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Continuous-variable three-color tripartite entangled state generated by a non-degenerate optical parameter oscillator

Yan Zhi-Hui Jia Xiao-Jun Xie Chang-De Peng Kun-Chi

Continuous-variable three-color tripartite entangled state generated by a non-degenerate optical parameter oscillator

Yan Zhi-Hui, Jia Xiao-Jun, Xie Chang-De, Peng Kun-Chi
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  • The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2010CB923103), the Science Fund for Creative Research Group of the National Natural Science Foundation of China (Grant No. 60821004), the National Natural Science Foundation of China (Grants Nos. 60736040, 11074157), and the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi, China.
    [1]

    Scarani V, Bechmann-Pasquinucci H, Cerf N J, Dušek M, Lütkenhaus N, Peev M 2009 Rev. Mod. Phys. 81 1301

    [2]

    Shor P W, Siam J 1997 Computer 26 1484

    [3]

    Furusawa A, S?rensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706

    [4]

    Li X Y, Pan Q, Jing J T, Zhang J, Xie C D, Peng K C 2002 Phys. Rev. Lett. 88 047904

    [5]

    Jia X J, Su X L, Pan Q, Gao J R, Xie C D, Peng K C 2004 Phys. Rev. Lett. 93 250503

    [6]

    Kimble H J 2008 Nature 453 1023

    [7]

    Jing J T, Zhang J, Yan Y, Zhao F G, Xie C D, Peng K C 2003 Phys. Rev. Lett. 90 167903

    [8]

    Su X L, Tan A H, Jia X J, Zhang J, Xie C D, Peng K C 2007 Phys. Rev. Lett. 98 070502

    [9]

    Tan A H, Wang Y, Jin X L, Su X L, Jia X J, Zhang J, Xie C D, Peng K C 2008 Phys. Rev. A 78 013828

    [10]

    Yonezawa H, Aoki T, Furusawa A 2004 Nature 431 430

    [11]

    Yoshikawa J, Miwa Y, Huck A, Andersen U L, van Loock P, Furusawa A 2008 Phys. Rev. Lett. 101 250501

    [12]

    Wang Y, Su X L, Shen H, Tan A H, Xie C D, Peng K C 2010 Phys. Rev. A 81 022311

    [13]

    Julsgaard B, Sherson J, Cirac J I, Fiurasek J, Polzik E S 2004 Nature 432 482

    [14]

    Dong R, Lassen M, Heersink J, Marquardt C, Filip R, Leuchs G, Andersen U L 2008 Nature Phys. 4 919

    [15]

    Reid M D, Drummond P D 1988 Phys. Rev. Lett. 60 2731

    [16]

    Pan Q, Wang H, Zhang Y, Su H, Xie C D, Peng K C, Yu Z G, Lu Q M 1998 Acta Phys. Sin. 47 1625 (in Chinese) [潘庆, 王海, 张云, 苏红, 谢常德, 彭堃墀, 于正刚, 路庆明 1998 物理学报 47 1625]

    [17]

    Li X Y, Jing J T, Zhang J, Pan Q, Xie C D, Peng K C 2002 Acta Phys. Sin. 51 966 (in Chinese) [李小英, 荆杰泰, 张靖, 潘庆, 谢常德, 彭堃墀 2002 物理学报 51 966]

    [18]

    Jia X J, Su X L, Pan Q, Xie C D, Peng K C 2005 Acta Phys. Sin. 54 2717 (in Chinese) [贾晓军, 苏晓龙, 潘 庆, 谢常德, 彭堃墀 2005 物理学报 54 2717]

    [19]

    Zhao C Y, Tan W H 2006 J. Opt. Soc. Am. B 23 2174

    [20]

    Zhao C Y, Tan W H 2007 J. Mod. Opt. 54 97

    [21]

    Heidmann A, Horowicz R J, Reynaud S, Giacobino E, Fabre C, Camy G 1987 Phys. Rev. Lett. 59 2555

    [22]

    Villar A S, Cruz L S, Cassemiro K N, Martinelli M, Nussenzveig P 2005 Phys. Rev. Lett. 95 243603

    [23]

    Su X L, Tan A H, Jia X J, Pan Q, Xie C D, Peng K C 2006 Opt. Lett. 31 1133

    [24]

    Jing J, Feng S, Bloomer R, Pfister O 2006 Phys. Rev. A 74 041804(R)

    [25]

    Shang Y N,Wang D, Yan Z H,WangWZ, Jia X J, Peng K C 2008 Acta Phys. Sin. 57 3514 (in Chinese) [商娅娜, 王东, 闫智辉, 王文哲, 贾晓军, 彭堃墀 2008 物理学报 57 3514]

    [26]

    Villar A S, Martinelli M, Fabre C, Nussenzveig P 2006 Phys. Rev. Lett. 97 140504

    [27]

    Coelho A S, Barbosa F A S, Cassemiro K N, Villar A S , Martinelli M, Nussenzveig P 2009 Science 326 823

    [28]

    Debuisschert T, Sizmann A, Giacobino E, Fabre C 1993 J. Opt. Soc. Am. B 10 1668

    [29]

    Heidmann A, Horowicz R J, Reynaud S, Giacobino E, Fabre C, Camy G 1987 Phys. Rev. Lett. 59 2555

    [30]

    Kasai K, Gao J R, Fabre C 1997 Europhys. Lett. 40 25

    [31]

    Gardiner C W, Collett M J 1985 Phys. Rev. A 31 3761

    [32]

    Bachor H A 1998 A Guide to Experiments in Quantum Optics (Weinheim: Wiley-VCh) p70

    [33]

    Cassemiro K N, Villar A S, Martinelli M, Nussenzveig P 2007 Opt. Express 15 18236

    [34]

    Cassemiro K N, Villar A S, Valente P, Martinelli M, Nussenzveig P 2007 Opt. Lett. 32 695

    [35]

    César J E S, Coelho A S, Cassemiro K N, Villar A S, Lassen M , Nussenzveig P, Martinelli M 2009 Phys. Rev. A 79 063816

    [36]

    Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722

    [37]

    Simon R 2000 Phys. Rev. Lett. 84 2726

    [38]

    Van Loock P, Furusawa A 2003 Phys. Rev. A 67 052315

  • [1]

    Scarani V, Bechmann-Pasquinucci H, Cerf N J, Dušek M, Lütkenhaus N, Peev M 2009 Rev. Mod. Phys. 81 1301

    [2]

    Shor P W, Siam J 1997 Computer 26 1484

    [3]

    Furusawa A, S?rensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706

    [4]

    Li X Y, Pan Q, Jing J T, Zhang J, Xie C D, Peng K C 2002 Phys. Rev. Lett. 88 047904

    [5]

    Jia X J, Su X L, Pan Q, Gao J R, Xie C D, Peng K C 2004 Phys. Rev. Lett. 93 250503

    [6]

    Kimble H J 2008 Nature 453 1023

    [7]

    Jing J T, Zhang J, Yan Y, Zhao F G, Xie C D, Peng K C 2003 Phys. Rev. Lett. 90 167903

    [8]

    Su X L, Tan A H, Jia X J, Zhang J, Xie C D, Peng K C 2007 Phys. Rev. Lett. 98 070502

    [9]

    Tan A H, Wang Y, Jin X L, Su X L, Jia X J, Zhang J, Xie C D, Peng K C 2008 Phys. Rev. A 78 013828

    [10]

    Yonezawa H, Aoki T, Furusawa A 2004 Nature 431 430

    [11]

    Yoshikawa J, Miwa Y, Huck A, Andersen U L, van Loock P, Furusawa A 2008 Phys. Rev. Lett. 101 250501

    [12]

    Wang Y, Su X L, Shen H, Tan A H, Xie C D, Peng K C 2010 Phys. Rev. A 81 022311

    [13]

    Julsgaard B, Sherson J, Cirac J I, Fiurasek J, Polzik E S 2004 Nature 432 482

    [14]

    Dong R, Lassen M, Heersink J, Marquardt C, Filip R, Leuchs G, Andersen U L 2008 Nature Phys. 4 919

    [15]

    Reid M D, Drummond P D 1988 Phys. Rev. Lett. 60 2731

    [16]

    Pan Q, Wang H, Zhang Y, Su H, Xie C D, Peng K C, Yu Z G, Lu Q M 1998 Acta Phys. Sin. 47 1625 (in Chinese) [潘庆, 王海, 张云, 苏红, 谢常德, 彭堃墀, 于正刚, 路庆明 1998 物理学报 47 1625]

    [17]

    Li X Y, Jing J T, Zhang J, Pan Q, Xie C D, Peng K C 2002 Acta Phys. Sin. 51 966 (in Chinese) [李小英, 荆杰泰, 张靖, 潘庆, 谢常德, 彭堃墀 2002 物理学报 51 966]

    [18]

    Jia X J, Su X L, Pan Q, Xie C D, Peng K C 2005 Acta Phys. Sin. 54 2717 (in Chinese) [贾晓军, 苏晓龙, 潘 庆, 谢常德, 彭堃墀 2005 物理学报 54 2717]

    [19]

    Zhao C Y, Tan W H 2006 J. Opt. Soc. Am. B 23 2174

    [20]

    Zhao C Y, Tan W H 2007 J. Mod. Opt. 54 97

    [21]

    Heidmann A, Horowicz R J, Reynaud S, Giacobino E, Fabre C, Camy G 1987 Phys. Rev. Lett. 59 2555

    [22]

    Villar A S, Cruz L S, Cassemiro K N, Martinelli M, Nussenzveig P 2005 Phys. Rev. Lett. 95 243603

    [23]

    Su X L, Tan A H, Jia X J, Pan Q, Xie C D, Peng K C 2006 Opt. Lett. 31 1133

    [24]

    Jing J, Feng S, Bloomer R, Pfister O 2006 Phys. Rev. A 74 041804(R)

    [25]

    Shang Y N,Wang D, Yan Z H,WangWZ, Jia X J, Peng K C 2008 Acta Phys. Sin. 57 3514 (in Chinese) [商娅娜, 王东, 闫智辉, 王文哲, 贾晓军, 彭堃墀 2008 物理学报 57 3514]

    [26]

    Villar A S, Martinelli M, Fabre C, Nussenzveig P 2006 Phys. Rev. Lett. 97 140504

    [27]

    Coelho A S, Barbosa F A S, Cassemiro K N, Villar A S , Martinelli M, Nussenzveig P 2009 Science 326 823

    [28]

    Debuisschert T, Sizmann A, Giacobino E, Fabre C 1993 J. Opt. Soc. Am. B 10 1668

    [29]

    Heidmann A, Horowicz R J, Reynaud S, Giacobino E, Fabre C, Camy G 1987 Phys. Rev. Lett. 59 2555

    [30]

    Kasai K, Gao J R, Fabre C 1997 Europhys. Lett. 40 25

    [31]

    Gardiner C W, Collett M J 1985 Phys. Rev. A 31 3761

    [32]

    Bachor H A 1998 A Guide to Experiments in Quantum Optics (Weinheim: Wiley-VCh) p70

    [33]

    Cassemiro K N, Villar A S, Martinelli M, Nussenzveig P 2007 Opt. Express 15 18236

    [34]

    Cassemiro K N, Villar A S, Valente P, Martinelli M, Nussenzveig P 2007 Opt. Lett. 32 695

    [35]

    César J E S, Coelho A S, Cassemiro K N, Villar A S, Lassen M , Nussenzveig P, Martinelli M 2009 Phys. Rev. A 79 063816

    [36]

    Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722

    [37]

    Simon R 2000 Phys. Rev. Lett. 84 2726

    [38]

    Van Loock P, Furusawa A 2003 Phys. Rev. A 67 052315

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  • Received Date:  21 June 2011
  • Accepted Date:  05 July 2011
  • Published Online:  05 January 2012

Continuous-variable three-color tripartite entangled state generated by a non-degenerate optical parameter oscillator

  • 1. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant No. 2010CB923103), the Science Fund for Creative Research Group of the National Natural Science Foundation of China (Grant No. 60821004), the National Natural Science Foundation of China (Grants Nos. 60736040, 11074157), and the Program for the Top Young Academic Leaders of Higher Learning Institutions of Shanxi, China.

Abstract: The quantum correlations between the output signal, the output idler and the reflected pump fields generated by non-degenerate optical parametric oscillator operating above the oscillation threshold are theoretically calculated with the semi-classical formulae. According to the multipartite entanglement criteria for the continuous variables, proposed by P. van Loock and A. Furusawa, the calculated results prove the existence of the quantum correlations between the amplitude and the phase quadrature for the three optical fields, i. e. they form a tripartite entangled state. We numerically calculate the dependence of the entanglement on the physical parameters of the optical oscillator and find the optimum operating conditions of the oscillator to produce the three-color tripartite entangled state, which provide the direct references for the design of the continuous variable multipartite entanglement generation systems.

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