搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于四波混频过程的纠缠光放大

徐笑吟 刘胜帅 荆杰泰

引用本文:
Citation:

基于四波混频过程的纠缠光放大

徐笑吟, 刘胜帅, 荆杰泰

Amplification of entangled beam based on four-wave mixing process

Xu Xiao-Yin, Liu Sheng-Shuai, Jing Jie-Tai
PDF
HTML
导出引用
  • 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.
    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.
      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.
      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).
    [1]

    Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865Google Scholar

    [2]

    Braunstein S L, Look P van 2005 Rev. Mod. Phys. 77 513Google 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 621Google Scholar

    [4]

    Ekert A K 1991 Phys. Rev. Lett. 67 661Google Scholar

    [5]

    Ralph T C 1999 Phys. Rev. A 61 010303Google Scholar

    [6]

    Naik D S, Peterson C G, White A G, Berglund A J, Kwiat P G 2000 Phys. Rev. Lett. 84 4733Google Scholar

    [7]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881Google Scholar

    [8]

    Zhang J, Peng K C 2000 Phys. Rev. A 62 064302Google Scholar

    [9]

    Heaney L, Vedral V 2009 Phys. Rev. Lett. 103 200502Google Scholar

    [10]

    Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663Google Scholar

    [11]

    Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575Google Scholar

    [12]

    Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706Google Scholar

    [13]

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

    [14]

    McCormick C F, Boyer V, Arimondo E, Lett P D 2007 Opt. Lett. 32 178Google Scholar

    [15]

    Boyer V, Marino A M, Pooser R C, Lett P D 2008 Science 321 544Google Scholar

    [16]

    Boyer V, Marino A M, Lett P D 2008 Phys. Rev. Lett. 100 143601Google Scholar

    [17]

    Kumar P, Kolobov M I 1994 Opt. Commun. 104 374Google 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 3141Google Scholar

    [19]

    McCormick C F, Marino A M, Boyer V, Lett P D 2008 Phys. Rev. A 78 043816Google Scholar

    [20]

    MacRae A, Brannan T, Achal R, Lvovsky A I 2012 Phys. Rev. Lett. 109 033601Google Scholar

    [21]

    Pooser R C, Lawrie B 2015 Optica 2 393Google Scholar

    [22]

    Marino A M, Trejo N V C, Lett P D 2012 Phys. Rev. A 86 023844Google Scholar

    [23]

    Li T, Anderson B E, Horrom T, Jones K M, Lett P D 2016 Opt. Express 24 19871Google Scholar

    [24]

    Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859Google Scholar

    [25]

    Fan W J, Lawrie B J, Pooser R C 2015 Phys. Rev. A 92 053812Google 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 025402Google Scholar

    [27]

    Abdisa G, Ahmed I, Wang X X, Liu Z C, Wang H X, Zhang Y P 2016 Phys. Rev. A 94 023849Google 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 014023Google 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 015401Google Scholar

    [30]

    Pooser R C, Marino A M, Boyer V, Jones K M, Lett P D 2009 Phys. Rev. Lett. 103 010501Google Scholar

    [31]

    Werner R F, Wolf M M 2001 Phys. Rev. Lett. 86 3658Google Scholar

    [32]

    Simon R 2000 Phys. Rev. Lett. 84 2726Google Scholar

    [33]

    Jasperse M, Turner L D, Scholten R E 2011 Opt. Express 19 3765Google Scholar

  • 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.

    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 ${G_1}$.

    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.

    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 ${G_1}$.

  • [1]

    Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865Google Scholar

    [2]

    Braunstein S L, Look P van 2005 Rev. Mod. Phys. 77 513Google 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 621Google Scholar

    [4]

    Ekert A K 1991 Phys. Rev. Lett. 67 661Google Scholar

    [5]

    Ralph T C 1999 Phys. Rev. A 61 010303Google Scholar

    [6]

    Naik D S, Peterson C G, White A G, Berglund A J, Kwiat P G 2000 Phys. Rev. Lett. 84 4733Google Scholar

    [7]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881Google Scholar

    [8]

    Zhang J, Peng K C 2000 Phys. Rev. A 62 064302Google Scholar

    [9]

    Heaney L, Vedral V 2009 Phys. Rev. Lett. 103 200502Google Scholar

    [10]

    Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663Google Scholar

    [11]

    Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575Google Scholar

    [12]

    Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706Google Scholar

    [13]

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

    [14]

    McCormick C F, Boyer V, Arimondo E, Lett P D 2007 Opt. Lett. 32 178Google Scholar

    [15]

    Boyer V, Marino A M, Pooser R C, Lett P D 2008 Science 321 544Google Scholar

    [16]

    Boyer V, Marino A M, Lett P D 2008 Phys. Rev. Lett. 100 143601Google Scholar

    [17]

    Kumar P, Kolobov M I 1994 Opt. Commun. 104 374Google 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 3141Google Scholar

    [19]

    McCormick C F, Marino A M, Boyer V, Lett P D 2008 Phys. Rev. A 78 043816Google Scholar

    [20]

    MacRae A, Brannan T, Achal R, Lvovsky A I 2012 Phys. Rev. Lett. 109 033601Google Scholar

    [21]

    Pooser R C, Lawrie B 2015 Optica 2 393Google Scholar

    [22]

    Marino A M, Trejo N V C, Lett P D 2012 Phys. Rev. A 86 023844Google Scholar

    [23]

    Li T, Anderson B E, Horrom T, Jones K M, Lett P D 2016 Opt. Express 24 19871Google Scholar

    [24]

    Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859Google Scholar

    [25]

    Fan W J, Lawrie B J, Pooser R C 2015 Phys. Rev. A 92 053812Google 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 025402Google Scholar

    [27]

    Abdisa G, Ahmed I, Wang X X, Liu Z C, Wang H X, Zhang Y P 2016 Phys. Rev. A 94 023849Google 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 014023Google 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 015401Google Scholar

    [30]

    Pooser R C, Marino A M, Boyer V, Jones K M, Lett P D 2009 Phys. Rev. Lett. 103 010501Google Scholar

    [31]

    Werner R F, Wolf M M 2001 Phys. Rev. Lett. 86 3658Google Scholar

    [32]

    Simon R 2000 Phys. Rev. Lett. 84 2726Google Scholar

    [33]

    Jasperse M, Turner L D, Scholten R E 2011 Opt. Express 19 3765Google Scholar

  • [1] 郝景晨, 杜培林, 孙恒信, 刘奎, 张静, 杨荣国, 郜江瑞. 双端腔Ⅱ类倍频产生四组份纠缠光场. 物理学报, 2024, 0(0): 0-0. doi: 10.7498/aps.73.20231630
    [2] 盖云冉, 郑康, 丁春玲, 郝向英, 金锐博. 基于半导体量子阱中四波混频效应的高效光学非互易. 物理学报, 2024, 73(1): 014201. doi: 10.7498/aps.73.20231212
    [3] 廖骎, 柳海杰, 王铮, 朱凌瑾. 基于不可信纠缠源的高斯调制连续变量量子密钥分发. 物理学报, 2023, 72(4): 040301. doi: 10.7498/aps.72.20221902
    [4] 曹雷明, 杜金鉴, 张凯, 刘胜帅, 荆杰泰. 基于四波混频过程产生介于锥形探针光和锥形共轭光之间的多模量子关联. 物理学报, 2022, 71(16): 160306. doi: 10.7498/aps.71.20220081
    [5] 董安琪, 张凯, 荆杰泰, 刘伍明. 基于级联四波混频过程产生四模簇态. 物理学报, 2022, 71(16): 160304. doi: 10.7498/aps.71.20220433
    [6] 翟淑琴, 康晓兰, 刘奎. 基于级联四波混频过程的量子导引. 物理学报, 2021, 70(16): 160301. doi: 10.7498/aps.70.20201981
    [7] Xiaoyin Xu, shengshuai liu, 荆杰泰. 基于四波混频过程的纠缠光放大. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211324
    [8] 余胜, 刘焕章, 刘胜帅, 荆杰泰. 基于四波混频过程和线性分束器产生四组份纠缠. 物理学报, 2020, 69(9): 090303. doi: 10.7498/aps.69.20200040
    [9] 仲银银, 潘晓州, 荆杰泰. 级联四波混频相干反馈控制系统量子纠缠特性. 物理学报, 2020, 69(13): 130301. doi: 10.7498/aps.69.20200042
    [10] 杨荣国, 张超霞, 李妮, 张静, 郜江瑞. 级联四波混频系统中纠缠增强的量子操控. 物理学报, 2019, 68(9): 094205. doi: 10.7498/aps.68.20181837
    [11] 王灿灿. 量子纠缠与宇宙学弗里德曼方程. 物理学报, 2018, 67(17): 179501. doi: 10.7498/aps.67.20180813
    [12] 邢贵超, 夏云杰. 与热库耦合的光学腔内三原子间的纠缠动力学. 物理学报, 2018, 67(7): 070301. doi: 10.7498/aps.67.20172546
    [13] 孙江, 孙娟, 王颖, 苏红新. 双光子共振非简并四波混频测量Ba原子里德伯态的碰撞展宽和频移. 物理学报, 2012, 61(11): 114214. doi: 10.7498/aps.61.114214
    [14] 赵建辉, 王海涛. 应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠. 物理学报, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
    [15] 孙江, 刘鹏, 孙娟, 苏红新, 王颖. 双光子共振非简并四波混频测量钡原子里德伯态碰撞展宽中的伴线研究. 物理学报, 2012, 61(12): 124205. doi: 10.7498/aps.61.124205
    [16] 周南润, 曾宾阳, 王立军, 龚黎华. 基于纠缠的选择自动重传量子同步通信协议. 物理学报, 2010, 59(4): 2193-2199. doi: 10.7498/aps.59.2193
    [17] 杨 磊, 李小英, 王宝善. 利用光纤中自发四波混频产生纠缠光子的实验装置. 物理学报, 2008, 57(8): 4933-4940. doi: 10.7498/aps.57.4933
    [18] 孙 江, 左战春, 郭庆林, 王英龙, 怀素芳, 王 颖, 傅盘铭. 应用双光子共振非简并四波混频测量Ba原子里德伯态. 物理学报, 2006, 55(1): 221-225. doi: 10.7498/aps.55.221
    [19] 孙 江, 左战春, 米 辛, 俞祖和, 吴令安, 傅盘铭. 引入量子干涉的双光子共振非简并四波混频. 物理学报, 2005, 54(1): 149-154. doi: 10.7498/aps.54.149
    [20] 王成志, 方卯发. 双模压缩真空态与原子相互作用中的量子纠缠和退相干. 物理学报, 2002, 51(9): 1989-1995. doi: 10.7498/aps.51.1989
计量
  • 文章访问数:  2558
  • PDF下载量:  91
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-07-17
  • 修回日期:  2021-10-23
  • 上网日期:  2022-02-23
  • 刊出日期:  2022-03-05

/

返回文章
返回