基于四波混频过程的纠缠光放大

徐笑吟; 刘胜帅; 荆杰泰

doi:10.7498/aps.71.20211324

摘要

双模纠缠态是量子信息领域一种重要的量子资源, 本文基于四波混频过程从理论上提出了对双模纠缠态的单个模式(单模放大方案)和对双模纠缠态的两个模式(双模放大方案)的放大. 利用光学分束器模型来模拟在光学传输过程中损耗引入的真空场噪声, 利用部分转置正定判据分析了两种不同的放大方案中四波混频过程的增益对初始双模纠缠态的纠缠程度的影响. 结果表明, 在特定的损耗情况下, 两个方案中初始双模纠缠态的纠缠度都随增益的增大而减小, 直至消失, 且双模放大方案中初始双模纠缠态纠缠消失得比单模放大方案中更快. 本文的理论结果为实验上实现基于四波混频过程的双模纠缠态的放大奠定了理论基础.

关键词:

Abstract

Two-mode entangled state is an important quantum resource for quantum information. In this paper, the amplification of a single mode of two-mode entangled state (single-mode amplification scheme) and two modes of two-mode entangled state (two-mode amplification scheme) are theoretically proposed. Here, the optical beam splitter model is used to simulate the vacuum noise introduced by the loss in the optical transmission process. By utilizing the positivity under partial transpose criterion, we analyze the effect of the gain of the four-wave mixing process on the entanglement degree of the initial two-mode entangled state in two different amplification schemes. In these two schemes, we set the gain of the initial two-mode entangled state generation process to be 1.5, 2.5 and 50.0 respectively, and then change the gain of the amplification process in a certain range. We also set the transmission efficiency of the amplified beams for each of the two schemes to be a definite value. The results show that the entanglement of the initial two-mode entangled state decreases with the gain increasing under the condition of specific transmission loss in two schemes. When the gain does not exceed a certain value, the entanglement of the initial two-mode entangled state can be maintained. Then, with the increase of the gain, the entanglement of the initial two-mode entangled state will disappear. Moreover, the entanglement of the initial two-mode entangled state of the two-mode amplification scheme disappears faster than that of the single-mode amplification scheme. Our theoretical results pave the way for the experimental realization of the amplification of two-mode entangled state based on four-wave mixing process.

Keywords:

作者及机构信息

1.
华东师范大学, 精密光谱科学与技术国家重点实验室, 上海　200062

2.
中国科学院超强激光科学卓越创新中心, 上海　201800

3.
浙江大学物理学系, 杭州 310027

4.
山西大学, 极端光学协同创新中心, 太原　030006

通信作者: 刘胜帅, ssliu@lps.ecnu.edu.cn ; 荆杰泰, jtjing@phy.ecnu.edu.cn

基金项目: 国家自然科学基金(批准号: 11874155, 91436211, 11374140)、国家重点基础研究发展计划(批准号: 2016YFA0302103)、上海市自然科学基金(批准号: 17ZR1442900)、上海市教育委员会科研创新计划(批准号: 2021-01-07-00-08-E00100)、上海市科学技术委员会科技创新行动计划基础研究领域项目(批准号: 20JC1416100)、上海市科技创新行动计划(批准号: 17JC1400401)、上海市市级科技重大专项(批准号: 2019SHZDZX01)、上海市青年科技英才扬帆计划(批准号: 21YF1410800)、闵行领军人才(批准号: 201971)和高等学校学科创新引智基地(111计划)(批准号: B12024)资助的课题.

Authors and contacts

1.
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China

2.
Center for Excellence in Ultra-intense Laser Science, Chinese Academy of Sciences, Shanghai 201800, China

3.
Department of Physics, Zhejiang University, Hangzhou 310027, China

4.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Liu Sheng-Shuai, ssliu@lps.ecnu.edu.cn ; Jing Jie-Tai, jtjing@phy.ecnu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11874155, 91436211, 11374140), the National Basic Research Program of China (Grant No. 2016YFA0302103), the Natural Science Foundation of Shanghai, China (Grant No. 17ZR1442900), the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 2021-01-07-00-08-E00100), the Basic Research Project of Shanghai Science and Technology Commission, China (Grant No. 20JC1416100), the Program of Scientific and Technological Innovation of Shanghai, China (Grant No. 17JC1400401), the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01), the Shanghai Sailing Program, China (Grant No. 21YF1410800), the Minhang Leading Talents, China (Grant No. 201971), and the Program of Introducing Talents of Discipline to Universities, China (Grant No. B12024).

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参考文献

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施引文献

图 1 一种对EPR光束进行单模放大的方案　(a) 对EPR光束进行单模放大的系统简图; (b) ⁸⁵Rb D1线的双Λ能级结构

Fig. 1. A scheme for single-mode amplification of EPR beams: (a) Simplified diagram of single-mode amplification of EPR beams; (b) double-Λ energy level structure of ⁸⁵Rb D1 line.

下载: 全尺寸图片幻灯片

图 2 ${G_1}$不同的情况下单模放大方案最小辛本征值与${G_2}$的关系

Fig. 2. Relationship between the smallest symplectic eigenvalue and ${G_2}$ of the single-mode amplification scheme under different value of ${G_1}$.

下载: 全尺寸图片幻灯片

图 3 一种对EPR光束进行双模放大的方案

Fig. 3. A scheme for two-mode amplification of EPR beams.

下载: 全尺寸图片幻灯片

图 4 ${G_1}$不同的情况下双模放大方案最小辛本征值与${G_2}$的关系

Fig. 4. Relationship between the smallest symplectic eigenvalue and ${G_2}$ of the two-mode amplification scheme under different value of ${G_1}$.

下载: 全尺寸图片幻灯片

[1]	Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865 Google Scholar
[2]	Braunstein S L, Look P van 2005 Rev. Mod. Phys. 77 513 Google Scholar
[3]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[4]	Ekert A K 1991 Phys. Rev. Lett. 67 661 Google Scholar
[5]	Ralph T C 1999 Phys. Rev. A 61 010303 Google Scholar
[6]	Naik D S, Peterson C G, White A G, Berglund A J, Kwiat P G 2000 Phys. Rev. Lett. 84 4733 Google Scholar
[7]	Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881 Google Scholar
[8]	Zhang J, Peng K C 2000 Phys. Rev. A 62 064302 Google Scholar
[9]	Heaney L, Vedral V 2009 Phys. Rev. Lett. 103 200502 Google Scholar
[10]	Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663 Google Scholar
[11]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Google Scholar
[12]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[13]	Li X Y, Pan Q, Jing J T, Zhang J, Xie C D, Peng K C 2002 Phys. Rev. Lett. 88 047904 Google Scholar
[14]	McCormick C F, Boyer V, Arimondo E, Lett P D 2007 Opt. Lett. 32 178 Google Scholar
[15]	Boyer V, Marino A M, Pooser R C, Lett P D 2008 Science 321 544 Google Scholar
[16]	Boyer V, Marino A M, Lett P D 2008 Phys. Rev. Lett. 100 143601 Google Scholar
[17]	Kumar P, Kolobov M I 1994 Opt. Commun. 104 374 Google Scholar
[18]	Qin Z Z, Jing J T, Zhou J, Liu C J, Pooser R C, Zhou Z F, Zhang W P 2012 Opt. Lett. 37 3141 Google Scholar
[19]	McCormick C F, Marino A M, Boyer V, Lett P D 2008 Phys. Rev. A 78 043816 Google Scholar
[20]	MacRae A, Brannan T, Achal R, Lvovsky A I 2012 Phys. Rev. Lett. 109 033601 Google Scholar
[21]	Pooser R C, Lawrie B 2015 Optica 2 393 Google Scholar
[22]	Marino A M, Trejo N V C, Lett P D 2012 Phys. Rev. A 86 023844 Google Scholar
[23]	Li T, Anderson B E, Horrom T, Jones K M, Lett P D 2016 Opt. Express 24 19871 Google Scholar
[24]	Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859 Google Scholar
[25]	Fan W J, Lawrie B J, Pooser R C 2015 Phys. Rev. A 92 053812 Google Scholar
[26]	Li Z P, Wang X L, Li C Y, Zhang Y F, Wen F, Ahmed I, Zhang Y P 2016 Laser Phys. Lett. 13 025402 Google Scholar
[27]	Abdisa G, Ahmed I, Wang X X, Liu Z C, Wang H X, Zhang Y P 2016 Phys. Rev. A 94 023849 Google Scholar
[28]	Li C B, Jiang Z H, Zhang Y Q, Zhang Z Y, Wen F, Chen H X, Zhang Y P, Xiao M 2017 Phys. Rev. Appl. 7 014023 Google Scholar
[29]	Li C B, Li W, Zhang D, Zhang Z Y, Gu B L, Li K K, Zhang Y P 2019 Laser Phys. Lett. 17 015401 Google Scholar
[30]	Pooser R C, Marino A M, Boyer V, Jones K M, Lett P D 2009 Phys. Rev. Lett. 103 010501 Google Scholar
[31]	Werner R F, Wolf M M 2001 Phys. Rev. Lett. 86 3658 Google Scholar
[32]	Simon R 2000 Phys. Rev. Lett. 84 2726 Google Scholar
[33]	Jasperse M, Turner L D, Scholten R E 2011 Opt. Express 19 3765 Google Scholar

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基于四波混频过程的纠缠光放大