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

N00N态的Wigner函数及N00N态作为输入的量子干涉

徐学翔 张英孔 张浩亮 陈媛媛

引用本文:
Citation:

N00N态的Wigner函数及N00N态作为输入的量子干涉

徐学翔, 张英孔, 张浩亮, 陈媛媛

Wigner function of N00N state and quantum interference with N00N state as input

Xu Xue-Xiang, Zhang Ying-Kong, Zhang Hao-Liang, Chen Yuan-Yuan
PDF
导出引用
  • 根据量子力学相干态表象下的Wigner函数公式, 推导了N00N态在相空间的Wigner分布函数的解析表达式. 基于相空间方法, 研究N00N态作为输入的量子干涉. 推导了与输入光场参数和干涉仪参数相关的输出端探测光子概率的解析表达式, 并进行了数值分析. 从分析结果发现, 当相移参数φ取0和π时, 输出量子态仍为N00N态. 当输入2002态时, 输出结果总是2002态, 与相移参数无关. 随着N的增加, 条件概率随相位的分布峰数一般只有一个, 两个, 三个或四个, 且峰变得更窄. 这些结果可以为实验提供理论指导.
    Using the formula of Wigner function in coherent representation, we have obtained the analytical expression for Wigner function of N00N state. Based on phase space method, we study the quantum interference with N00N state as input. We derive the analytical expression of conditional probability related with the input parameter N and phase parameter φ and analyze it numerically. It is shown that, when φ is 0 or π, the output is just N00N state. It is also shown that, for 2002 state as input, the output must be 2002 state, which is independent of phase parameters. Moreover, as the number of input photon N increases, the phase probability distributions remain to have one, two, three and four peaks and get narrower. All these results can offer theoretical reference for experiments.
    • 基金项目: 国家自然科学基金 (批准号: 11175113, 11264018, 11247301), 江西省自然科学基金 (批准号: 2011BAB202004)和江西省教育厅科技项目 (批准号: GJJ12171)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113, 11264018, 11247301), the Natural Science Foundation of Jiangxi Province, China (Grant No. 2011BAB202004), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ12171).
    [1]

    Hariharan P 2003 Optical interferometry, (2nd Edn) (Elsevier)

    [2]

    Taylor G I 1909 Proceedings of the Cambridge Philosophical Society 15 14

    [3]

    Paul H 1986 Rev. Mod. Phys. 58 209

    [4]

    Dirac P A M 1930 The Principles of Quantum Mechanics (Clarendon: Oxford University Press)

    [5]

    Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 204

    [6]

    Mandel L 1999 Rev. Mod. Phys. 71 S274

    [7]

    Glauber R J 1995 Am. J. Phys. 63 12

    [8]

    Long G L, Deng F G, Zeng J Y 2011 Recent Progress in Quantum Mechanics, fifth volume (Beijing: Tsinghua University Press) [龙桂鲁, 邓富国, 曾谨言 2011 量子力学新进展 第五辑 (北京: 清华大学出版社)]

    [9]

    Bahder T B, Lopata P A 2006 Phase Sensitivity of a Mach-Zehnder Quantum Sensor (Conference proceedings of QCMC)

    [10]

    Escher B M, de Matos Filho R L, Davidovich L 2011 Nature Phys. 7 406

    [11]

    Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222

    [12]

    Grangier P, Slusher R E, Yurke B, LaPorta A 1986 Phys. Rev. Lett. 59 2153

    [13]

    O'Brien J L 2007 Science 318 1393

    [14]

    Dorner U, Dobrzanski R D, Smith B J, Lundeen J S, Wasilewski W, Banaszek K, Walmsley I A 2009 Phys. Rev. Lett. 102 040403

    [15]

    Gerry C C, Mimih J 2010 Contemp. Phys. 51 497

    [16]

    Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330

    [17]

    Bouwmeester D, Ekert A, Zeilinger A 2000 The Physics of Quantum Information (Berlin: Springer-Verlag)

    [18]

    Dowling J P 2008 Contemp. Phys. 49 125

    [19]

    Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033

    [20]

    Ekert A K, knight P L 1991 Phys. Rev. A 43 3934

    [21]

    Windhager A, Suda M, Pache C, Peev M, Poppe A 2011 Opt. Commu. 284 1907

    [22]

    Xu X X, Jia F, Hu L Y, Duan Z L, Guo Q, Ma S J 2012 J. Mod. Opt. 59 1624

    [23]

    Schleich W P 2001 Quantum Optics in Phase space (Berlin: Verlag)

    [24]

    Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661

    [25]

    Zhang H L, Jia Fang, Xu X X, Guo Q, Tao X Y, Hu L Y 2013 Acta Phys. Sin. 62 014208

    [26]

    Hu L Y, Xu X X, Fan H Y 2010 J. Opt. Soc. Am. B 27 286

    [27]

    Glauber R 1963 Phys. Rev. 131 2766

    [28]

    Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag) Appendix A

    [29]

    Hu L Y, Fan H Y 2009 Chin Phys. B 18 4657

    [30]

    Leonhardt U 1997 Measuring the quantum state of light (Cambridge: Cambridge University Press)

    [31]

    Wang K, Zhu S 2003 Euro Phys. Lett. 64 22

    [32]

    Wang K, Yang G 2004 Chin. Phys. Lett. 21 302

  • [1]

    Hariharan P 2003 Optical interferometry, (2nd Edn) (Elsevier)

    [2]

    Taylor G I 1909 Proceedings of the Cambridge Philosophical Society 15 14

    [3]

    Paul H 1986 Rev. Mod. Phys. 58 209

    [4]

    Dirac P A M 1930 The Principles of Quantum Mechanics (Clarendon: Oxford University Press)

    [5]

    Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 204

    [6]

    Mandel L 1999 Rev. Mod. Phys. 71 S274

    [7]

    Glauber R J 1995 Am. J. Phys. 63 12

    [8]

    Long G L, Deng F G, Zeng J Y 2011 Recent Progress in Quantum Mechanics, fifth volume (Beijing: Tsinghua University Press) [龙桂鲁, 邓富国, 曾谨言 2011 量子力学新进展 第五辑 (北京: 清华大学出版社)]

    [9]

    Bahder T B, Lopata P A 2006 Phase Sensitivity of a Mach-Zehnder Quantum Sensor (Conference proceedings of QCMC)

    [10]

    Escher B M, de Matos Filho R L, Davidovich L 2011 Nature Phys. 7 406

    [11]

    Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222

    [12]

    Grangier P, Slusher R E, Yurke B, LaPorta A 1986 Phys. Rev. Lett. 59 2153

    [13]

    O'Brien J L 2007 Science 318 1393

    [14]

    Dorner U, Dobrzanski R D, Smith B J, Lundeen J S, Wasilewski W, Banaszek K, Walmsley I A 2009 Phys. Rev. Lett. 102 040403

    [15]

    Gerry C C, Mimih J 2010 Contemp. Phys. 51 497

    [16]

    Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330

    [17]

    Bouwmeester D, Ekert A, Zeilinger A 2000 The Physics of Quantum Information (Berlin: Springer-Verlag)

    [18]

    Dowling J P 2008 Contemp. Phys. 49 125

    [19]

    Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033

    [20]

    Ekert A K, knight P L 1991 Phys. Rev. A 43 3934

    [21]

    Windhager A, Suda M, Pache C, Peev M, Poppe A 2011 Opt. Commu. 284 1907

    [22]

    Xu X X, Jia F, Hu L Y, Duan Z L, Guo Q, Ma S J 2012 J. Mod. Opt. 59 1624

    [23]

    Schleich W P 2001 Quantum Optics in Phase space (Berlin: Verlag)

    [24]

    Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661

    [25]

    Zhang H L, Jia Fang, Xu X X, Guo Q, Tao X Y, Hu L Y 2013 Acta Phys. Sin. 62 014208

    [26]

    Hu L Y, Xu X X, Fan H Y 2010 J. Opt. Soc. Am. B 27 286

    [27]

    Glauber R 1963 Phys. Rev. 131 2766

    [28]

    Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag) Appendix A

    [29]

    Hu L Y, Fan H Y 2009 Chin Phys. B 18 4657

    [30]

    Leonhardt U 1997 Measuring the quantum state of light (Cambridge: Cambridge University Press)

    [31]

    Wang K, Zhu S 2003 Euro Phys. Lett. 64 22

    [32]

    Wang K, Yang G 2004 Chin. Phys. Lett. 21 302

  • [1] 王振宇, 李志雄, 袁怀洋, 张知之, 曹云姗, 严鹏. 磁子学中的拓扑物态与量子效应. 物理学报, 2023, 72(5): 057503. doi: 10.7498/aps.72.20221997
    [2] 牛明丽, 王月明, 李志坚. 基于量子Fisher信息的耗散相互作用光-物质耦合常数的估计. 物理学报, 2022, 71(9): 090601. doi: 10.7498/aps.71.20212029
    [3] 李靖, 刘运全. 基于相对论自由电子的量子物理. 物理学报, 2022, 71(23): 233302. doi: 10.7498/aps.71.20221289
    [4] 张超江, 许洪光, 徐西玲, 郑卫军. ${\bf Ta_4C}_{ n}^{\bf -/0}$ (n = 0—4)团簇的电子结构、成键性质及稳定性. 物理学报, 2021, 70(2): 023601. doi: 10.7498/aps.70.20201351
    [5] 危语嫣, 高子凯, 王思颖, 朱雅静, 李涛. 基于单光子双量子态的确定性的安全量子通讯. 物理学报, 2021, (): . doi: 10.7498/aps.70.20210907
    [6] 刘尚阔, 王涛, 李坤, 曹昆, 张玺斌, 周艳, 赵建科, 姚保利. 光源光谱特性对空间相机调制传递函数检测的影响. 物理学报, 2021, 70(13): 134208. doi: 10.7498/aps.70.20201575
    [7] 翟泽辉, 郝温静, 刘建丽, 段西亚. 用于光学薛定谔猫态制备的滤波设计与滤波腔腔长测量. 物理学报, 2020, 69(18): 184204. doi: 10.7498/aps.69.20200589
    [8] 王俊萍, 张文慧, 李瑞鑫, 田龙, 王雅君, 郑耀辉. 宽频带压缩态光场光学参量腔的设计. 物理学报, 2020, 69(23): 234204. doi: 10.7498/aps.69.20200890
    [9] 马堃, 陈展斌, 黄时中. 等离子体屏蔽效应对Ar16+基态和激发态能级的影响. 物理学报, 2019, 68(2): 023102. doi: 10.7498/aps.68.20181915
    [10] 石泰峡, 董丽娟, 陈永强, 刘艳红, 刘丽想, 石云龙. 人工磁导体对无线能量传输空间场的调控. 物理学报, 2019, 68(21): 214203. doi: 10.7498/aps.68.20190862
计量
  • 文章访问数:  7755
  • PDF下载量:  566
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-10-31
  • 修回日期:  2013-02-22
  • 刊出日期:  2013-06-05

/

返回文章
返回