Abstract

Quantum fluctuation and quantum entanglement in competing nonlinear processes of type II second-harmonic generation in a triple-resonant cavity is analyzed. Operating above threshold with intracavity loss, the mean amplitude and the entanglement of reflected subharmonic field as a function of pump and loss parameters are calculated. It is found that the two eigenmodes become unbalanced when internal loss intervenes. The dependence of the entanglement characteristics of two reflected subharmonic modes on output coupling efficiency μb/μ, pump parameter σ, and normalized frequency Ω are discussed. Under appropriate conditions, this system can be exploited as a bright entanglement resource.

© 2005 Optical Society of America

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  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] [PubMed]
  2. T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
    [CrossRef]
  3. W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
    [CrossRef]
  4. J. Gao, Z. Zhai, Y. Li, T. Zhang, S. Wang, and J. Guo, "Experimental investigation of continuous-variable quantum teleportation," presented at Chinese Physics Society 2003 Fall Meeting, Hefei, China, September, 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]
  6. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
    [CrossRef]
  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] [PubMed]
  8. S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
    [CrossRef] [PubMed]
  9. K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
    [CrossRef]
  10. Z. Y. Ou, "Quantum nondemolition measurement and squeezing in type-II harmonic generation with triple resonance," Phys. Rev. A 49, 4902-4911 (1994).
    [CrossRef] [PubMed]
  11. M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
    [CrossRef] [PubMed]
  12. U. L. Andersen and P. Buchhave, "Squeezing and entanglement in doubly resonant, type-II, second-harmonic generation," J. Opt. Soc. Am. B 20, 1947-1958 (2003).
    [CrossRef]
  13. Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
    [CrossRef]
  14. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, "Inseparability criterion for continuous variable systems," Phys. Rev. Lett. 84, 2722-2725 (2000).
    [CrossRef] [PubMed]
  15. W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
    [CrossRef]
  16. Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
    [CrossRef]

2004 (1)

Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
[CrossRef]

2003 (6)

W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
[CrossRef]

U. L. Andersen and P. Buchhave, "Squeezing and entanglement in doubly resonant, type-II, second-harmonic generation," J. Opt. Soc. Am. B 20, 1947-1958 (2003).
[CrossRef]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[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]

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]

2002 (1)

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

2000 (2)

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

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

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] [PubMed]

1997 (1)

K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
[CrossRef]

1996 (1)

M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
[CrossRef] [PubMed]

1994 (1)

Z. Y. Ou, "Quantum nondemolition measurement and squeezing in type-II harmonic generation with triple resonance," Phys. Rev. A 49, 4902-4911 (1994).
[CrossRef] [PubMed]

1988 (1)

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

Andersen , U. L.

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] [PubMed]

Bachor, H. A.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Bowen, W. P.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
[CrossRef]

Braunstein, S. L.

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

Buchhave, P.

Buchler, B. C.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Chou, C. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Cirac, J. I.

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

Collet, M. J.

M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
[CrossRef] [PubMed]

Duan, L.-M.

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

Fabre, C.

K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
[CrossRef]

Fuchs, C. A.

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

Furusawa, A.

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]

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

Gao, J.

Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
[CrossRef]

Gao, J. R.

K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
[CrossRef]

Giedke, G.

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

Goh, K. W.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

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]

Jack, M. W.

M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
[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]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Kasai, K.

K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
[CrossRef]

Kimble, H. J.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

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

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

Lam, P. K.

W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Li, X.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Li, Y.

Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
[CrossRef]

Lodahl, P.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Ou, Z. Y.

Z. Y. Ou, "Quantum nondemolition measurement and squeezing in type-II harmonic generation with triple resonance," Phys. Rev. A 49, 4902-4911 (1994).
[CrossRef] [PubMed]

Pan, Q.

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Peng, K.

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]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

Polzik, E. S.

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

Ralph, T. C.

W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Schnable, R.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[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] [PubMed]

Symul, T.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[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] [PubMed]

Treps, N.

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[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] [PubMed]

Walls, D. F.

M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
[CrossRef] [PubMed]

Wang, H.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

Xie, C.

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]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[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]

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] [PubMed]

Zhai, Z.

Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
[CrossRef]

Zhang, 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]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

Zhang, T. C.

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

Zhang, Y.

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[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]

Zoller, P.

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

Europhys. Lett. (1)

K. Kasai, J. R. Gao, and C. Fabre, "Observation of squeezing using cascaded nonlinearity," Europhys. Lett. 40, 25-30 (1997).
[CrossRef]

J. Mod. Opt. (1)

W. P. Bowen, P. K. Lam, and T. C. Ralph, "Biased EPR entanglement and its application to teleportation," J. Mod. Opt. 50, 801-813 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Phys. Rev. A (7)

Y. Zhang, H. Wang, X. Li, J. Jing, C. Xie, and K. Peng, "Experimental generation of bright two-mode quadrature squeezed light from a narrow-band nondegenerate optical parametric amplifier," Phys. Rev. A 62, 023813 (2000).
[CrossRef]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, "Generation of squeezed light by intracavity frequency doubling," Phys. Rev. A 38, 4931-4934 (1988).
[CrossRef] [PubMed]

Z. Y. Ou, "Quantum nondemolition measurement and squeezing in type-II harmonic generation with triple resonance," Phys. Rev. A 49, 4902-4911 (1994).
[CrossRef] [PubMed]

M. W. Jack, M. J. Collet, and D. F. Walls, "Asymmetrically pumped nondegenerate second-harmonic generation inside a cavity," Phys. Rev. A 53, 1801-1811 (1996).
[CrossRef] [PubMed]

Z. Zhai, Y. Li, and J. Gao, "Entanglement characteristics of subharmonic modes reflected from a cavity for type-II second-harmonic generation," Phys. Rev. A 69, 044301 (2004).
[CrossRef]

T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, "Quantum teleportation of light beams," Phys. Rev. A 67, 033802 (2003).
[CrossRef]

W. P. Bowen, N. Treps, B. C. Buchler, R. Schnable, T. C. Ralph, H. A. Bachor, T. Symul, and P. K. Lam, "Experimental investigation of continuous-variable quantum teleportation," Phys. Rev. A 67, 032302 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

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]

X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, "Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam," Phys. Rev. Lett. 88, 047904 (2002).
[CrossRef]

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]

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

Science (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] [PubMed]

Other (1)

J. Gao, Z. Zhai, Y. Li, T. Zhang, S. Wang, and J. Guo, "Experimental investigation of continuous-variable quantum teleportation," presented at Chinese Physics Society 2003 Fall Meeting, Hefei, China, September, 2003.

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Figures (6)

Fig. 1
Fig. 1

Sketch of experimental setup.

Fig. 2
Fig. 2

Dependence of amplitude of the two output eigenmodes on pump parameter (σ) with γ=γb=0.02, γ0=0.001 for solid curve and γ=0.02, γb=0.018, γ0=0.001 for dashed curve.

Fig. 3
Fig. 3

Correlation spectra VX1+X2out as a function of normalized frequency Ω with μ=μb=40, σ=1.1 (solid curve), σ=4 (dashed curve), and σ=8 (dotted curve).

Fig. 4
Fig. 4

Correlation spectra VY1-Y2(Ω) as a function of normalized frequency Ω with μ=μb=40, σ=1.1 (solid curve), σ=4 (dashed curve), and σ=8 (dotted curve).

Fig. 5
Fig. 5

VX1+X2(Ω)VY1-Y2(Ω) as a function of normalized frequency Ω with μ=μb=40, σ=1.1 (solid curve), σ=4 (dashed curve), and σ=8 (dotted curve).

Fig. 6
Fig. 6

VX1+X2(Ω)VY1-Y2(Ω) as a function of normalized frequency Ω and output coupling efficiency μb/μ with μ=40, σ=2.

Equations (48)

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τα˙0(t)=-γ0α0(t)-χα1(t)α2(t)+2γ0c0(t),
τα˙1(t)=-γ1α1(t)+χα2*(t)α0(t)+2γb1α1in exp(iϕ1)+2γc1c1(t),
τα˙2(t)=-γ2α2(t)+χα1*(t)α0(t)+2γb2α2in exp(iϕ2)+2γc2c2(t),
ri=1-γbi,
ti=2γbi.
γ1=γ2=γ,
γb1=γb2=γb,
γc1=γc2=γc.
α¯0=-χα¯1α¯2γ0,
-γ-χ2γ0|α¯2|2α¯1+2γbβ=0,
-γ-χ2γ0|α¯1|2α¯2+2γbβ=0.
βth=(2γ3γ0/χ2γb)1/2,
σ=β/βth.
α¯1=α¯2=α,
α=γγ0σ/χ
α¯0=-γσ2/χ,
σ=[σ+(σ2+1/27)1/2]1/3-13(σ+(σ2+1/27)1/2)-1/3,
α¯1=γγ0σ/χ-[γγ0(σ2-1)]1/2/χ,
α¯2=γγ0σ/χ+[γγ0(σ2-1)]1/2/χ,
α¯0=-γ/χ.
α1out=α2out=αout=(2γγ0/χ2γb)1/2(σγb-σγ),
α0out=-σ2γ2γ0/χ,
α1out=(2γγ0/χ2γb)1/2[σγb-σγ-γb(σ2-1)1/2],
α2out=(2γγ0/χ2γb)1/2[σγb-σγ+γb(σ2-1)1/2],
α0out=-γ2γ0/χ.
τδα˙0(t)=-γ0δα0(t)-χ[α¯2δα1(t)+α¯1δα2(t)]+2γ0c0(t),
τδα˙1(t)=-γδα1(t)+χ[α¯0δα2*(t)+α¯2δα0(t)]+2γbb1(t)+2γcc1(t),
τδα˙2(t)=-γδα2(t)+χ[α¯0δα1*(t)+α¯1δα0(t)]+2γbb2(t)+2γcc2(t),
O=12(X+iY),
τδX˙0(t)=-γ0δX0(t)-χ[α¯2δX1(t)+α¯1δX2(t)]+2γ0δXc0(t),
τδX˙1(t)=-γδX1(t)+χ[α¯0δX2(t)+α¯2δX0(t)]+2γbδXb1(t)+2γcδXc1(t),
τδX˙2(t)=-γδX2(t)+χ[α¯0δX1(t)+α¯1δX0(t)]+2γbδXb2(t)+2γcδXc2(t),
τδY˙0(t)=-γ0δY0(t)-χ[α¯2δY1(t)+α¯1δY2(t)]+2γ0δYc0(t),
τδY˙1(t)=-γδY1(t)-χ[α¯0δY2(t)-α¯2δY0(t)]+2γbδYb1(t)+2γcδYc1(t),
τδY˙2(t)=-γδY2(t)-χ[α¯0δY1(t)-α¯1δY0(t)]+2γbδYb2(t)+2γcδYc2(t).
δX1(Ω)=δXco 2γ0D{2γ[γγ0(σ2-1)]1/2+iγγγ0Ω[σ+(σ2-1)1/2]}+1D(2γbδXb1+2γcδXc1)[2γγ0σ×[σ-σ2-1]-γ2Ω2+iγΩ(γ+γ0)]+1D(2γbδXb2+2γcδXc2)×[-2γγ0-iγ2Ω],
δX2(Ω)=δXco 2γ0D{-2γ[γγ0(σ2-1)]1/2+iγΩγγ0[σ-(σ2-1)1/2]}+1D(2γbδXb2+2γcδXc2){2γγ0σ×[σ+(σ2-1)]-γ2Ω2+iγΩ(γ+γ0)}+1D(2γbδXb1+2γcδXc1)×[-2γγ0-iγ2Ω],
δY1(Ω)=δYco 2γ0B{2σγγγ0+iΩγγγ0×[σ+(σ2-1)1/2]}+1B(2γbδXb1+2γcδXc1){2γγ0σ×[σ-(σ2-1)1/2]-Ω2γ2+iΩγ(γ+γ0)}+iγ2ΩB(2γbδXb2+2γcδXc2),
δY2(Ω)=δYco 2γ0B{2σγγγ0+iΩγγγ0×[σ-(σ2-1)1/2]}+1B(2γbδXb2+2γcδXc2){2γγ0σ×[σ+(σ2-1)1/2]-Ω2γ2+iΩγ(γ+γ0)}+iγ2ΩB(2γbδXb1+2γcδXc1),
δX(Ω)1out+δX(Ω)2out=4iΩσμμμbDδXc0-(δXb1+δXb2)+1D(2μbδXb1+2μcμbδXc1)×{2µ[σ2-σ(σ2-1)1/2-1]-Ω2μ2+iΩμ}+1D(2μbδXb2+2μcμbδXc2){2µ[σ2+σ(σ2-1)1/2-1]-Ω2μ2+iΩμ},
δY(Ω)1out-δY(Ω)2out=4iΩμμμbB(σ2-1)1/2δYco-(δYb1-δYb2)+1B(2μbδYb1+2μbμcδYc1)×{2µ[σ2-σ(σ2-1)1/2]-Ω2μ2+iΩμ}-1B(2μbδYb2+2μbμcδYc2)×{2µ[σ2+σ(σ2-1)1/2]-Ω2μ2+iΩμ},
B=4µ2σ2-Ω2μ2(1+2µ)+4iΩμ2σ2-iΩ3μ3,
D=4µ2(σ2-1)-Ω2μ2(1+2µ)+4iΩμ2σ2-iΩ3μ3,
μb=γb/γ0,μc=γc/γ0,μ=μb+μc.
VX1+X2out=[δX1out(Ω)+δX2out(Ω)][δX1out(Ω)+δX2out(Ω)]+,
VY1-Y2out=[δY1out(Ω)-δY2out(Ω)][δY1out(Ω)-δY2out(Ω)]+.
VX1+X2out+VY1-Y2out<2.
VX1+X2outVY1-Y2out<1,

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