europhys. Lett. 40, 25–30 (1997).
[Crossref]

Jing, J.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
[Crossref]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Kasai, K.

K. Kasai, G. Jiangrui, and C. Fabre, “Observation of squeezing using cascaded nonlinearity,” Europhys. Lett. 40, 25–30 (1997).
[Crossref]

Khoury, A. Z.

Kimble, H. J.

S. J. van Enk, N. Lütkenhaus, and H. J. Kimble, “Experimental procedures for entanglement verification,” Phys. Rev. A 75, 052318 (2007).
[Crossref]

A. Furusawa, J. L. Sørensen, 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]

King, P. J.

Laurat, J.

Leuchs, 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]

Li, X.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

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]

Lütkenhaus, N.

S. J. van Enk, N. Lütkenhaus, and H. J. Kimble, “Experimental procedures for entanglement verification,” Phys. Rev. A 75, 052318 (2007).
[Crossref]

Martinelli, M.

A. S. Villar, K. N. Cassemiro, K. Dechoum, A. Z. Khoury, M. Martinelli, and P. Nussenzveig, “Entanglement in the above-threshold optical parametric oscillator,” J. Opt. Soc. Am. B 24, 249–256 (2007).
[Crossref]

K. N. Cassemiro, A. S. Villar, P. Valente, M. Martinelli, and P. Nussenzveig, “Experimental observation of three-color optical quantum correlations,” Opt. Lett. 32, 695–697 (2007).
[Crossref] [PubMed]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
[Crossref] [PubMed]

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.

K. N. Cassemiro, A. S. Villar, P. Valente, M. Martinelli, and P. Nussenzveig, “Experimental observation of three-color optical quantum correlations,” Opt. Lett. 32, 695–697 (2007).
[Crossref] [PubMed]

A. S. Villar, K. N. Cassemiro, K. Dechoum, A. Z. Khoury, M. Martinelli, and P. Nussenzveig, “Entanglement in the above-threshold optical parametric oscillator,” J. Opt. Soc. Am. B 24, 249–256 (2007).
[Crossref]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
[Crossref] [PubMed]

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]

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. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

Peng, K.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum Dense Coding Exploiting a Bright Einstein-Podolsky-Rosen Beam,” Phys. Rev. Lett. 88, 047904 (2002).
[Crossref] [PubMed]

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]

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]

D. Wang, Y. Shang, X. J. Jia, C. D. Xie, and K. C. Peng, “Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator,” http://arxiv.org/abs/0709.4520.

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]

Pfister, O.

J. Jing, S. Feng, R. Bloomer, and O. Pfister, “Experimental continuous-variable entanglement of phase-locked bright optical beams,” Phys. Rev. A 74, 041804(R) (2006).
[Crossref]

Polzik, E. S.

A. Furusawa, J. L. Sørensen, 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]

Reid, M. D.

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]

Savage, R. L.

Seel, S. U.

Shang, Y.

D. Wang, Y. Shang, X. J. Jia, C. D. Xie, and K. C. Peng, “Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator,” http://arxiv.org/abs/0709.4520.

Simon, R.

R. Simon, “Peres-Horodecki Separability Criterion for Continuous Variable Systems,” Phys. Rev. Lett. 84, 2726–2729 (2000).
[Crossref] [PubMed]

Sørensen, J. L.

A. Furusawa, J. L. Sørensen, 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.

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]

Uehara, N.

Valente, P.

van Enk, S. J.

S. J. van Enk, N. Lütkenhaus, and H. J. Kimble, “Experimental procedures for entanglement verification,” Phys. Rev. A 75, 052318 (2007).
[Crossref]

van Loock, P.

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[Crossref]

Villar, A. S.

K. N. Cassemiro, A. S. Villar, P. Valente, M. Martinelli, and P. Nussenzveig, “Experimental observation of three-color optical quantum correlations,” Opt. Lett. 32, 695–697 (2007).
[Crossref] [PubMed]

A. S. Villar, K. N. Cassemiro, K. Dechoum, A. Z. Khoury, M. Martinelli, and P. Nussenzveig, “Entanglement in the above-threshold optical parametric oscillator,” J. Opt. Soc. Am. B 24, 249–256 (2007).
[Crossref]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold OPO,” Phys. Rev. Lett. 97, 140504 (2006).
[Crossref] [PubMed]

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]

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D. Wang, Y. Shang, X. J. Jia, C. D. Xie, and K. C. Peng, “Dependence of quantum correlations of twin beams on pump finesse of optical parametric oscillator,” http://arxiv.org/abs/0709.4520.

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Figures (5)

Fig. 1.
Fig. 1. Sketch of the experimental setup. PBS: polarizing beam splitter.
Fig. 2.
Fig. 2. Noise measurements of the terms appearing in the tripartite entanglement criteria of Ineqs. (1)–(3) (pump power relative to threshold σ=P/Pth =1.14). As functions of cavity detuning Δ, black full circles + line curves correspond to the noises in the sum of quadratures of two beams, solid red line to their difference, and blue open circles + line to a corrected noise, in which information from the remaining beam is included. Amplitude quadratures are measured at large cavity detuning |Δ|≳3 and at Δ=0; phase quadratures are measured at Δ=±0.5. (a) The considered pair of beams is signal and idler, and the corrected sum curve includes the term β0 coming from correlations with the pump beam; (b) signal-pump beams and difference correction using idler; (c) idler-pump beams and difference correction using signal. The corrected sum in (a) presents the first direct observation of a quantum correlation among the phases of pump, signal, and idler: the noise is 26% below the SQL.
Fig. 3.
Fig. 3. Noise behaviors as functions of pump power σ. (a) Terms appearing in Ineq (1): the well-known squeezing in the subtraction of twins’ intensity fluctuations Δ2 p̂- is shown in the red circles, noise of twins’ sum of phase fluctuations Δ2 q̂+ are the black squares and the phase noise corrected by information from the pump Δ2 q̂+ are the blue triangles. (b) Amplitude (red circles) and phase (black squares) noise of the pump beam reflected by the OPO cavity. Solid lines are tentative fits to the ad hoc model explained in the text. Predictions differ from the usual ones only for the phase quadratures. Theoretical curves have the same colors as the experimental curve to which they relate.
Fig. 4.
Fig. 4. Reflected pump phase noise, as a function of the analysis frequency. Pump power is close to threshold, but temperature is tuned to avoid triple resonance. In (a), the pump polarization is such that the phase matching conditions are fulfilled, whereas in (b) the Borthogonal polarization is used. Measurements are normalized to the shot noise level (0 dB level).
Fig. 5.
Fig. 5. Behaviors of the noise terms appearing in Ineq (2) as functions of pump power σ. The red circles correspond to the first term in the inequality and the blue triangles to the second one. The former presents the observation of amplitude quantum correlations between one of the twin beams and the reflected pump beam: there is ≈12% of squeezing for higher σ values. The solid lines are the predictions of the model explained in the text, without added noise. Theoretical curves have the same color as the experimental symbol to which they relate.

Equations (7)

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V 0 = Δ 2 ( p ̂ 1 p ̂ 2 2 ) + Δ 2 ( q ̂ 1 + q ̂ 2 2 α 0 q ̂ 0 ) 2 ,
V 1 = Δ 2 ( p ̂ 0 + p ̂ 1 2 ) + Δ 2 ( q ̂ 1 q ̂ 0 2 α 2 q ̂ 2 ) 2 ,
V 2 = Δ 2 ( p ̂ 0 + p ̂ 2 2 ) + Δ 2 ( q ̂ 2 q ̂ 0 2 α 1 q ̂ 1 ) 2 ,
Δ 2 q ˜ + ' = Δ 2 q ̂ + β 0 , β 0 = ( C q ̂ 0 q ̂ 1 + C q ̂ 0 q ̂ 2 ) 2 2 Δ 2 q ̂ 0 ,
Δ 2 p ̂ 0 j = Δ 2 ( p ̂ 0 + p ̂ j 2 ) ,
Δ 2 q ˜ 0 j ' = Δ 2 ( q ̂ j q ̂ 0 2 + α j q ̂ j ) .
Δ 2 q ˜ 0 j ' = Δ 2 q ̂ 0 j β j ' , β j ' = ( C q ̂ 0 q ̂ j C q ̂ j q ̂ j ' ) 2 2 Δ 2 q ̂ j ' ,

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