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通信波段稀土离子掺杂固态量子存储进展

李城, 敬波, 廖金宇, 陈钰洁, 宋日尧, 张天乐, 宋海智, 周强

李城, 敬波, 廖金宇, 陈钰洁, 宋日尧, 张天乐, 宋海智, 周强. 通信波段稀土离子掺杂固态量子存储进展[J]. 激光技术, 2022, 46(1): 45-57. DOI: 10.7510/jgjs.issn.1001-3806.2022.01.003
引用本文: 李城, 敬波, 廖金宇, 陈钰洁, 宋日尧, 张天乐, 宋海智, 周强. 通信波段稀土离子掺杂固态量子存储进展[J]. 激光技术, 2022, 46(1): 45-57. DOI: 10.7510/jgjs.issn.1001-3806.2022.01.003
LI Cheng, JING Bo, LIAO Jinyu, CHEN Yujie, SONG Riyao, ZHANG Tianle, SONG Haizhi, ZHOU Qiang. Advances of rare earth ions doped solid-state quantum memory at telecom band[J]. LASER TECHNOLOGY, 2022, 46(1): 45-57. DOI: 10.7510/jgjs.issn.1001-3806.2022.01.003
Citation: LI Cheng, JING Bo, LIAO Jinyu, CHEN Yujie, SONG Riyao, ZHANG Tianle, SONG Haizhi, ZHOU Qiang. Advances of rare earth ions doped solid-state quantum memory at telecom band[J]. LASER TECHNOLOGY, 2022, 46(1): 45-57. DOI: 10.7510/jgjs.issn.1001-3806.2022.01.003

通信波段稀土离子掺杂固态量子存储进展

基金项目: 

国家自然科学基金资助项目 12004068

国家自然科学基金资助项目 61775025

国家重点研发计划资助项目 2018YFA0307400

中国博士后科学基金资助项目 2020M683275

中国博士后科学基金资助项目 2021T140093

详细信息
    作者简介:

    李城(1997-),男,硕士研究生,现主要从事光量子存储方面的研究

    通讯作者:

    周强, E-mail:zhouqiang@uestc.edu.cn

  • 中图分类号: O431.2

Advances of rare earth ions doped solid-state quantum memory at telecom band

  • 摘要: 量子互联网是实现多方量子通信、分布式量子计算等量子信息技术的重要基础,量子存储器作为实现互联网的重要部件,对量子信息技术的发展、应用具有举足轻重的作用。如今遍布全球的光纤网络已经是信息传输的有力载体,通信波段的量子存储器因容易嵌入到当前的光纤网络中而备受重视。聚焦于稀土离子掺杂固态体系的通信波段光量子存储,首先介绍稀土离子掺杂固态量子存储的基本原理,包括稀土掺杂材料特性以及存储协议等,然后介绍目前的研究现状,最后简要分析其未来的发展趋势,并对量子互联网的构建做出展望。
    Abstract: Quantum internet is an important basis for realizing multi-party quantum communication, distributed quantum computing, and other quantum information technologies. Quantum memory, as a significant part for realizing Internet, plays a pivotal role in the development and application of quantum information technology. Nowadays, the global optical fiber network has become a powerful carrier of information transmission, and quantum memory in communication band is highly valued because it is easy to be embedded in the current optical fiber network. Focus on telecom band optical quantum memory with rare earth ions doped solid-state system, the basic principle of rare earth ions doped solid-state quantum memory was firstly introduced, including rare earth doped material properties and memory protocol. the current state of the art was then introduced. Finally, a brief analysis on its future development trend was given, and the prospect for the construction of quantum Internet was made.
  • 随着飞机载荷日益轻量化的要求,机载激光测照辐射器在不断向小型化和轻量化发展。在冲击振动以及高低温等严苛的机载环境下,其机械结构的微小形变,都将影响到激光辐射器输出的光轴稳定性与能量稳定性[1]。常用的激光测照辐射器设计构型多为激光二极管(laser diode, LD)侧面抽运的高斯虚共焦非稳定谐振腔构型[2],参考文献[3] ~ 参考文献[9]中采用侧面抽运方式,对小型激光测照器进行设计,能够获得较为均匀的激光工作物质激励,该型谐振腔在满足虚共焦条件下能够保证输出的激光具有良好的准直特性,通过高斯膜斑尺寸来控制腔内模式实现高光束质量输出[3-9]。LD端面抽运技术是将半导体激光器阵列发出的抽运光从端面注入激光工作物质,其光光转化效率更高、集成度更好,有利于实现激光测照器小型化,同时应用基于正交直角棱镜的大基模尺寸稳定谐振腔技术,能够在保证光束质量的同时,获得高机械稳定性,具有广阔的研究前景[10]

    目前,LUO等人[11-12]研究了直角棱镜腔的偏振耦合输出特性,并采用双直角棱镜腔,研制了一台20 Hz、60 mJ的激光测照器。ZHANG等人[13]利用半圆柱面LD侧面抽运结合直角棱镜谐振腔研制了重频20 Hz、单脉冲能量75 mJ、光轴漂移量小于0.1 mrad、远场发散角2.2 mrad的激光器样机。LIU等人利用侧面抽运的porro棱镜腔技术,研究了1.57 μm激光器获得20 Hz重频、单脉冲能量86 mJ、发散角5 mrad的光参量振荡激光器样机[14-15]。LI等人[16]对石英直角棱镜的相位补偿进行了理论研究,并验证了波片补偿Porro棱镜相位延迟的实际效果。

    本文作者使用了一种峰值功率千瓦量级的LD端面抽运阵列对Nd ∶YAG晶体进行端面抽运,利用带曲率设计的正交直角棱镜,将谐振腔工作点调至大基模尺寸稳定谐振腔,并对比了正交偏振关门与特殊波片关门两种电光调Q关门方式,获得了重频20 Hz、单脉冲能量80 mJ高光束质量激光实验输出。

    在双直角棱镜腔中,光束经过直角棱镜后都会发生全内反射,其依靠耦合输出端的直角棱镜配合起偏器(偏振片或偏振分光棱镜)与波片来对激光的偏振态进行控制并耦合输出,耦合输出端的光学结构模型主要由直角棱镜、波片和偏振分光棱镜(polarization beam splitter, PBS)构成,如图 1所示。

    图 1 直角棱镜耦合输出端模型
    图  1  直角棱镜耦合输出端模型
    Figure  1.  Coupling output model of Porro prism

    图 1所示的坐标系下, 沿着图中x方向上的p偏振光首先需要经过任意波片。图 1所在空间的自然坐标系相对于波片的快慢轴坐标系会存在一个夹角θ (θ为波片快轴与图 1水平方向上x轴的夹角)。该角度可看成是波片在旋转过程中与x方向的任意夹角, 因为波片内的快慢轴坐标的存在, 偏振光透射波片时,需要先后进行两次坐标系变换, 其中坐标变化矩阵\boldsymbol{A}_{1}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right], 同时波片本身会产生附加相位\varphi。该波片产生的快慢轴的相位延时延迟矩阵\boldsymbol{A}_{2}= \left[\begin{array}{cc}1 & 0 \\ 0 & \exp (\mathrm{i} \varphi)\end{array}\right]

    经上述分析,可得任意波片的琼斯矩阵为:

    \begin{gathered} \boldsymbol{A}=\boldsymbol{A}_1 \boldsymbol{A}_2 \boldsymbol{A}_1= \\ {\left[\begin{array}{cc} \cos ^2 \theta+\sin ^2 \theta \exp (\mathrm{i} \varphi) & \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)] \\ \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)] & \sin ^2 \theta+\cos ^2 \theta \exp (\mathrm{i} \varphi) \end{array}\right]} \end{gathered} (1)

    随后,入射光透过波片后还需要经过直角棱镜,直角棱镜对光束会起到两个作用,第1个是产生光束转向, 其中转向矩阵\boldsymbol{B}_{1}=\left[\begin{array}{cc}-1 & 0 \\ 0 & 1\end{array}\right], 在直角棱镜内会发生两次全内反射, 根据菲涅耳公式可知, 全反射后的p偏振光与s偏振光会产生一定的相位差, 该相位差主要由直角棱镜的材料所确定, 实验选用直角棱镜的材料为\mathrm{K} 9玻璃, 其在两个方向上产生的相位差[3]分别为\varphi_{x}=-0.4402 {\rm{ \mathsf{ π} }} , \varphi_{y}=-0.2201 {\rm{ \mathsf{ π} }}。因此直接棱镜内的直角面单次反射的相移矩阵\boldsymbol{B}_{2}=\left[\begin{array}{cc}\exp \left(\mathrm{i} \varphi_{x}\right) & 0 \\ 0 & \exp \left(\mathrm{i} \varphi_{y}\right)\end{array}\right]

    则直角棱镜经过两次全内反射的琼斯矩阵为:

    \boldsymbol{B}=\boldsymbol{B}_1 \boldsymbol{B}_2 \boldsymbol{B}_2=\left[\begin{array}{cc} -\exp \left(\mathrm{i} 2 \varphi_x\right) & 0 \\ 0 & \exp \left(\mathrm{i} 2 \varphi_y\right) \end{array}\right] (2)

    一束沿着x方向的p偏振光\left[\begin{array}{l} E_{x_0} \\ E_{y_0} \end{array}\right]=\left[\begin{array}{l} 1 \\ 0 \end{array}\right]经过上面的光路后,入射到偏振分光棱镜输出时的琼斯矩阵为\left[\begin{array}{l} E_{x_1} \\ E_{y_1} \end{array}\right],两者具有下述关系:

    \left[\begin{array}{l} E_{x_1} \\ E_{y_1} \end{array}\right]=\boldsymbol{D}\left[\begin{array}{l} E_{x_0} \\ E_{y_0} \end{array}\right]=\boldsymbol{A} \boldsymbol{B} \boldsymbol{A}\left[\begin{array}{l} E_{x_0} \\ E_{y_0} \end{array}\right]=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]\left[\begin{array}{l} 1 \\ 0 \end{array}\right] (3)

    式中, 不同下标的E表示不同的电场强度分量;D = ABA; abcd分别为:

    \left\{\begin{array}{l} a=-\left[\cos ^{2} \theta+\sin ^{2} \theta \exp (\mathrm{i} \varphi)\right]^{2} \exp \left(\mathrm{i} 2 \varphi_{x}\right)+\sin ^{2} \theta \cos ^{2} \theta[1-\exp (\mathrm{i} \varphi)]^{2} \exp \left(\mathrm{i} 2 \varphi_{y}\right) \\ b=-\left[\cos ^{2} \theta+\sin ^{2} \theta \exp (\mathrm{i} \varphi)\right] \exp \left(\mathrm{i} 2 \varphi_{x}\right) \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)]+\left[\sin ^{2} \theta+\cos ^{2} \theta \exp (\mathrm{i} \varphi)\right] \exp \left(\mathrm{i} 2 \varphi_{y}\right) \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)] \\ c=-\left[\cos ^{2} \theta+\sin ^{2} \theta \exp (\mathrm{i} \varphi)\right] \exp \left(\mathrm{i} 2 \varphi_{x}\right) \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)]+\left[\sin ^{2} \theta+\cos ^{2} \theta \exp (\mathrm{i} \varphi)\right] \exp \left(\mathrm{i} 2 \varphi_{y}\right) \sin \theta \cos \theta[1-\exp (\mathrm{i} \varphi)] \\ d=\left[\sin ^{2} \theta+\cos ^{2} \theta \exp (\mathrm{i} \varphi)\right]^{2} \exp \left(\mathrm{i} 2 \varphi_{y}\right)-\sin ^{2} \theta \cos ^{2} \theta[1-\exp (\mathrm{i} \varphi)]^{2} \exp \left(\mathrm{i} 2 \varphi_{x}\right) \end{array}\right. (4)

    计算时选用了目前常用的\lambda / 4波片与半波片进行旋转调制, 可以得到两种波片旋转下, s偏振光经过偏振分光棱镜耦合输出的透过率与快轴旋转角度\theta的关系。

    图 2\lambda / 4波片旋转0^{\circ} \sim 180^{\circ}可获得的最大耦合输出透过率约为78 \%, 半波片可获得的最大耦合输出透过率约为58 \%。实验中选择了半波片进行耦合输出透过率的控制, 上述构型转动波片等效于调节激光器半反镜的反射率。

    图 2 s偏振光耦合透过率与波片旋转角度的关系
    图  2  s偏振光耦合透过率与波片旋转角度的关系
    Figure  2.  Relationship between the coupling transmittance of s-polarized light and the rotation angle of wave-plate

    Q技术是在激光器中获得高峰值功率输出的有效技术途径, 在构成调Q的前提时, 需要使得谐振腔内具备调Q开门和关门两种状态, 电光调Q技术是基于谐振腔内的偏振控制而设计的, 采用加压调Q, 目前主要有两种构型方式: 一种是采用正交偏振片技术进行调Q关门; 另一种则是采用特殊波片进行腔内的关门。

    正交偏振态关门时, p偏振光经过调Q晶体后被其后端正交放置的偏振分光棱镜反射出谐振腔, 谐振腔无法振荡, 而当调Q晶体施加半波电压时, 能够在谐振腔内边振荡边耦合输出; 特殊波片关门时, 需要根据直角棱镜的材料特性进行设计, 关门时需要旋转波片使得腔内处于关门状态, 由于图 3中的直角棱镜与图 1耦合输出端的直角棱镜为正交放置, x方向上的p偏振光入射时的琼斯矩阵为\left[\begin{array}{l}E_{x_{0}} \\ E_{y_{0}}\end{array}\right]=\left[\begin{array}{l}1 \\ 0\end{array}\right], 但是相对于图 3中的正交放置的直角棱镜的参考坐标系, 可以理解为入射的p偏振光旋转了90^{\circ}, 此时p偏振光入射时的琼斯矩阵为\left[\begin{array}{l}E_{x_{0}{ }^{\prime}} \\ E_{y^{\prime}}{ }^{\prime}\end{array}\right]=\left[\begin{array}{l}0 \\ 1\end{array}\right]

    图 3 两种不同偏振态控制关门方式示意图
    图  3  两种不同偏振态控制关门方式示意图
    Figure  3.  Schematic diagram of control closed methods by two different polarization state

    将调Q晶体看成是与xy轴成45°角的波片,其相位延迟与施加的电压有关,设其琼斯矩阵为K :

    \begin{gathered} \boldsymbol{K}=\left[\begin{array}{ll} e & f \\ g & h \end{array}\right]= \\ {\left[\begin{array}{cc} \frac{1+\exp (\mathrm{i} {\rm{ \mathsf{ δ} }} k)}{2} & \frac{1-\exp (\mathrm{i} {\rm{ \mathsf{ δ} }} k)}{2} \\ \frac{1-\exp (\mathrm{i} {\rm{ \mathsf{ δ} }} k)}{2} & \frac{1+\exp (\mathrm{i} {\rm{ \mathsf{ δ} }} k)}{2} \end{array}\right] \stackrel{\substack{e=h \\ f=g}}{\longrightarrow}\left[\begin{array}{ll} e & f \\ f & e \end{array}\right]} \end{gathered} (5)

    式中, e, f, g, h是2阶矩阵\boldsymbol{K}中的各个参数; \delta k是相位延迟量, 与其调Q晶体上施加的高压有关(实验中采用了\lambda / 4波电压)。于是根据图 3中的关门状态变化, 可得到在该直角棱镜坐标系下, 入射光经过波片和直角棱镜组合的琼斯矩阵变化后偏振态的转变满足\left[\begin{array}{l}0 \\ 1\end{array}\right] \stackrel{D}{\longrightarrow}\left[\begin{array}{l}1 \\ 0\end{array}\right], 而经过调Q晶体、波片和直角棱镜组合再次经过直角棱镜的偏振态的转变满足\left[\begin{array}{l}0 \\ 1\end{array}\right] \stackrel{\boldsymbol{K D K}}{\longrightarrow}\left[\begin{array}{l}0 \\ 1\end{array}\right]。仿真中主要关注y方向的偏振态, 对应于其琼斯矩阵上x方向上的归一化的幅值。

    Q晶体不施加电压时, p偏振光经过\boldsymbol{D}变换后变成s偏振光; 当调Q晶体施加1 / 4波电压, p偏振光经过\boldsymbol{K D} \boldsymbol{K}变换后变成p偏振光。所选择的直角棱镜的材料不同, 维持关门状态时所用到的波片不同, 如图 4所示。针对常用的K9玻璃制作的直角棱镜, 选用0.648 \lambda波片或0.352 \lambda波片能够保证其关门状态。

    图 4 两种波片实现调Q关门状态
    图  4  两种波片实现调Q关门状态
    Figure  4.  Simulation results of two kinds of wave-plates to realize the Q-switched closed state

    为了控制激光输出光束质量,获得高光束质量,小发散角的激光输出,在构型上需要将直角棱镜的透光面加工成曲面来进行腔型控制。图 5为激光器光路原理图。图中,KTP(kalium titanyl phosphate)为磷酸钛氧钾, LDA(laser diode array)为激光二极管阵列。

    图 5 激光器光路原理图
    图  5  激光器光路原理图
    Figure  5.  Schematic diagram of laser light path

    在光路构型上进行了波片关门(见图 5a)和正交偏振关门(见图 5b)两种状态的对比实验,两种构型选用了相同的LD端面抽运系统,其中抽运源为多巴条状的阵列,耦合系统能将抽运光耦合至Nd ∶YAG激光棒中,并通过分光镜实现抽运光路的折转,使得抽运光光路与振荡激光光路相互垂直。带有曲率设计的直角棱镜在腔型设计分析时, 一般根据厚透镜矩阵将其等效成一个厚透镜。

    图 6所示为该型谐振腔的循环矩阵。其中E和T为带曲率设计的直角棱镜等效厚透镜,F为凸镜,L1L2表示距离。上述模型需要将谐振腔的参量因子控制在0.99左右,来实现大基膜稳定谐振腔设计。但是由于该类谐振腔处于临界腔附近,热不灵敏性差,抽运功率的变化引起激光器的热焦距扰动时,会使得谐振腔稳定性参数变小(参数变小时会影响到基模的光场分布,进而影响到激光输出光束质量)或沦为非稳腔,这些扰动对维持好光束性能是不利的,因此需要将端面抽运激光棒的热焦距准确测量出来,并保持固定的抽运功率进行抽运,根据腔型的曲率匹配和设计,可以得到谐振腔内各个位置处的基模光束分布图。

    图 6 谐振腔循环矩阵组成
    图  6  谐振腔循环矩阵组成
    Figure  6.  Circular matrix composition of the resonator

    图 7中横坐标距离与图 6中循环矩阵相互对应,说明光需要经过L1的距离、YAG的长度距离、L2的距离、再一次经过L2的距离、YAG的长度距离和L1的距离,是光在谐振腔内往返一次的循环。从图 7可知, 谐振腔内激光棒附近的基模光斑直径约为1.6 mm,而设计的激光棒的直径为5 mm,实际多阶模束腰的直径要少于该值;根据高阶模公式, 预测该谐振腔可起振4阶次横模。

    图 7 谐振腔内基模光场分布
    图  7  谐振腔内基模光场分布
    Figure  7.  Distribution of TEM00 mode light field in resonator

    利用激光器电源驱动LD阵列,其工作重频为1 Hz/20 Hz,放电脉宽为200 μs,采用NOVA-Ⅱ型能量计测量波片关门时的LD端面抽运激光器的输出性能,激光器输出的能量与转化效率(包含激光器的动静比与光光效率)情况如图 8所示。

    图 8 波片关门下激光输出能量与效率曲线
    图  8  波片关门下激光输出能量与效率曲线
    Figure  8.  Laser output energy and efficiency under wave-plate closed state

    在20 Hz的条件下,LD端面抽运的结构存在一个热焦距建立和稳定的过程,经过该过程后才能够满足大基模尺寸稳定谐振腔的条件,在20 Hz的条件下容易获得更高的基模能量提取,该重频下激光获得的最大单脉冲能量为80 mJ,光光转化效率能达到12.4%,LD端面抽运的最大动静比约为61%。

    更换成正交偏振开关进行调Q关门后获得激光输出的性能曲线如图 9所示。

    图 9 正交偏振关门下激光输出能量与效率曲线
    图  9  正交偏振关门下激光输出能量与效率曲线
    Figure  9.  Laser output energy and efficiency under orthogonal polarization closed state

    在两种关门状态下,试验的腔型一致,但正交偏振关门的方式需要在光路中多增加一个PBS,该关门方式的腔长略长,两种情况下的静态能量相仿,但是采用正交偏振进行调Q关门时,其动态输出的斜率效率和能量明显要低于波片关门的情况,此时相同抽运注入下能够获得的最大能量约为72.2 mJ,最大的光光转化效率约为11%。

    实验时利用光束质量分析仪对两种关门情况下的激光输出光束质量进行了测量和对比,其中利用正交偏振调Q进行关门时所获得的光束质量输出结果如图 10所示。

    图 10 正交偏振关门下激光输出光束质量
    图  10  正交偏振关门下激光输出光束质量
    Figure  10.  Laser output beam quality under orthogonal polarization closed state

    通过图 10可以看到, 两个方向光束质量并不相同, 其中水平x方向上的光束质量M_{x}{ }^{2} \approx 8, 坚直y方向的光束质量M_{y}{ }^{2} \approx 6.4, 两个方向的发散角分别为1.99 \mathrm{mrad}1.6 \mathrm{mrad}

    利用同样的装置测试0.648λ波片进行调Q关门的光束质量结果如图 11所示。两个方向上光场依然不对称,波片关门的总体效果要比正交偏振关门的效果要更好,该构型的腔长相对较短,更加匹配大基模尺寸稳定谐振的条件, 其中, 水平x方向上的光束质量M_{x}{ }^{2} \approx 5.7, 坚直y方向的光束质量M_{y}{ }^{2} \approx 4.8, 两个方向的发散角分别为1.65 \mathrm{mrad}1.36 \mathrm{mrad}, 通过套孔法实测的激光发散角约为1.5 \mathrm{mrad}; 根据理论计算公式, 激光器的光束质量理论值约为5.5, 理论结果与实测的M^{2}结果相仿。

    图 11 波片关门下激光输出光束质量
    图  11  波片关门下激光输出光束质量
    Figure  11.  Laser output beam quality under wave-plate closed state

    本文中研究了一种LD端面抽运的正交直角棱镜腔激光器,通过理论与实验对比了正交偏振调Q关门和特殊波片关门两种技术途径,均能获得较好的激光性能输出结果。利用0.648λ波片作用于K9材料的直角棱镜进行调Q关门,验证了理论仿真与实验相仿,该设计能够获得良好的关门状态;通过带曲率设计的正交直角棱镜腔,在满足大基模尺寸谐振腔条件下,能够获得重频20 Hz、单脉冲能量80 mJ、光束质量Mx2≈5.7、My2≈4.8的高光束质量的激光输出,该性能指标能够满足常规机载小型化激光测照的使用要求。本文中的技术内容对机载小型化激光测照系统激光辐射器的设计与研制具有一定的参考与借鉴作用。

  • 图  1   AFC吸收线型的制备

    图  2   CRIB协议能级示意图

    图  3   原子频梳(AFC)示意图

    图  4   AFC协议存储时序(一般存储与按需存储)示意图

    图  5   AFC协议存储过程能级示意图

    图  6   双脉冲回波示意图[24]

    图  7   ROSE协议示意图[27]

    图  8   CRIB协议存储实验图[33]

    图  9   AFC存储实验图[35]

    图  10   频率上转换存储实验装置及特性图[36]

    图  11   掺铒光纤存储实验装置及测量结果图[37]

    图  12   片上存储实验装置及测量结果图[41]

    图  13   通信波段多路复用的宽带单光子存储实验装置及测量结果图[44]

    图  14   ROSE实验中磁场、光束及其偏振方向[46]

    图  15   ROSE回波及其效率[46]

    图  16   ROSE效率与光学厚度的函数曲线[46]

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    1. 魏世海,张雪莹,廖金宇,樊博宇,范云茹,周强. 集成固态光量子存储器件研究进展. 信息通信技术与政策. 2023(07): 44-52 . 百度学术

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  • 收稿日期:  2021-08-15
  • 修回日期:  2021-08-30
  • 发布日期:  2022-01-24

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