Abstract

An experimentally feasible intracavity coupler scheme is proposed to generate bright quadripartite continuous-variable (CV) entanglement by the coupled second-harmonic generation processes. By solving the steady-state equations and calculating the correlation spectra of the four output beams, we show that the four output beams are all entangled with each other according to the sufficient inseparability criterion for multipartite CV entanglement. By utilizing the upconversion process, the generated four entanglement fields have macroscopic intensities as soon as the input fields are turned on.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
    [CrossRef]
  2. P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
    [CrossRef]
  3. M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
    [CrossRef]
  4. P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
    [CrossRef]
  5. J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
    [CrossRef]
  6. J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
    [CrossRef]
  7. T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
    [CrossRef]
  8. 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]
  9. 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]
  10. Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
    [CrossRef]
  11. M. D. Reid and P. D. Drummond, “Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).
    [CrossRef]
  12. 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]
  13. 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]
  14. N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
    [CrossRef]
  15. A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
    [CrossRef]
  16. 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]
  17. A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
    [CrossRef]
  18. O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
    [CrossRef]
  19. J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
    [CrossRef]
  20. A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
    [CrossRef]
  21. A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
    [CrossRef]
  22. Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
    [CrossRef]
  23. J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
    [CrossRef]
  24. J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
    [CrossRef]
  25. H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
    [CrossRef]
  26. S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
    [CrossRef]
  27. L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
    [CrossRef]
  28. Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
    [CrossRef]
  29. J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
    [CrossRef]
  30. M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
    [CrossRef]
  31. N. Olivier and M. K. Olsen, “Bright entanglement and the Einstein–Podolsky–Rosen paradox with coupled parametric oscillators,” Opt. Commun. 259, 781–788 (2006).
    [CrossRef]
  32. M. K. Olsen and P. D. Drummond, “Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical downconverters,” Phys. Rev. A 71, 053803 (2005).
    [CrossRef]
  33. M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
    [CrossRef]
  34. M. K. Oslen, “Bright entanglement in the intracavity nonlinear coupler,” Phys. Rev. A 73, 053806 (2006).
    [CrossRef]
  35. J. Guo, Z. H. Zhai, and J. R. Gao, “Bright quadripartite continuous variable entanglement from coupled intracavity nonlinearities,” J. Opt. Soc. Am. B 27, 518–523 (2010).
    [CrossRef]
  36. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [CrossRef]
  37. M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
    [CrossRef]
  38. C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
    [CrossRef]
  39. P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
    [CrossRef]
  40. P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
    [CrossRef]
  41. K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
    [CrossRef]

2010 (2)

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

J. Guo, Z. H. Zhai, and J. R. Gao, “Bright quadripartite continuous variable entanglement from coupled intracavity nonlinearities,” J. Opt. Soc. Am. B 27, 518–523 (2010).
[CrossRef]

2009 (4)

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef]

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

2008 (1)

M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
[CrossRef]

2007 (1)

2006 (5)

M. K. Oslen, “Bright entanglement in the intracavity nonlinear coupler,” Phys. Rev. A 73, 053806 (2006).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

N. Olivier and M. K. Olsen, “Bright entanglement and the Einstein–Podolsky–Rosen paradox with coupled parametric oscillators,” Opt. Commun. 259, 781–788 (2006).
[CrossRef]

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef]

2005 (4)

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (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]

M. K. Olsen and P. D. Drummond, “Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical downconverters,” Phys. Rev. A 71, 053803 (2005).
[CrossRef]

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

2004 (2)

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

A. Ferraro, M. G. A. Paris, M. Bondani, A. Allevi, E. Puddu, and A. Andreoni, “Three-mode entanglement by interlinked nonlinear interactions in optical χ(2) media,” J. Opt. Soc. Am. B 21, 1241–1249 (2004).
[CrossRef]

2003 (5)

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

J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
[CrossRef]

M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
[CrossRef]

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

2002 (1)

J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
[CrossRef]

2001 (1)

P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
[CrossRef]

2000 (1)

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[CrossRef]

1999 (1)

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

1998 (1)

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]

1995 (1)

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[CrossRef]

1993 (1)

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[CrossRef]

1992 (2)

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]

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[CrossRef]

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]

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]

1985 (1)

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

1984 (1)

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

1981 (1)

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

1980 (1)

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

1978 (1)

K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
[CrossRef]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Allevi, A.

Andreoni, A.

Aoki, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Bache, M.

M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
[CrossRef]

Barbosa, F. A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef]

Bondani, M.

Bowen, W. P.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

Bradley, A. S.

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
[CrossRef]

Braiman, Y.

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[CrossRef]

Braunstein, S. L.

P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
[CrossRef]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[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]

Cassemiro, K. N.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[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]

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]

Christiansen, P. L.

M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
[CrossRef]

Coelho, A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef]

Colet, P.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[CrossRef]

Collett, M. J.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[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]

Drummond, P. D.

M. K. Olsen and P. D. Drummond, “Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical downconverters,” Phys. Rev. A 71, 053803 (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]

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

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
[CrossRef]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Fabiny, L.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[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 optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef]

Feng, S.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

Ferraro, A.

Fiurášek, J.

J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
[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]

Furusawa, A.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

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]

Gaididei, Y. B.

M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
[CrossRef]

Gao, J. R.

J. Guo, Z. H. Zhai, and J. R. Gao, “Bright quadripartite continuous variable entanglement from coupled intracavity nonlinearities,” J. Opt. Soc. Am. B 27, 518–523 (2010).
[CrossRef]

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

Grosse, N. B.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

Guo, J.

J. Guo, Z. H. Zhai, and J. R. Gao, “Bright quadripartite continuous variable entanglement from coupled intracavity nonlinearities,” J. Opt. Soc. Am. B 27, 518–523 (2010).
[CrossRef]

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

Herec, J.

J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
[CrossRef]

Hiraoka, T.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Jennings, G.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

Jing, J. T.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

Jonathan, D.

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

Kennedy, T. A. B.

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[CrossRef]

Khibnik, A.

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[CrossRef]

Kimble, H. J.

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]

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]

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[CrossRef]

Lam, P. K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

Leng, H. Y.

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Lenstra, D.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[CrossRef]

Li, H. X.

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Mallon, M. J.

M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
[CrossRef]

Martinelli, M.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[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]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[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]

McKenzie, K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

McNeil, K. J.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
[CrossRef]

Midgley, S. L. W.

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

Mišta, L.

J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
[CrossRef]

Murao, M.

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

Nussenzveig, P.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[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]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[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]

Olivier, N.

N. Olivier and M. K. Olsen, “Bright entanglement and the Einstein–Podolsky–Rosen paradox with coupled parametric oscillators,” Opt. Commun. 259, 781–788 (2006).
[CrossRef]

Olsen, M. K.

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
[CrossRef]

N. Olivier and M. K. Olsen, “Bright entanglement and the Einstein–Podolsky–Rosen paradox with coupled parametric oscillators,” Opt. Commun. 259, 781–788 (2006).
[CrossRef]

M. K. Olsen and P. D. Drummond, “Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical downconverters,” Phys. Rev. A 71, 053803 (2005).
[CrossRef]

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
[CrossRef]

Oslen, M. K.

M. K. Oslen, “Bright entanglement in the intracavity nonlinear coupler,” Phys. Rev. A 73, 053806 (2006).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[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]

Paris, M. G. A.

Peng, K. C.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
[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]

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]

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[CrossRef]

Pfister, O.

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
[CrossRef]

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

Plenio, M. B.

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

Podolsky, B.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
[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]

Pooser, R.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

Pooser, R. C.

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
[CrossRef]

Puddu, E.

Reid, M. D.

M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
[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]

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

Rosen, N.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Roy, R.

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[CrossRef]

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]

Takei, N.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Valente, P.

van Loock, P.

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

P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
[CrossRef]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[CrossRef]

Vedral, V.

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

Villar, A. S.

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[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]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[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]

Wakui, K.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Walls, D. F.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
[CrossRef]

Wang, J. F.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

Wiesenfeld, K.

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[CrossRef]

Xie, C. D.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
[CrossRef]

Xie, D.

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

Xie, Z. D.

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Xu, P.

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Yan, Y.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

Yao, H. M.

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Yin, Y. L.

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

Yonezawa, H.

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

Yu, X. Q.

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Yu, Y. B.

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Zhai, Z. H.

J. Guo, Z. H. Zhai, and J. R. Gao, “Bright quadripartite continuous variable entanglement from coupled intracavity nonlinearities,” J. Opt. Soc. Am. B 27, 518–523 (2010).
[CrossRef]

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

Zhang, J.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
[CrossRef]

Zhang, J. X.

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

Zhao, F. G.

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

Zhao, J. S.

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

Zhu, S. N.

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Zou, H. X.

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

Appl. Phys. B (1)

Z. Y. Ou, S. F. Pereira, and H. J. Kimble, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables in nondegenerate parametric amplification,” Appl. Phys. B 55, 265–278 (1992).
[CrossRef]

J. Opt. B (1)

J. Herec, J. Fiurášek, and L. Mišta, “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419–426 (2003).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

M. J. Mallon, M. D. Reid, and M. K. Olsen, “Bright continuous-variable entanglement from the quantum optical dimer,” J. Phys. B 41, 015501 (2008).
[CrossRef]

Opt. Acta (2)

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation I,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transitions in sub/second harmonic generation II,” Opt. Acta 28, 211–225 (1981).
[CrossRef]

Opt. Commun. (4)

K. J. McNeil, P. D. Drummond, and D. F. Walls, “Self pulsing in second harmonic generation,” Opt. Commun. 27, 292–294 (1978).
[CrossRef]

N. Olivier and M. K. Olsen, “Bright entanglement and the Einstein–Podolsky–Rosen paradox with coupled parametric oscillators,” Opt. Commun. 259, 781–788 (2006).
[CrossRef]

J. F. Wang, X. Q. Yu, Y. B. Yu, P. Xu, Z. D. Xie, H. Y. Leng, and S. N. Zhu, “Direct generation of bright quadripartite continuous-variable entanglement use cascaded χ2 nonlinear interactions in a quasi-periodic optical superlattice,” Opt. Commun. 282, 253–257 (2009).
[CrossRef]

J. F. Wang, J. S. Zhao, H. Y. Leng, X. Q. Yu, Z. D. Xie, Y. L. Yin, P. Xu, and S. N. Zhu, “Quadripartite entanglement from cascaded χ2 nonlinear interactions,” Opt. Commun. 282, 3729–3733 (2009).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).
[CrossRef]

Phys. Rev. A (17)

M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156–161 (1999).
[CrossRef]

J. Zhang, C. D. Xie, and K. C. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,” Phys. Rev. A 66, 032318 (2002).
[CrossRef]

H. Y. Leng, J. F. Wang, Y. B. Yu, X. Q. Yu, P. Xu, Z. D. Xie, J. S. Zhao, and S. N. Zhu, “Scheme to generate continuousvariable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

S. L. W. Midgley, A. S. Bradley, O. Pfister, and M. K. Olsen, “Quadripartite continuous-variable entanglement via quadruply concurrent down-conversion,” Phys. Rev. A 81, 063834 (2010).
[CrossRef]

L. Fabiny, P. Colet, R. Roy, and D. Lenstra, “Coherence and phase dynamics of spatially coupled solid-state lasers,” Phys. Rev. A 47, 4287–4296 (1993).
[CrossRef]

Y. Braiman, T. A. B. Kennedy, K. Wiesenfeld, and A. Khibnik, “Entrainment of solid-state laser arrays,” Phys. Rev. A 52, 1500–1506 (1995).
[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]

O. Pfister, S. Feng, G. Jennings, R. Pooser, and D. Xie, “Multipartite continuous-variable entanglement from concurrent nonlinearities,” Phys. Rev. A 70, 020302(R) (2004).
[CrossRef]

J. Guo, H. X. Zou, Z. H. Zhai, J. X. Zhang, and J. R. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
[CrossRef]

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

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30, 1386–1391 (1984).
[CrossRef]

C. W. Gardiner and M. J. Collett, “Input and output in damped quantum systems: quantum stochastic differential equations and the master equation,” Phys. Rev. A 31, 3761–3774 (1985).
[CrossRef]

M. K. Olsen and P. D. Drummond, “Entanglement and the Einstein–Podolsky–Rosen paradox with coupled intracavity optical downconverters,” Phys. Rev. A 71, 053803 (2005).
[CrossRef]

M. K. Oslen, “Bright entanglement in the intracavity nonlinear coupler,” Phys. Rev. A 73, 053806 (2006).
[CrossRef]

M. Bache, Y. B. Gaididei, and P. L. Christiansen, “Nonclassical statistics of intracavity coupled χ(2) waveguides: the quantum optical dimer,” Phys. Rev. A 67, 043802 (2003).
[CrossRef]

A. S. Bradley, M. K. Olsen, O. Pfister, and R. C. Pooser, “Bright tripartite entanglement in triply concurrent parametric oscillation,” Phys. Rev. A 72, 053805 (2005).
[CrossRef]

Y. B. Yu, Z. D. Xie, X. Q. Yu, H. X. Li, P. Xu, H. M. Yao, and S. N. Zhu, “Generation of three-mode continuous-variable entanglement by cascaded nonlinear interactions in a quasi-periodic superlattice,” Phys. Rev. A 74, 042332 (2006).
[CrossRef]

Phys. Rev. Lett. (9)

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]

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96, 063601 (2006).
[CrossRef]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef]

T. Aoki, N. Takei, H. Yonezawa, K. Wakui, T. Hiraoka, and A. Furusawa, “Experimental creation of a fully inseparable tripartite continuous-variable state,” Phys. Rev. Lett. 91, 080404 (2003).
[CrossRef]

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

P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
[CrossRef]

J. T. Jing, J. Zhang, Y. Yan, F. G. Zhao, C. D. Xie, and K. C. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
[CrossRef]

P. van Loock and S. L. Braunstein, “Multipartite entanglement for continuous variables: a quantum teleportation network,” Phys. Rev. Lett. 84, 3482–3485 (2000).
[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]

Science (2)

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]

A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, “Three-color entanglement,” Science 326, 823–826 (2009).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for the proposed scheme.

Fig. 2.
Fig. 2.

Real parts of the eigenvalues of the drift matrix M versus the normalized FW pump power σ=ε/εth for the general case ΔaJa and ΔaJa.

Fig. 3.
Fig. 3.

Real parts of the eigenvalues of the drift matrix M versus the normalized FW pump power σ=ε/εth for the special case Δa=Ja and Δa=Ja.

Fig. 4.
Fig. 4.

Quantum correlation spectra versus the normalized analysis frequency Ω=ωτ/γa.

Fig. 5.
Fig. 5.

Quantum correlation spectra versus the normalized detuning Δ/γa.

Fig. 6.
Fig. 6.

Quantum correlation spectra versus the normalized analysis frequency Ω=ωτ/γa.

Fig. 7.
Fig. 7.

Quantum correlation spectra versus the normalized pump power σ=ε/εth.

Fig. 8.
Fig. 8.

Quantum correlation spectra versus the linear coupling parameter Ja.

Equations (23)

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

H^tol=H^sys+H^couple+H^bath.
H^sys=iκ2[a^1+2b^1a^12b^1++a^2+2b^2a^22b^2+][δa(a^1+a^1+a^2+a^2)+δb(b^1+b^1+b^2+b^2)],
H^couple=Ja[a^1+a^2+a^1a^2+]+Jb[b^1+b^2+b^1b^2+],
H^bath=n=12[Γ^ana^n++Γ^bnb^n+]+.c.,
τda^1dt=(γa1+iΔa)a^1+κa^1+b^1iJaa^2+2γa1a^1in,τda^2dt=(γa2+iΔa)a^2+κa^2+b^2iJaa^1+2γa2a^2in,τdb^1dt=(γb1+iΔb)b^1κ2a^12iJbb^2+2γb1b^1in,τdb^2dt=(γb2+iΔb)b^2κ2a^22iJbb^1+2γb2b^2in.
(γa+iΔa)α1+κα1*β1iJaα2+2γaα1in=0,(γa+iΔa)α2+κα2*β2iJaα1+2γaα2in=0,(γb+iΔb)β1κ2α12iJbβ2+2γbβ1in=0,(γb+iΔb)β2κ2α22iJbβ1+2γbβ2in=0,
β=κα22γb2+μb2,
ϕa=arccos{αε[γa+κ2α2μb2(γb2+μb2)]},
ϕb=2ϕaarctan(μbγb)
ε2=α2[(γa2+μa2)+κ4α44(γb2+μb2)+κ2α2(γaγbμaμb)(γb2+μb2)].
τdDdt=MD+BDin
D=[δX^a1,δX^a2,δX^b1,δX^b2,δY^a1,δY^a2,δY^b1,δY^b2]T,
Din=[δX^a1in,δX^a2in,δX^b1in,δX^b2in,δY^a1in,δY^a2in,δY^b1in,δY^b2in]T,
M=(γa+p0m0Δa+qJan00γa+p0mJaΔa+q0nm0γb0n0ΔbJb0m0γb0nJbΔbΔa+qJan0γap0m0JaΔa+q0n0γap0mn0ΔbJbm0γb00nJbΔb0m0γb),
B=(2γa000000002γa000000002γb000000002γb000000002γa000000002γa000000002γb000000002γb).
β=κα22γb
εαγaκ2α32γb=0.
N=9εκ4γb+81ε2κ8γb2+24κ6γa3γb33,
α=2γaγb31/3NN32/3κ2,
ϕa=arccos[αε(γa+κ2α22γb)],
ϕb=2ϕa.
Dout=[B(iωτIM)1BI]Din.
IS1=δ2(X^a1+X^b1)+δ2(Y^a1+g2Y^a2Y^b1+g4Y^b2)4,IIS2=δ2(X^b1X^b2)+δ2(g1Y^a1+g2Y^a2+Y^b1+Y^b2)4,IIIS3=δ2(X^a1X^a2)+δ2(Y^a1+Y^a2+g3Y^b1+g4Y^b2)4,

Metrics