Abstract

The bright two-color tripartite entanglement is investigated in the process of type II second harmonic generation (SHG) operating above threshold. The two pump fields and the second harmonic field are proved to be entangled, and the dependence of the entanglement degree on pump parameterσ and normalized frequency Ω is also analyzed.

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  1. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2008

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(24), 243601 (2008).
[CrossRef] [PubMed]

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

2007

2006

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(14), 140504 (2006).
[CrossRef] [PubMed]

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96(6), 063601 (2006).
[CrossRef] [PubMed]

2005

2003

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(16), 167903 (2003).
[CrossRef] [PubMed]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

2000

S. L. Braunstein and P. van Loock, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).
[CrossRef] [PubMed]

1997

1992

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992).
[CrossRef]

1991

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[CrossRef] [PubMed]

1984

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30(3), 1386–1391 (1984).
[CrossRef]

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(24), 243601 (2008).
[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(6), 063601 (2006).
[CrossRef] [PubMed]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).
[CrossRef] [PubMed]

Cassemiro, K. N.

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(3), 1386–1391 (1984).
[CrossRef]

Coudreau, T.

Deutsch, D.

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992).
[CrossRef]

Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[CrossRef] [PubMed]

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(14), 140504 (2006).
[CrossRef] [PubMed]

L. Longchambon, N. Treps, T. Coudreau, J. Laurat, and C. Fabre, “Experimental evidence of spontaneous symmetry breaking in intracavity type II second-harmonic generation with triple resonance,” Opt. Lett. 30(3), 284–286 (2005).
[CrossRef] [PubMed]

Fan, D.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

Furusawa, A.

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

Gao, J.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[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(3), 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(24), 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(6), 063601 (2006).
[CrossRef] [PubMed]

Guo, J.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

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(16), 167903 (2003).
[CrossRef] [PubMed]

Jozsa, R.

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992).
[CrossRef]

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(24), 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(6), 063601 (2006).
[CrossRef] [PubMed]

Laurat, J.

Liu, K.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

Longchambon, L.

Martinelli, M.

McKenzie, K.

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96(6), 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(24), 243601 (2008).
[CrossRef] [PubMed]

Nussenzveig, P.

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(16), 167903 (2003).
[CrossRef] [PubMed]

Schiller, S.

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(24), 243601 (2008).
[CrossRef] [PubMed]

Schneider, K.

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(24), 243601 (2008).
[CrossRef] [PubMed]

Treps, N.

Valente, P.

van Loock, P.

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

S. L. Braunstein and P. van Loock, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).
[CrossRef] [PubMed]

Villar, A. S.

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(16), 167903 (2003).
[CrossRef] [PubMed]

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(16), 167903 (2003).
[CrossRef] [PubMed]

Yang, R.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

Zhai, S.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

Zhang, J.

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[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(16), 167903 (2003).
[CrossRef] [PubMed]

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(16), 167903 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Zhai, R. Yang, D. Fan, J. Guo, K. Liu, J. Zhang, and J. Gao, “Tripartite entanglement from the cavity with second-order harmonic generation,” Phys. Rev. A 78(1), 014302 (2008).
[CrossRef]

M. J. Collett and C. W. Gardiner, “Squeezing of intracavity and traveling-wave light fields produced in parametric amplification,” Phys. Rev. A 30(3), 1386–1391 (1984).
[CrossRef]

P. van Loock and A. Furusawa, “Detecting genuine multipartite continuous-variable entanglement,” Phys. Rev. A 67(5), 052315 (2003).
[CrossRef]

Phys. Rev. Lett.

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(14), 140504 (2006).
[CrossRef] [PubMed]

N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. 96(6), 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(24), 243601 (2008).
[CrossRef] [PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
[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(16), 167903 (2003).
[CrossRef] [PubMed]

S. L. Braunstein and P. van Loock, “Multipartite entanglement for continuous variables: A quantum teleportation network,” Phys. Rev. Lett. 84(15), 3482–3485 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

The sketch of SHG

Fig. 2
Fig. 2

The dependence of amplitude of the two output harmonic modes on pump parameter (σ) . solid line: γ=0.02 , γb=0.018 , γ0=0.1 ; dashed line: with γ=γb=0.02 , γ0=0.1 ;

Fig. 3
Fig. 3

The quantum correlation spectra S1out (solid curve), S2out (dashed curve) and S3out (dash-dotted curve)versus normalized pump parameter( σ=β/βth ) with γ=0 .03;γb=0 .027;γ0=0 .1;γb0=0 .09;Ω=0 .2 .

Fig. 4
Fig. 4

The quantum correlation spectra S1out (solid curve), S2out (dashed curve) and S3out (dash-dotted curve) versus normalized frequency with γ=0 .03;γb=0 .027;γ0=0 .1;γb0=0.09;σ=1 .5 .

Equations (17)

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τa^˙0(t)=γ0a^0(t)χa^1(t)a^2(t)+2γb0a^0in(t)eiϕ0+2γc0c^0(t)
τa^˙1(t)=γ1a^1(t)+χa^2+(t)a^0(t)+2γb1a^1in(t)eiϕ1+2γc1c^1(t)
τa^˙2(t)=γ2a^2(t)+χa^1+(t)a^0(t)+2γb2a^2in(t)eiϕ2+2γc2c^2(t)
γ0α0χα1α2=0
γα1+χα2*α0+2γbβ=0
γα2+χα1*α0+2γbβ=0
βth=2γ3γ0χ2γb
σ=ββth
S1out=δ2(Y^1outY^2out)+δ2(X^1out+X^2outg1X^0out)4
S2out=δ2(Y^0out+Y^1out)+δ2(X^1out+g2X^2outX^0out)4
S3out=δ2(Y^0out+Y^2out)+δ2(g3X^1out+X^2outX^0out)4
δ2(Y^1outY^2out)=[δY^1out(ω)δY^2out(ω)][δY^1out(ω)δY^2out(ω)]+
δ2(Y^0out+Y^1out)=[δY^0out(ω)+δY^1out(ω)][δY^0out(ω)+δY^1out(ω)]+
δ2(Y^0out+Y^2out)=[δY^0out(ω)+δY^2out(ω)][δY^0out(ω)+δY^2out(ω)]+
δ2(X^1out+X^2outg1X^0out)=[δX^1out(ω)+δX^2out(ω)g1δX^0out(ω)]×[δX^1out(ω)+δX^2out(ω)g1δX^0out(ω)]+
δ2(X^1out+g2X^2outX^0out)=[δX^1out(ω)+g2δX^2out(ω)δX^0out(ω)]×[δX^1out(ω)+g2δX^2out(ω)δX^0out(ω)]+
δ2(g3X^1out+X^2outX^0out)=[g3δX^1out(ω)+δX^2out(ω)δX^0out(ω)]×[g3δX^1out(ω)+δX^2out(ω)δX^0out(ω)]+

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