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

周期调制四通道光学波导的宇称-时间对称特性调控和动力学研究

张光成 孙武 周志鹏 全秀娥 叶伏秋

引用本文:
Citation:

周期调制四通道光学波导的宇称-时间对称特性调控和动力学研究

张光成, 孙武, 周志鹏, 全秀娥, 叶伏秋

Parity-time symmetry characterization and dynamics of periodically modulated four-channel optical waveguides

Zhang Guang-Cheng, Sun Wu, Zhou Zhi-Peng, Quan Xiu-E, Ye Fu-Qiu
PDF
HTML
导出引用
  • 光学系统中周期调制主要是通过周期性变化的复折射率材料来实现, 类似于周期驱动系统的量子隧穿行为, 宇称-时间(PT)对称光学波导系统中光的传播可以通过周期调制来进行有效操控. 本文设计了一种通过周期调制波导与增益型-耗散型波导交叉放置调控PT对称性的物理模型, 在高频近似下讨论了周期调制对体系能谱的影响, 最后结合解析和数值的方法揭示了光在非厄米四通道光学波导中的动力学演化. 结果表明, 与以往周期调制波导与增益型-耗散型波导平行放置的四通道光学波导体系相比, 不仅可以通过周期调制调窄完全实能谱的存在范围, 且可以更早地观测到实能谱. 此外, 调制参数变化时, 四通道波导的相对光强和光学周期更为稳定. 该理论研究给出了一种更为高效、稳定的调控PT对称的构型.
    The control of parity-time (PT) symmetry in cosmic-time PT symmetry system is of great significance, but the experimental realization of such an optical configuration using current technology faces enormous challenges. On the contrary, the periodic modulation method is a more feasible alternative. It is worth noting that periodic modulation in optical system is mainly performed through the cyclic change of complex refractive index materials. Unlike the traditional method of aligning periodically modulated waveguides in parallel to gain-dissipative waveguides to satisfy PT symmetry, an innovative physical model introduced in this work, features the cross-placement of these waveguides, marking it the first instance to use this configuration to manipulate PT symmetry. In this work, the influence of periodic modulation on the energy spectrum of the system in the high-frequency approximation is studied, and the dynamical evolution of light in a non-Hermitian four-channel optical waveguide is elucidated through a synergistic method of combining analytical method and numerical method. Adjusting the modulation parameter A/ω reveals a dual capability: it modulates the range of the real energy spectrum and precisely controls the PT symmetry of the system. Notably, at A/ω = 0, this structure exhibits a completely real energy spectrum, which is different from the traditional parallel four-channel waveguide configuration. Furthermore, as A/ω varies from 0 to 2.4, the relative intensity and optical periodicity in each waveguide exhibit enhanced stability compared with their traditionally arranged counterparts. Furthermore, our examination of PT symmetry’s effect on light tunneling dynamics in individual waveguide reveals that in the unbroken PT symmetry phase, light oscillates periodically between waveguides, whereas in the broken PT symmetry phase, light propagation in each waveguide becomes stable. In the presence of waveguide coupling, it is observed that each waveguide in the system can obtain steady-state light regardless of the initial light injection point. Furthermore, under weak coupling between the gain-dissipative two-channel waveguide and the neutral waveguide, light, regardless of its entry point, will localize in the gain waveguide with propagation distance, disappear from other waveguides, and ultimately reach a steady-state configuration. The findings reveal that unlike the scenario of traditional four-channel optical waveguide system, the periodic modulation not only narrows the range of existence for the fully real energy spectrum but also enables its earlier observation. Furthermore, the relative light intensity and optical periodicity in the four-channel waveguide exhibit greater stability against variations of modulation parameters. Hence, this theoretical exploration not only profoundly summarizes the universal principle of PT-symmetric tetramers, but also elucidates that spontaneous PT symmetry breaking greatly changes the optical transmission characteristics, transforming periodic light propagation into steady-state illumination, and providing an enhanced and more robust configuration for the manipulation of PT symmetry.
      通信作者: 叶伏秋, 912012237@qq.com
    • 基金项目: 国家自然科学基金(批准号: 12165008)资助的课题.
      Corresponding author: Ye Fu-Qiu, 912012237@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12165008).
    [1]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [2]

    Long Y, Xue H R, Zhang B L 2022 Phys. Rev. B 105 L100102Google Scholar

    [3]

    Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar

    [4]

    Xia S Q, Kaltsas D, Song D H, Komis I, Xu J J, Szameit A, Buljan H, Makris K G, Chen Z G 2021 Science 372 72Google Scholar

    [5]

    Moiseyev N 2011 Non-Hermitian Quantum Mechanics (Cambridge: Cambridge University Press) p211

    [6]

    Witoński P, Mossakowska-Wyszyńska A, Szczepański P 2023 Crystals 13 258Google Scholar

    [7]

    Li H J, Jia Q W, Lü B, Cao F Z, Yang G X, Liu D H, Shi J W 2023 Opt. Express 31 14986Google Scholar

    [8]

    Şeker E, Olyaeefar B, Dadashi K, Şengül S, Teimourpour M H, El-Ganainy R, Demir A 2023 Sci. Appl. 12 149

    [9]

    付林雪, 范孟军, 丁亚琼, 付新铭 2023 应用物理 13 183Google Scholar

    Fu L X, Fan M J, Ding Y Q, Fu X M 2023 Appl. Phys. 13 183Google Scholar

    [10]

    Yao S Y, Wang Z 2018 Phys. Rev. Lett. 121 086803Google Scholar

    [11]

    Ke S L, Wen W T, Zhao D, Wang Y 2023 Phys. Rev. A 107 053508Google Scholar

    [12]

    Zhu W W, Gong J B 2023 Phys. Rev. B 108 035406Google Scholar

    [13]

    Tang W Y, Ding K, Ma G C 2021 Phys. Rev. Lett. 127 034301Google Scholar

    [14]

    Parkavi J R, Chandrasekar V K, Lakshmanan M 2021 Phys. Rev. A 103 023721Google Scholar

    [15]

    郭志伟, 陈鸿 2024 物理 53 33Google Scholar

    Guo Z W, Chen H 2024 Physics 53 33Google Scholar

    [16]

    El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, Christodoulides D N 2018 Nat. Phys. 14 11Google Scholar

    [17]

    Morfonios C V, Kalozoumis P A, Diakonos F K, Schmelcher P 2017 Ann. Phys. 385 623Google Scholar

    [18]

    王洪飞, 解碧野, 詹鹏, 卢明辉, 陈延峰 2019 物理学报 68 224206Google Scholar

    Wang H F, Xie B Y, Zhan P, Lu M H, Chen Y F 2019 Acta Phys. Sin. 68 224206Google Scholar

    [19]

    Jin L 2018 Phys. Rev. A 98 022117Google Scholar

    [20]

    Xu H S, Jin L 2021 Phys. Rev. A 104 012218Google Scholar

    [21]

    Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J H, Rechtsman M C, Segev M, Christodoulides D N, Khajavikhan M 2018 Phys. Rev. Lett. 120 113901Google Scholar

    [22]

    Ge L, Türeci H E 2013 Phys. Rev. A 88 53810Google Scholar

    [23]

    Zhang J, Feng Z, Sun X 2022 arXiv. 2201 00948 [physics.optics]

    [24]

    柴若衡, 刘文玮, 程化, 田建国, 陈树琪 2021 光学学报 41 0123001Google Scholar

    Cai R H, Liu W W, Chen H, Tian J G, Chen S Q 2021 Acta Opt. Sin. 41 0123001Google Scholar

    [25]

    Longhi S 2009 Phys. Rev. Lett. 103 123601Google Scholar

    [26]

    Klaiman S, Günther U, Moiseyev N 2008 Phys. Rev. Lett. 101 080402Google Scholar

    [27]

    Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar

    [28]

    曲登科, 范毅, 薛鹏 2022 物理学报 71 130301Google Scholar

    Qu D K, Fan Y, Xue P 2022 Acta. Phys. Sin. 71 130301Google Scholar

    [29]

    Feng L, Wong Z J, Ma R M, Wang Y, Zhang X 2014 Science 346 972Google Scholar

    [30]

    Miao P, Zhang Z F, Sun J B, Walasik W, Longhi S, Litchinitser N M, Feng L 2016 Science 353 464Google Scholar

    [31]

    Zhu B, Zhong H H, Jia J, Ye F Q, Fu L B 2020 Phys. Rev. A 102 053510Google Scholar

    [32]

    Morandotti R, Peschel U, Aitchison J S, Eisenberg H S, Silberberg Y 1999 Phys. Rev. Lett. 83 4756Google Scholar

    [33]

    Trompeter H, Pertsch T, Lederer F, Michaelis D, Streppel U, Bräuer A, Peschel U 2006 Phys. Rev. Lett. 96 023901Google Scholar

    [34]

    Trompeter H, Krolikowski W, Neshev D N, Desyatnikov A S, Sukhorukov A A, Kivshar Y S, Lederer F 2006 Phys. Rev. Lett. 96 053903Google Scholar

    [35]

    朱博 2016 硕士学位论文 (吉首: 吉首大学)

    Zhu B 2016 M. S. Thesis (Jishou: Jishou University

  • 图 1  理论模型示意图. G和L分别为增益波导和耗散波导, P为周期调制的中性波导, ab分别代表不同光波导之间的耦合强度

    Fig. 1.  Schematic illustration of the theoretical framework depicts gain (G) and dissipation (L) waveguides, alongside periodically modulated neutral waveguides (P), the coupling strengths between these optical waveguides are denoted by symbols a and b, respectively.

    图 2  准能谱的虚部$ \left| {{\text{Im}}(\varepsilon )} \right| $与参数A/ω和参数γ的关系图

    Fig. 2.  Plot of the imaginary part of the quasi-energy spectrum with the parameters A/ω and γ.

    图 3  对于不同的驱动振幅A, 准能谱随非厄米参数γ的变化, 其中驱动频率ω = 10, 实线表示高频近似下的解析解, 圆圈表示由哈密顿量(2)式求得的数值解 (a), (b) A/ω = 0; (c), (d) A/ω = 1.2; (e), (f) A/ω = 2.4

    Fig. 3.  For varying driving amplitudes (A), the quasi-energy spectrum undergoes modifications in response to the non-Hermitian parameter (γ), with the driving frequency fixed at (ω = 10), the analytical solution under the high-frequency approximation is represented by solid lines, while the numerical solution derived from Hamiltonian Eq. (2) is depicted by circles: (a), (b) A/ω = 0; (c), (d) A/ω = 1.2; (e), (f) A/ω = 2.4.

    图 4  当调制参数$ A/\omega = 0 $, 系统处于厄米($ \gamma = 0 $, (a)—(d))、非厄米(实准能量, $ \gamma = 0.3 $ (e)—(h))和非厄米(复准能量, $ \gamma = $$ 2.4 $, (i)—(l))状态时光从不同的波导入射后光在波导中的隧穿情况. 第1列表示光从增益波导入射; 第2列和第4列表示光从周期调制的中性波导入射; 第3列表示光从耗散波导入射. 其中增益波导中的相对光强用红色表示, 两根中性波导中的相对光强分别用蓝色、黑色表示, 耗散波导中的相对光强用绿色表示, 其他参数选择$ a = b = 1 $, $ \omega = 10 $

    Fig. 4.  At a modulation parameter of (A/ω = 0), the system exhibits a unique configuration encompassing Hermitian ($ \gamma = 0 $, (a)–(d)), non-Hermitian with real reference energy ($ \gamma = 0.3 $, (e)–(h)), and non-Hermitian with complex quasi-energy ($ \gamma = 2.4 $, (i)–(l)) states. The configuration of light sources is specified as follows: the first column corresponds to light injection from the gain wave, the second and fourth columns signify light introduction from a periodically modulated neutral wave, and the third column represents light injected from the dissipative wave. The relative intensities of light are distinguished by color: red for the gain waveguide, blue and black for the two neutral waveguides, and green for the dissipative waveguide. For the remaining parameters, a = b = 1 and ω = 10.

    图 5  当调制参数$ A/\omega = 1.2 $, 系统处于厄米($ \gamma = 0 $, (a)—(d))、非厄米(实准能量, $ \gamma = 0.3 $, (e)—(h))和非厄米(复准能量, $ \gamma = 1.8 $, (i)—(l))状态时光从不同的波导入射后光在波导中的隧穿情况, 第1列表示光从增益波导入射; 第2列和第4列表示光从周期调制的中性波导入射; 第3列表示光从耗散波导入射, 其中增益波导中的相对光强用红色表示, 两根中性波导中的相对光强分别用蓝色、黑色表示, 耗散波导中的相对光强用绿色表示, 其他参数选择$ a = b = 1 $, $ \omega = 10 $

    Fig. 5.  At a modulation parameter (A/ω = 1.2), the system manifests in three distinct states: Hermitian ($ \gamma = 0 $, (a)–(d)), non-Hermitian with real reference energy ($ \gamma = 0.3 $, (e)–(h)), and non-Hermitian with complex quasi-energy ($ \gamma = 1.8 $, (i)–(l)). The source configuration is consistent, with the first column depicting light injection from the gain wave, the second and fourth columns signifying light introduction from a periodically modulated neutral wave, and the third column representing light injection from the dissipative wave. The relative intensities of light are represented by distinct colors: red for the gain waveguide, blue and black for the two neutral waveguides, and green for the dissipative waveguide. For the remaining parameters, a = b = 1 and ω = 10.

    图 6  当调制参数$ A/\omega = 2.4 $, 系统处于厄米($ \gamma = 0 $, (a)—(d))和非厄米(复准能量, $ \gamma = 1.8 $, (e)—(h))状态时光从不同的波导入射后光在波导中的隧穿情况, 第1列表示光从增益波导入射; 第2列和第4列表示光从周期调制的中性波导入射; 第3列表示光从耗散波导入射, 其中增益波导中的相对光强用红色表示, 两根中性波导中的相对光强分别用蓝色、黑色表示, 耗散波导中的相对光强用绿色表示, 其他参数选择$ a = b = 1 $, $ \omega = 10 $

    Fig. 6.  At a modulation parameter of (A/ω = 2.4), the system assumes both Hermitian (γ = 0, (a)–(d)) and non-Hermitian (complex quasi-energy, γ = 1.8, (e)–(h)) states. The arrangement of light sources is as follows: the first column signifies light injection from the gain wave; the second and fourth columns represent light introduction from a periodically modulated neutral wave; whereas the third column denotes light injection from the dissipative wave. The relative intensities of light are color-coded: red for the gain waveguide, blue and black for the two neutral waveguides, and green for the dissipative waveguide. For the remaining parameters, a = b = 1 and ω = 10.

  • [1]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [2]

    Long Y, Xue H R, Zhang B L 2022 Phys. Rev. B 105 L100102Google Scholar

    [3]

    Bender C M 2007 Rep. Prog. Phys. 70 947Google Scholar

    [4]

    Xia S Q, Kaltsas D, Song D H, Komis I, Xu J J, Szameit A, Buljan H, Makris K G, Chen Z G 2021 Science 372 72Google Scholar

    [5]

    Moiseyev N 2011 Non-Hermitian Quantum Mechanics (Cambridge: Cambridge University Press) p211

    [6]

    Witoński P, Mossakowska-Wyszyńska A, Szczepański P 2023 Crystals 13 258Google Scholar

    [7]

    Li H J, Jia Q W, Lü B, Cao F Z, Yang G X, Liu D H, Shi J W 2023 Opt. Express 31 14986Google Scholar

    [8]

    Şeker E, Olyaeefar B, Dadashi K, Şengül S, Teimourpour M H, El-Ganainy R, Demir A 2023 Sci. Appl. 12 149

    [9]

    付林雪, 范孟军, 丁亚琼, 付新铭 2023 应用物理 13 183Google Scholar

    Fu L X, Fan M J, Ding Y Q, Fu X M 2023 Appl. Phys. 13 183Google Scholar

    [10]

    Yao S Y, Wang Z 2018 Phys. Rev. Lett. 121 086803Google Scholar

    [11]

    Ke S L, Wen W T, Zhao D, Wang Y 2023 Phys. Rev. A 107 053508Google Scholar

    [12]

    Zhu W W, Gong J B 2023 Phys. Rev. B 108 035406Google Scholar

    [13]

    Tang W Y, Ding K, Ma G C 2021 Phys. Rev. Lett. 127 034301Google Scholar

    [14]

    Parkavi J R, Chandrasekar V K, Lakshmanan M 2021 Phys. Rev. A 103 023721Google Scholar

    [15]

    郭志伟, 陈鸿 2024 物理 53 33Google Scholar

    Guo Z W, Chen H 2024 Physics 53 33Google Scholar

    [16]

    El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, Christodoulides D N 2018 Nat. Phys. 14 11Google Scholar

    [17]

    Morfonios C V, Kalozoumis P A, Diakonos F K, Schmelcher P 2017 Ann. Phys. 385 623Google Scholar

    [18]

    王洪飞, 解碧野, 詹鹏, 卢明辉, 陈延峰 2019 物理学报 68 224206Google Scholar

    Wang H F, Xie B Y, Zhan P, Lu M H, Chen Y F 2019 Acta Phys. Sin. 68 224206Google Scholar

    [19]

    Jin L 2018 Phys. Rev. A 98 022117Google Scholar

    [20]

    Xu H S, Jin L 2021 Phys. Rev. A 104 012218Google Scholar

    [21]

    Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J H, Rechtsman M C, Segev M, Christodoulides D N, Khajavikhan M 2018 Phys. Rev. Lett. 120 113901Google Scholar

    [22]

    Ge L, Türeci H E 2013 Phys. Rev. A 88 53810Google Scholar

    [23]

    Zhang J, Feng Z, Sun X 2022 arXiv. 2201 00948 [physics.optics]

    [24]

    柴若衡, 刘文玮, 程化, 田建国, 陈树琪 2021 光学学报 41 0123001Google Scholar

    Cai R H, Liu W W, Chen H, Tian J G, Chen S Q 2021 Acta Opt. Sin. 41 0123001Google Scholar

    [25]

    Longhi S 2009 Phys. Rev. Lett. 103 123601Google Scholar

    [26]

    Klaiman S, Günther U, Moiseyev N 2008 Phys. Rev. Lett. 101 080402Google Scholar

    [27]

    Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar

    [28]

    曲登科, 范毅, 薛鹏 2022 物理学报 71 130301Google Scholar

    Qu D K, Fan Y, Xue P 2022 Acta. Phys. Sin. 71 130301Google Scholar

    [29]

    Feng L, Wong Z J, Ma R M, Wang Y, Zhang X 2014 Science 346 972Google Scholar

    [30]

    Miao P, Zhang Z F, Sun J B, Walasik W, Longhi S, Litchinitser N M, Feng L 2016 Science 353 464Google Scholar

    [31]

    Zhu B, Zhong H H, Jia J, Ye F Q, Fu L B 2020 Phys. Rev. A 102 053510Google Scholar

    [32]

    Morandotti R, Peschel U, Aitchison J S, Eisenberg H S, Silberberg Y 1999 Phys. Rev. Lett. 83 4756Google Scholar

    [33]

    Trompeter H, Pertsch T, Lederer F, Michaelis D, Streppel U, Bräuer A, Peschel U 2006 Phys. Rev. Lett. 96 023901Google Scholar

    [34]

    Trompeter H, Krolikowski W, Neshev D N, Desyatnikov A S, Sukhorukov A A, Kivshar Y S, Lederer F 2006 Phys. Rev. Lett. 96 053903Google Scholar

    [35]

    朱博 2016 硕士学位论文 (吉首: 吉首大学)

    Zhu B 2016 M. S. Thesis (Jishou: Jishou University

  • [1] 江翠, 李家锐, 亓迪, 张莲莲. 具有宇称-时间反演对称性的虚势能对T-型石墨烯结构能谱和边缘态的影响. 物理学报, 2024, 0(0): . doi: 10.7498/aps.73.20240871
    [2] 张慧洁, 贺衎. 哈密顿量宇称-时间对称性的刻画. 物理学报, 2024, 73(4): 040302. doi: 10.7498/aps.73.20230458
    [3] 王利凯, 王宇倩, 郭志伟, 江海涛, 李云辉, 羊亚平, 陈鸿. 基于高阶非厄密物理的磁共振无线电能传输研究进展. 物理学报, 2024, 0(0): . doi: 10.7498/aps.73.20241079
    [4] 蒋宏帆, 林机, 胡贝贝, 张肖. 非宇称时间对称耦合器中的非局域孤子. 物理学报, 2023, 72(10): 104205. doi: 10.7498/aps.72.20230082
    [5] 曲登科, 范毅, 薛鹏. 高维宇称-时间对称系统中的信息恢复与临界性. 物理学报, 2022, 0(0): . doi: 10.7498/aps.71.20220511
    [6] 曲登科, 范毅, 薛鹏. 高维宇称-时间对称系统中的信息恢复与临界性. 物理学报, 2022, 71(13): 130301. doi: 10.7498/aps.70.20220511
    [7] 高洁, 杭超. 里德伯原子中非厄米电磁诱导光栅引起的弱光孤子偏折及其操控. 物理学报, 2022, 71(13): 133202. doi: 10.7498/aps.71.20220456
    [8] 唐原江, 梁超, 刘永椿. 宇称-时间对称与反对称研究进展. 物理学报, 2022, 71(17): 171101. doi: 10.7498/aps.71.20221323
    [9] 胡洲, 曾招云, 唐佳, 罗小兵. 周期驱动的二能级系统中的准宇称-时间对称动力学. 物理学报, 2022, 71(7): 074207. doi: 10.7498/aps.70.20220270
    [10] 胡洲, 曾招云, 唐佳, 罗小兵. 周期驱动的二能级系统中的准宇称-时间对称动力学. 物理学报, 2022, 0(0): 0-0. doi: 10.7498/aps.71.20220270
    [11] 党婷婷, 王娟芬, 安亚东, 刘香莲, 张朝霞, 杨玲珍. 亮孤子在宇称时间对称波导中的传输和控制. 物理学报, 2015, 64(6): 064211. doi: 10.7498/aps.64.064211
    [12] 田艳, 黄丽, 罗懋康. 噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响. 物理学报, 2013, 62(5): 050502. doi: 10.7498/aps.62.050502
    [13] 张恒, 段文山. 双势阱中玻色-费米混合气体的周期调制效应. 物理学报, 2013, 62(16): 160303. doi: 10.7498/aps.62.160303
    [14] 苟学强, 闫明, 令伟栋, 赵红玉, 段文山. 费米气体在光晶格中的自俘获现象及其周期调制. 物理学报, 2013, 62(13): 130308. doi: 10.7498/aps.62.130308
    [15] 邢耀亮, 杨志安. 半导体光折变介质中光束传输的自囚禁及周期调制. 物理学报, 2013, 62(13): 130302. doi: 10.7498/aps.62.130302
    [16] 陈德彝, 王忠龙. 噪声间关联程度的时间周期调制对单模激光随机共振的影响. 物理学报, 2008, 57(6): 3333-3336. doi: 10.7498/aps.57.3333
    [17] 胡 昕, 江少恩, 崔延莉, 黄翼翔, 丁永坤, 刘忠礼, 易荣清, 李朝光, 张景和, 张华全. 一种时间分辨三通道软X射线光谱仪. 物理学报, 2007, 56(3): 1447-1451. doi: 10.7498/aps.56.1447
    [18] 王冠芳, 傅立斌, 赵 鸿, 刘 杰. 双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应. 物理学报, 2005, 54(11): 5003-5013. doi: 10.7498/aps.54.5003
    [19] 吴璧如, 徐云飞, 郑幼凤, 胡永炎, 陆杰. 镱的奇宇称自电离谱. 物理学报, 1990, 39(7): 48-53. doi: 10.7498/aps.39.48
    [20] 刘耀阳. 0→Λ+γ过程与宇称守恒. 物理学报, 1961, 17(12): 587-591. doi: 10.7498/aps.17.587
计量
  • 文章访问数:  793
  • PDF下载量:  42
  • 被引次数: 0
出版历程
  • 收稿日期:  2024-05-14
  • 修回日期:  2024-06-25
  • 上网日期:  2024-07-09
  • 刊出日期:  2024-08-20

/

返回文章
返回