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

类氢原子核质量对电子状态的影响

刘兆斌 李凯 曾天海 王锋 宋新兵 邵彬 邹健

引用本文:
Citation:

类氢原子核质量对电子状态的影响

刘兆斌, 李凯, 曾天海, 王锋, 宋新兵, 邵彬, 邹健

Influence of hydrogen-like nucleus mass on electronic state

Liu Zhao-Bin, Li Kai, Zeng Tian-Hai, Wang Feng, Song Xin-Bing, Shao Bin, Zou Jian
PDF
HTML
导出引用
  • 在孤立的两体复合系统中, 讨论其中一体的变化如何影响另一体的状态, 有助于了解单粒子混合态与纯态的关系. 本文讨论5个孤立的一维类氢原子模型系统, 原子核的质量互不相同. 这5个两体(电子与原子核)复合系统的相对运动状态都处于纠缠态, 其中电子状态都用约化密度矩阵表示的混合态描述. 在原子核质量趋近无穷大的一维氢原子模型中, 电子处于纯态. 为比较这里的纯态和混合态, 在位置表象中计算了这些混合态的纯度、它们分别与纯态的保真度、以及所有这些态的相干性. 研究表明, 原子核的质量越大, 纯度和保真度越接近1, 混合态的相干性与纯态的也越接近. 这样的纯态及其相干性可以是这种混合态及其相干性的近似, 并与原子核及库仑相互作用有关.
    In an isolated two-body composite system, the discussion of how the change of one body affects the state of the other will help to know the relation of a single particle's mixed and pure states. Given 5 one-dimensional hydrogen-like atoms models, each Coulomb interaction potential keeps invariant, while the masses of the nuclei are different. These two-body composite systems stay in their respective entangled state, each electron stays in a mixed state. If we suppose a one-dimensional hydrogen atom model having infinite nuclear mass, the electron stays in a pure state. We select position representation. The wave function of the ground state of the atom has the form of the square root of a δ function. To avoid calculation trouble of δ function, we select the first excited state and the superposed state of the first and the second excited states. We compare the two pure states, the first excited state and the superposed state, with those corresponding mixed states by fidelity and l1 norm coherence, and calculate the purities of the mixed states. The summations become integrations due to the position variable having a continuous eigenvalue spectrum. We investigate the changes in these quantities with the increase of the nuclear mass. The results show that the purities of the mixed states and the fidelities increase with the nuclear mass increasing. However, the coherences of the mixed states decrease with the nuclear mass increasing. This can be explained as that a mixed state with non-zero coherence may approach to a pure eigenstate, while the latter has zero coherence in the eigenspace. These mean that the greater a nuclear mass is, the closer the mixed state approaches to the corresponding pure state. Therefore, the two pure states are the approximations of the corresponding mixed states. The entangled state of the electron and the nucleus is related with the nuclear mass and the Coulomb interaction potential. So, each electron mixed state and its coherence are related with the nucleus and their Coulomb interaction potential. If the nuclear mass is great, the nucleus is approximately motionless or its state is approximately unchanged, and the Coulomb interaction potential approximates to the external Coulomb potential of the electron. The electron approximately stays in a pure state. The state and its coherence are related with the nucleus and the Coulomb interaction. From other point of view, the entangled state of the nucleus and the electron approximates to the product state of the unchanged nucleus state and the electron state. In this case, an electron mixed state approximates to its corresponding pure state, and then these states and their coherences are all related with the nucleus and the Coulomb interaction.
      通信作者: 曾天海, zengtianhai@bit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11674024, 11875086)和北京市自然科学基金(批准号: 2192049)资助的课题
      Corresponding author: Zeng Tian-Hai, zengtianhai@bit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11674024, 11875086) and the Natural Science Foundation of Beijing, China (Grant No. 2192049)
    [1]

    曾谨言 2007 量子力学 (卷Ⅰ) (北京: 科学出版社) 第305−307, 235−238 页

    Zeng J Y 2007 Quantum Mechanics (Vol. 1) (Beijing: Science Press) pp305−307, 235−238 (in Chinese)

    [2]

    张永德 2017 量子力学(北京: 科学出版社) 第21 页

    Zhang Y D 2017 Quantum Mechanics (Beijing: Science Press) p21 (in Chinese)

    [3]

    Landau L D, Lifshitz E M 2007 Quantum Mechanics (Singapore: Elsevier Pte Ltd.) pp39, 51

    [4]

    喀兴林 2001 高等量子力学(北京: 高等教育出版社) 第192−199, 84−88页

    Ka X L 2001 Advanced Quantum Mechanics (Bijing: Higher Education Press) pp192−199, 84−88 (in Chinese)

    [5]

    Gamel O, James D F V 2012 Phys. Rev. A 86 033830Google Scholar

    [6]

    Uhlmann A 1976 Rep. Math. Phys. 9 273Google Scholar

    [7]

    Jozsa R 1994 J. Mod. Opt. 41 2315Google Scholar

    [8]

    Nielsen M A, Chuang I L 2003 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp409−413

    [9]

    李承祖, 黄明球, 陈平行, 梁林梅 2000 量子通信和量子计算 (长沙: 国防科技大学出版社) 第130−131页

    Li C Z, Huang M Q, Chen P X, Liang L M 2000 Quantum Communication and Quantum Computation (Changsha: University of National Defence Technology Press) pp130−131 (in Chinese)

    [10]

    Hou J C, Qi X F 2012 Sci. China, Ser. G 55 1820Google Scholar

    [11]

    Aberg J 2006 arXiv: 0612146 [quant-ph]

    [12]

    Bartlett S D, Rudolph T, Spekkens R W, Turner P S 2006 New J. Phys. 8 58Google Scholar

    [13]

    Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401Google Scholar

    [14]

    Chen J X, Grogan S, Johnston N, Li C K, Plosker S 2016 Phys. Rev. A 94 042313Google Scholar

    [15]

    Yu X D, Zhang D J, Liu C L, Tong D M 2016 Phys. Rev. A 93 060303Google Scholar

    [16]

    Hu M L, Hu X, Wang J C, Peng Y, Zhang Y R, Fan H 2017 arXiv 1703.01852 [quant-phGoogle Scholar

    [17]

    Qi X F, Gao T, Yan F L 2017 J. Phys. A: Math. Theor. 50 285301Google Scholar

    [18]

    Song X K, Huang Y Q, Ling J J, Yung M H 2018 Phys. Rev. A 98 050302Google Scholar

    [19]

    Zhou G Y, Huang L J, Pan J Y, Hu L Y, Huang J H 2018 Front. Phys. 13 130701Google Scholar

    [20]

    Yu C S, Li D M, Zhou N N 2019 EPL 125 50001Google Scholar

    [21]

    Li K, Liu Z B, Zeng T H 2019 Int. J. Theor. Phys. 58 3252Google Scholar

    [22]

    吕鑫 2020 物理学报 69 070301Google Scholar

    Lü X 2020 Acta Phys. Sin. 69 070301Google Scholar

    [23]

    Loudon R 1959 Am. J. Phys. 27 649Google Scholar

    [24]

    钱伯初 1989 大学物理 7 5

    Qian B C 1989 College Physics 7 5

    [25]

    Bertet P, Osnaghi S, Rauschenbeutel A, Nogues G, Auffeves A, Brune M, Raimond J M, Haroche S 2001 Nature 411 166Google Scholar

    [26]

    Zeng T H 2013 arXiv: 1307.1851 [gen-ph]

    [27]

    Fayngold M, Fayngold V 2013 Quantum Mechanics and Quantum Information (Germany: Wiley-VCH) p603

    [28]

    曾天海 2016 大学物理 35 20Google Scholar

    Zeng T H 2016 College Physics 35 20Google Scholar

    [29]

    曾天海 2017 现代物理 7 8Google Scholar

    Zeng T H 2017 Modern Physics 7 8Google Scholar

    [30]

    Zeng T H, Sun Z Z, Shao B 2020 Int. J. Theor. Phys. 59 229Google Scholar

  • 图 1  纯度变化趋势图, 横坐标表示原子核质量和电子质量之比 (a) 第一激发态; (b) 叠加态

    Fig. 1.  Purity vs. the ratio of mass between nucleus and electron: (a) The first excited state; (b) the superposition of the first and the second excited states

    图 2  保真度变化趋势图, 横坐标表示原子核质量和电子质量之比 (a) 第一激发态; (b) 叠加态

    Fig. 2.  Fidelity vs. the ratio of mass between nucleus and electron: (a) the first excited state; (b) the superposition of the first and the second excited states

    图 3  相干性变化趋势图, 横坐标表示原子核质量和电子质量之比 (a)第一激发态; (b)叠加态

    Fig. 3.  Coherence vs. the ratio of mass between nucleus and electron: (a) The first excited state; (b) the superposition of the first and the second excited states

  • [1]

    曾谨言 2007 量子力学 (卷Ⅰ) (北京: 科学出版社) 第305−307, 235−238 页

    Zeng J Y 2007 Quantum Mechanics (Vol. 1) (Beijing: Science Press) pp305−307, 235−238 (in Chinese)

    [2]

    张永德 2017 量子力学(北京: 科学出版社) 第21 页

    Zhang Y D 2017 Quantum Mechanics (Beijing: Science Press) p21 (in Chinese)

    [3]

    Landau L D, Lifshitz E M 2007 Quantum Mechanics (Singapore: Elsevier Pte Ltd.) pp39, 51

    [4]

    喀兴林 2001 高等量子力学(北京: 高等教育出版社) 第192−199, 84−88页

    Ka X L 2001 Advanced Quantum Mechanics (Bijing: Higher Education Press) pp192−199, 84−88 (in Chinese)

    [5]

    Gamel O, James D F V 2012 Phys. Rev. A 86 033830Google Scholar

    [6]

    Uhlmann A 1976 Rep. Math. Phys. 9 273Google Scholar

    [7]

    Jozsa R 1994 J. Mod. Opt. 41 2315Google Scholar

    [8]

    Nielsen M A, Chuang I L 2003 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) pp409−413

    [9]

    李承祖, 黄明球, 陈平行, 梁林梅 2000 量子通信和量子计算 (长沙: 国防科技大学出版社) 第130−131页

    Li C Z, Huang M Q, Chen P X, Liang L M 2000 Quantum Communication and Quantum Computation (Changsha: University of National Defence Technology Press) pp130−131 (in Chinese)

    [10]

    Hou J C, Qi X F 2012 Sci. China, Ser. G 55 1820Google Scholar

    [11]

    Aberg J 2006 arXiv: 0612146 [quant-ph]

    [12]

    Bartlett S D, Rudolph T, Spekkens R W, Turner P S 2006 New J. Phys. 8 58Google Scholar

    [13]

    Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401Google Scholar

    [14]

    Chen J X, Grogan S, Johnston N, Li C K, Plosker S 2016 Phys. Rev. A 94 042313Google Scholar

    [15]

    Yu X D, Zhang D J, Liu C L, Tong D M 2016 Phys. Rev. A 93 060303Google Scholar

    [16]

    Hu M L, Hu X, Wang J C, Peng Y, Zhang Y R, Fan H 2017 arXiv 1703.01852 [quant-phGoogle Scholar

    [17]

    Qi X F, Gao T, Yan F L 2017 J. Phys. A: Math. Theor. 50 285301Google Scholar

    [18]

    Song X K, Huang Y Q, Ling J J, Yung M H 2018 Phys. Rev. A 98 050302Google Scholar

    [19]

    Zhou G Y, Huang L J, Pan J Y, Hu L Y, Huang J H 2018 Front. Phys. 13 130701Google Scholar

    [20]

    Yu C S, Li D M, Zhou N N 2019 EPL 125 50001Google Scholar

    [21]

    Li K, Liu Z B, Zeng T H 2019 Int. J. Theor. Phys. 58 3252Google Scholar

    [22]

    吕鑫 2020 物理学报 69 070301Google Scholar

    Lü X 2020 Acta Phys. Sin. 69 070301Google Scholar

    [23]

    Loudon R 1959 Am. J. Phys. 27 649Google Scholar

    [24]

    钱伯初 1989 大学物理 7 5

    Qian B C 1989 College Physics 7 5

    [25]

    Bertet P, Osnaghi S, Rauschenbeutel A, Nogues G, Auffeves A, Brune M, Raimond J M, Haroche S 2001 Nature 411 166Google Scholar

    [26]

    Zeng T H 2013 arXiv: 1307.1851 [gen-ph]

    [27]

    Fayngold M, Fayngold V 2013 Quantum Mechanics and Quantum Information (Germany: Wiley-VCH) p603

    [28]

    曾天海 2016 大学物理 35 20Google Scholar

    Zeng T H 2016 College Physics 35 20Google Scholar

    [29]

    曾天海 2017 现代物理 7 8Google Scholar

    Zeng T H 2017 Modern Physics 7 8Google Scholar

    [30]

    Zeng T H, Sun Z Z, Shao B 2020 Int. J. Theor. Phys. 59 229Google Scholar

  • [1] 吴晓东, 黄端. 基于非理想量子态制备的实际连续变量量子秘密共享方案. 物理学报, 2024, 73(2): 020304. doi: 10.7498/aps.73.20230138
    [2] 文镇南, 易有根, 徐效文, 郭迎. 无噪线性放大的连续变量量子隐形传态. 物理学报, 2022, 71(13): 130307. doi: 10.7498/aps.71.20212341
    [3] 罗均文, 吴德伟, 李响, 朱浩男, 魏天丽. 微波连续变量极化纠缠. 物理学报, 2019, 68(6): 064204. doi: 10.7498/aps.68.20181911
    [4] 张洪波, 张希仁. 用于实现散射介质中时间反演的数字相位共轭的相干性. 物理学报, 2018, 67(5): 054201. doi: 10.7498/aps.67.20172308
    [5] 贾芳, 刘寸金, 胡银泉, 范洪义. 量子隐形传态保真度的新公式及应用. 物理学报, 2016, 65(22): 220302. doi: 10.7498/aps.65.220302
    [6] 杨光, 廉保旺, 聂敏. 振幅阻尼信道量子隐形传态保真度恢复机理. 物理学报, 2015, 64(1): 010303. doi: 10.7498/aps.64.010303
    [7] 秦猛, 李延标, 白忠, 王晓. 不同方向Dzyaloshinskii-Moriya相互作用和磁场对自旋系统纠缠和保真度退相干的影响. 物理学报, 2014, 63(11): 110302. doi: 10.7498/aps.63.110302
    [8] 聂敏, 张琳, 刘晓慧. 量子纠缠信令网Poisson生存模型及保真度分析. 物理学报, 2013, 62(23): 230303. doi: 10.7498/aps.62.230303
    [9] 满天龙, 万玉红, 江竹青, 王大勇, 陶世荃. 孪生光束干涉法测量光源的空间相干性. 物理学报, 2013, 62(21): 214203. doi: 10.7498/aps.62.214203
    [10] 饶黄云, 刘义保, 江燕燕, 郭立平, 王资生. 三能级混合态的量子几何相位. 物理学报, 2012, 61(2): 020302. doi: 10.7498/aps.61.020302
    [11] 靳爱军, 王泽锋, 侯静, 郭良, 姜宗福. 光子晶体光纤反常色散区抽运产生超连续谱的相干特性分析. 物理学报, 2012, 61(12): 124211. doi: 10.7498/aps.61.124211
    [12] 闫智辉, 贾晓军, 谢常德, 彭堃墀. 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. 物理学报, 2012, 61(1): 014206. doi: 10.7498/aps.61.014206
    [13] 靳爱军, 王泽锋, 侯静, 郭良, 姜宗福, 肖瑞. 复自相干度度量超连续谱相干性. 物理学报, 2012, 61(15): 154201. doi: 10.7498/aps.61.154201
    [14] 潘长宁, 方见树, 彭小芳, 廖湘萍, 方卯发. 耗散系统中实现原子态量子隐形传态的保真度. 物理学报, 2011, 60(9): 090303. doi: 10.7498/aps.60.090303
    [15] 吕菁芬, 马善钧. 光子扣除(增加)压缩真空态与压缩猫态的保真度. 物理学报, 2011, 60(8): 080301. doi: 10.7498/aps.60.080301
    [16] 陈进建, 韩正甫, 赵义博, 桂有珍, 郭光灿. 平衡零拍测量对连续变量量子密钥分配的影响. 物理学报, 2007, 56(1): 5-9. doi: 10.7498/aps.56.5
    [17] 夏云杰, 王光辉, 杜少将. 双模最小关联混合态作为量子信道实现量子隐形传态的保真度. 物理学报, 2007, 56(8): 4331-4336. doi: 10.7498/aps.56.4331
    [18] 张登玉, 郭 萍, 高 峰. 强热辐射环境中两能级原子量子态保真度. 物理学报, 2007, 56(4): 1906-1910. doi: 10.7498/aps.56.1906
    [19] 邓文基, 刘 平, 徐 晓. 混合态的不确定关系与压缩效应. 物理学报, 2004, 53(11): 3668-3672. doi: 10.7498/aps.53.3668
    [20] 杨东升, 吴柏枚, 李 波, 郑卫华, 李世燕, 陈仙辉, 曹烈兆. MgB2混合态热导率的反常增强. 物理学报, 2003, 52(8): 2015-2019. doi: 10.7498/aps.52.2015
计量
  • 文章访问数:  6099
  • PDF下载量:  113
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-10-22
  • 修回日期:  2020-11-16
  • 上网日期:  2021-03-23
  • 刊出日期:  2021-04-05

/

返回文章
返回