利用非简并光学参量振荡腔产生连续变量三色三组分纠缠态

闫智辉; 贾晓军; 谢常德; 彭堃墀

doi:10.7498/aps.61.014206

摘要

利用半经典理论方法计算了运转于阈值以上的非简并光学参量振荡腔输出信号场、闲置场及反射抽运场的关联特性. 根据 van Loock 等提出的连续变量多组分纠缠判据, 计算结果表明, 常温下这三个光场的正交振幅分量与正交位相分量之间存在三组分量子关联, 得到了三色三组分纠缠态光场. 数值计算了关联噪声对参量振荡腔物理参数的依赖关系, 找出了产生三色三组分纠缠态产生的最佳运转条件, 为连续变量多组分纠缠态光场产生系统的设计提供了直接参考.

关键词:

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.

Keywords:

continuous-variable /
non-degenerate optical parameter oscillator /
three-color tripartite entangled state

作者及机构信息

1.
山西大学光电研究所, 量子光学与光量子器件国家重点实验室, 太原 030006

基金项目: 国家重点基础研究发展计划(批准号:2010CB923103)、国家自然科学基金创新研究群体科学基金(批准号:60821004)、国家自然科学基金(批准号: 60736040,11074157) 和山西省高等学校优秀青年学术带头人支持计划资助的课题.

Authors and contacts

1.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

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.

参考文献

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[3]	Furusawa A, S?rensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706
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[8]	Su X L, Tan A H, Jia X J, Zhang J, Xie C D, Peng K C 2007 Phys. Rev. Lett. 98 070502
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[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)
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[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

施引文献

[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 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 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 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 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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