Abstract

The continuous variable quadripartite entanglement properties of the output fields by the coupled intracavity parametric downconversions processes are analyzed theoretically. In the above-threshold region, it shows that the four output lights are multicolored entangled beams in separable locations with four-mode amplitude quadratures correlation and relative phase quadratures correlation.

© 2010 Optical Society of America

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  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] [PubMed]
  2. M. Murao, D. Jonathan, M. B. Plenio, and V. Vedral, “Quantum telecloning and multiparticle entanglement,” Phys. Rev. A 59, 156-161 (1999).
    [CrossRef]
  3. P. van Loock and S. L. Braunstein, “Telecloning of continuous quantum variables,” Phys. Rev. Lett. 87, 247901 (2001).
    [CrossRef] [PubMed]
  4. J. Zhang, C. Xie, and K. Peng, “Controlled dense coding for continuous variables using three-particle entangled states,”Phys. Rev. A 66, 032318 (2002).
    [CrossRef]
  5. J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).
    [CrossRef] [PubMed]
  6. 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] [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. X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
    [CrossRef] [PubMed]
  9. M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
    [CrossRef]
  10. J. Guo, H. Zou, Z. Zhai, J. Zhang, and J. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (2005).
    [CrossRef]
  11. 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]
  12. C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
    [CrossRef]
  13. 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]
  14. A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
    [CrossRef] [PubMed]
  15. 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]
  16. 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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
    [CrossRef]
  17. 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]
  18. 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]
  19. 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] [PubMed]
  20. 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] [PubMed]
  21. J. Herec, J. Fiurášek, and L. Mišta Jr., “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419-426 (2003).
    [CrossRef]
  22. M. Bache, Yu. 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]
  23. H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1998).
    [CrossRef]
  24. 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] [PubMed]
  25. 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]
  26. P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
    [CrossRef]
  27. 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] [PubMed]
  28. N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
    [CrossRef] [PubMed]

2009 (3)

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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[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] [PubMed]

2008 (2)

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

2007 (2)

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

2006 (4)

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]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

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] [PubMed]

2005 (3)

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. Zou, Z. Zhai, J. Zhang, and J. Gao, “Generation of continuous-variable tripartite entanglement using cascaded nonlinearities,” Phys. Rev. A 71, 034305 (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]

2004 (1)

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

2003 (5)

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

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] [PubMed]

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 Jr., “Entanglement generation in continuously coupled parametric generators,” J. Opt. B 5, 419-426 (2003).
[CrossRef]

M. Bache, Yu. 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]

2002 (1)

J. Zhang, C. Xie, and K. 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] [PubMed]

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] [PubMed]

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)

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (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] [PubMed]

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] [PubMed]

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]

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]

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] [PubMed]

Assad, S.

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

Bache, M.

M. Bache, Yu. 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] [PubMed]

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] [PubMed]

Bradley, A. S.

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[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] [PubMed]

Braunstein, S. L.

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

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

Briegel, H.-J.

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (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] [PubMed]

Christiansen, P. L.

M. Bache, Yu. 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]

Cirac, J. I.

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1998).
[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] [PubMed]

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] [PubMed]

Collett, M. J.

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]

Dr, W.

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1998).
[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]

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] [PubMed]

Fabre, C.

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

Fiurášek, J.

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

Furusawa, A.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

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]

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] [PubMed]

Gaididei, Yu. B.

M. Bache, Yu. 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.

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

Gardiner, C. W.

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, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Guo, J.

J. Guo, H. Zou, Z. Zhai, J. Zhang, and J. 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 Jr., “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] [PubMed]

Jia, X.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

Jing, J.

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

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] [PubMed]

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] [PubMed]

Lam, P. K.

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Leng, H. Y.

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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (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]

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] [PubMed]

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]

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] [PubMed]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Mehmet, M.

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

Mišta, L.

J. Herec, J. Fiurášek, and L. Mišta Jr., “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] [PubMed]

Nussenzveig1, P.

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

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.

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[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]

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]

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]

Peng, K.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

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

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

Pennarun, C.

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[CrossRef]

Pfister, O.

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]

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]

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]

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] [PubMed]

Schnabel, R.

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

Su, X.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

Symul, T.

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Tan, A.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

Ukai, R.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

van Loock, P.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

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] [PubMed]

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

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] [PubMed]

A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

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] [PubMed]

Wang, J. F.

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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (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] [PubMed]

Xie, C.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

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

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

Xie, Z. D.

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 continuous-variable 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]

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

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]

Yonezawa, H.

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

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] [PubMed]

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]

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 continuous-variable 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 continuous-variable 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]

Yukawa, M.

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

Zhai, Z.

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

Zhang, J.

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

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

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

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

Zhao, F.

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

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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[CrossRef]

Zhu, S. N.

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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (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]

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]

Zoller, P.

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

Zou, H.

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

J. Opt. B (1)

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

Nature (1)

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

Opt. Commun. (2)

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]

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]

Phys. Rev. A (14)

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] [PubMed]

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] [PubMed]

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]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67, 052315 (2003).
[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 continuous-variable quadripartite entanglement by intracavity downconversion cascaded with double sum-frequency generations,” Phys. Rev. A 79, 032337 (2009).
[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. Bache, Yu. 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]

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

M. Yukawa, R. Ukai, P. van Loock, and A. Furusawa, “Experimental generation of four-mode continuous-variable cluster states,” Phys. Rev. A 78, 012301 (2008).
[CrossRef]

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

C. Pennarun, A. S. Bradley, and M. K. Olsen, “Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation,” Phys. Rev. A 76, 063812 (2007).
[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, M. Martinelli, C. Fabre, and P. Nussenzveig1, “Direct production of tripartite pump-signal-idler entanglement in the above-threshold optical parametric oscillator,” Phys. Rev. Lett. 97, 140504 (2006).
[CrossRef] [PubMed]

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

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] [PubMed]

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

H.-J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Quantum repeaters: the role of imperfect local operations in quantum communication,” Phys. Rev. Lett. 81, 5932-5935 (1998).
[CrossRef]

X. Su, A. Tan, X. Jia, J. Zhang, C. Xie, and K. Peng, “Experimental preparation of quadripartite cluster and Greenberger-Horne-Zeilinger entangled states for continuous variables,” Phys. Rev. Lett. 98, 070502 (2007).
[CrossRef] [PubMed]

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] [PubMed]

N. B. Grosse, S. Assad, M. Mehmet, R. Schnabel, T. Symul, and P. K. Lam, “Observation of entanglement between two light beams spanning an octave in optical frequency,” Phys. Rev. Lett. 100, 243601 (2008).
[CrossRef] [PubMed]

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

Science (1)

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] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Sketch of coupled optical oscillators. Two nonlinear waveguides A and B are put inside a cavity. Pump a 2 and b 2 from one laser are incident into the cavity through mirror M. Fields a 1 and b 1 are created, respectively, by the processes of parametric downconversion. a 1 in , a 2 in , b 1 in , b 2 in are the incoming fields, a 1 out , a 2 out , b 1 out , b 2 out are the corresponding outgoing fields.

Fig. 2
Fig. 2

Quantum correlation spectra versus normalized frequency Ω = ϖ τ γ 1 for σ = ε ε th = 1.2 .

Fig. 3
Fig. 3

Quantum correlation spectra as functions of pump parameter σ = ε ε th at Ω = 0 .

Fig. 4
Fig. 4

Quantum correlation spectra as functions of coupling parameter J 1 at Ω = 0 and σ = 1.2 .

Equations (57)

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

H ̂ tot = H ̂ sys + H ̂ couple + H ̂ bath ,
H ̂ sys = [ ( δ 1 a ̂ 1 + a ̂ 1 δ 2 a ̂ 2 + a ̂ 2 ) + ( δ 1 b ̂ 1 + b ̂ 1 δ 2 b ̂ 2 + b ̂ 2 ) ] + [ i κ 2 ( a ̂ 1 + 2 a ̂ 2 a ̂ 1 2 a ̂ 2 + ) + i κ 2 ( b ̂ 1 + 2 b ̂ 2 b ̂ 1 2 b ̂ 2 + ) ] .
H ̂ couple = J 1 ( a ̂ 1 b ̂ 1 + + b ̂ 1 a ̂ 1 + ) + J 2 ( a ̂ 2 b ̂ 2 + + b ̂ 2 a ̂ 2 + ) .
H ̂ bath = i + d ϖ κ ( ϖ ) [ Γ ̂ a 1 + a ̂ 1 + Γ ̂ a 2 + a ̂ 2 + Γ ̂ b 1 + b ̂ 1 + Γ ̂ b 2 + b ̂ 2 ] + h.c.
κ ( ϖ ) = γ π ,
τ d a ̂ 1 d t = ( γ 1 + i Δ 1 ) a ̂ 1 + κ a ̂ 1 + a ̂ 2 i J 1 b ̂ 1 + 2 γ 1 a ̂ 1 in ,
τ d a ̂ 2 d t = ( γ 2 + i Δ 2 ) a ̂ 2 κ 2 a ̂ 1 2 i J 2 b ̂ 2 + 2 γ 2 a ̂ 2 in ,
τ d b ̂ 1 d t = ( γ 1 + i Δ 1 ) b ̂ 1 + κ b ̂ 1 + b ̂ 2 i J 1 a ̂ 1 + 2 γ 1 b ̂ 1 in ,
τ d b ̂ 2 d t = ( γ 2 + i Δ 2 ) b ̂ 2 κ 2 b ̂ 1 2 i J 2 a ̂ 2 + 2 γ 2 b ̂ 2 in .
( γ 1 + i Δ 1 ) α 1 + κ α 1 * α 2 i J 1 β 1 = 0 ,
( γ 2 + i Δ 2 ) α 2 κ 2 α 1 2 i J 2 β 2 + 2 γ 2 α 2 in = 0 ,
( γ 1 + i Δ 1 ) β 1 + κ β 1 * β 2 i J 1 α 1 = 0 ,
( γ 2 + i Δ 2 ) β 2 κ 2 β 1 2 i J 2 α 2 + 2 γ 2 β 2 in = 0 .
α 1 = β 1 = 0 ,
α 2 = β 2 = ε γ 2 + i ( J 2 Δ 2 ) .
α 1 = β 1 = A 1 e i θ 1 ,
A 1 = 2 κ 2 [ ε 2 κ 2 ( γ 1 μ 2 + γ 2 μ 1 ) 2 + ( μ 1 μ 2 γ 1 γ 2 ) ] ,
θ 1 = arccos 1 2 + ε 2 κ 2 ( γ 1 μ 2 + γ 2 μ 1 ) 2 2 ε κ ,
α 2 = β 2 = A 2 e i θ 2 ,
A 2 = γ 1 2 + μ 1 2 κ ,
θ 2 = arctan μ 1 γ 1 + 2 θ 1 ,
μ 1 = J 1 Δ 1 ,
μ 2 = J 2 Δ 2 .
ε th = [ γ 1 2 + ( J 1 Δ 1 ) 2 ] [ γ 2 2 + ( J 2 Δ 2 ) 2 ] κ .
a ̂ j = α j + 1 2 ( δ X ̂ a j + i δ Y ̂ a j ) ,
b ̂ j = β j + 1 2 ( δ X ̂ b j + i δ Y ̂ b j ) .
τ ( d δ X ̂ a 1 d t d δ X ̂ a 2 d t d δ X ̂ b 1 d t d δ X ̂ b 2 d t d δ Y ̂ a 1 d t d δ Y ̂ a 2 d t d δ Y ̂ b 1 d t d δ Y ̂ b 2 d t ) = ( M 1 M 2 M 3 M 4 ) ( δ X ̂ a 1 δ X ̂ a 2 δ X ̂ b 1 δ X ̂ b 2 δ Y ̂ a 1 δ Y ̂ a 2 δ Y ̂ b 1 δ Y ̂ b 2 ) + ( N 0 0 N ) ( δ X ̂ a 1 in δ X ̂ a 2 in δ X ̂ b 1 in δ X ̂ b 2 in δ Y ̂ a 1 in δ Y ̂ a 2 in δ Y ̂ b 1 in δ Y ̂ b 2 in ) ,
M 1 = ( γ 1 + f h 0 0 h γ 2 0 0 0 0 γ 1 + f h 0 0 h γ 2 ) ,
M 2 = ( Δ 1 + p q J 1 0 q Δ 2 0 J 2 J 1 0 Δ 1 + p q 0 J 2 q Δ 2 ) ,
M 3 = ( Δ 1 + p q J 1 0 q Δ 2 0 J 2 J 1 0 Δ 1 + p q 0 J 2 q Δ 2 ) ,
M 4 = ( γ 1 f h 0 0 h γ 2 0 0 0 0 γ 1 f h 0 0 h γ 2 ) ,
N = ( 2 γ 1 0 0 0 0 2 γ 2 0 0 0 0 2 γ 1 0 0 0 0 2 γ 2 ) ,
f = κ A 2 cos θ 2 ,
h = κ A 1 cos θ 1 ,
p = κ A 2 sin θ 2 ,
q = κ A 1 sin θ 1 .
( out ) = { ( N 0 0 N ) [ i ϖ τ I ( M 1 M 2 M 3 M 4 ) ] ( N 0 0 N ) I } ( in ) ,
( out ) = ( δ X ̂ a 1 out ( ϖ ) δ X ̂ a 2 out ( ϖ ) δ X ̂ b 1 out ( ϖ ) δ X ̂ b 2 out ( ϖ ) δ Y ̂ a 1 out ( ϖ ) δ Y ̂ a 2 out ( ϖ ) δ Y ̂ b 1 out ( ϖ ) δ Y ̂ b 2 out ( ϖ ) ) , ( in ) = ( δ X ̂ a 1 in ( ϖ ) δ X ̂ a 2 in ( ϖ ) δ X ̂ b 1 in ( ϖ ) δ X ̂ b 2 in ( ϖ ) δ Y ̂ a 1 in ( ϖ ) δ Y ̂ a 2 in ( ϖ ) δ Y ̂ b 1 in ( ϖ ) δ Y ̂ b 2 in ( ϖ ) ) .
δ 2 ( Y ̂ a 1 Y ̂ a 2 ) + δ 2 ( X ̂ a 1 + X ̂ a 2 + g b 1 X ̂ b 1 + g b 2 X ̂ b 2 ) > 4 ,
δ 2 ( Y ̂ a 1 + Y ̂ b 1 ) + δ 2 ( X ̂ a 1 + g a 2 X ̂ a 2 X ̂ b 1 + g b 2 X ̂ b 2 ) > 4 ,
δ 2 ( Y ̂ a 1 + Y ̂ b 2 ) + δ 2 ( X ̂ a 1 + g a 2 X ̂ a 2 + g b 1 X ̂ b 1 X ̂ b 2 ) > 4 ,
δ 2 ( Y ̂ a 2 + Y ̂ b 1 ) + δ 2 ( g a 1 X ̂ a 1 + X ̂ a 2 X ̂ b 1 + g b 2 X ̂ b 2 ) > 4 ,
δ 2 ( Y ̂ a 2 + Y ̂ b 2 ) + δ 2 ( g a 1 X ̂ a 1 + X ̂ a 2 + g b 1 X ̂ b 1 X ̂ b 2 ) > 4 ,
δ 2 ( Y ̂ b 1 Y ̂ b 2 ) + δ 2 ( g a 1 X ̂ a 1 + g a 2 X ̂ a 2 + X ̂ b 1 + X ̂ b 2 ) > 4 ,
ρ ̂ = m η m ρ ̂ m , a 1 a 2 b 1 ρ ̂ m , b 2 ( 17 ) , ( 19 ) , ( 20 ) ,
ρ ̂ = m η m ρ ̂ m , a 1 a 2 b 2 ρ ̂ m , b 1 ( 16 ) , ( 18 ) , ( 20 ) ,
ρ ̂ = m η m ρ ̂ m , a 1 b 1 b 2 ρ ̂ m , a 2 ( 15 ) , ( 18 ) , ( 19 ) ,
ρ ̂ = m η m ρ ̂ m , a 2 b 1 b 2 ρ ̂ m , a 1 ( 15 ) , ( 16 ) , ( 17 ) ,
ρ ̂ = m η m ρ ̂ m , a 1 a 2 ρ ̂ m , b 1 b 2 ( 16 ) , ( 17 ) , ( 18 ) , ( 19 ) ,
ρ ̂ = m η m ρ ̂ m , a 1 b 1 ρ ̂ m , a 2 b 2 ( 15 ) , ( 17 ) , ( 18 ) , ( 20 ) ,
ρ ̂ = m η m ρ ̂ m , a 1 b 2 ρ ̂ m , a 2 b 1 ( 15 ) , ( 16 ) , ( 19 ) , ( 20 ) .
S a 1 a 2 = δ 2 ( Y ̂ a 1 Y ̂ a 2 ) + δ 2 ( X ̂ a 1 + X ̂ a 2 + g b 1 X ̂ b 1 + g b 2 X ̂ b 2 ) < 4 ,
S a 1 b 1 = δ 2 ( Y ̂ a 1 + Y ̂ b 1 ) + δ 2 ( X ̂ a 1 + g a 2 X ̂ a 2 X ̂ b 1 + g b 2 X ̂ b 2 ) < 4 ,
S b 1 b 2 = δ 2 ( Y ̂ b 1 Y ̂ b 2 ) + δ 2 ( g a 1 X ̂ a 1 + g a 2 X ̂ a 2 + X ̂ b 1 + X ̂ b 2 ) < 4 .
α 1 = β 1 = A 1 = 1 κ 2 ε κ 2 γ 1 γ 2 ,
α 2 = β 2 = A 2 = γ 1 κ ,
ε th = γ 1 γ 2 κ .

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