电子竞技影响认知功能的作用机制

刘承宜; 唐璐; 孙莎莎; 白慕炜; 龚妍春; 蔺海旗

doi:10.6054/j.jscnun.2020019

电子竞技影响认知功能的作用机制

刘承宜^1, ,,
唐璐¹,
孙莎莎²,
白慕炜^{1, 3},
龚妍春^{1, 4},
蔺海旗^{1, 5}

1.
华南师范大学体育科学学院，广州 510006
2.
仲恺农业工程学院人文与社会科学学院，广州 510225
3.
广东药科大学体育学院，广州 510006
4.
江西科技师范大学生命科学学院，南昌 330038
5.
华南理工大学体育学院，广州 510006

基金项目:

国家重点研发计划项目 2017YFB0403800

详细信息

通讯作者:
刘承宜, 教授, Email:liutcy@scnu.edu.cn

中图分类号: G623.8
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出版历程
- 收稿日期: 2019-11-29
- 网络出版日期: 2021-03-21
- 刊出日期: 2020-04-24

The Mechanism of Esport Influencing Cognitive Function

LIU Chengyi^1, ,,
TANG Lu¹,
SUN Shasha²,
BAI Muwei^{1, 3},
GONG Yanchun^{1, 4},
LIN Haiqi^{1, 5}

1.
School of Physical Education & Sports Science, South China Normal University, Guangzhou 510006, China
2.
College of Humanities and Social Sciences, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China
3.
School of Physical Education, Guangdong Pharmaceutical University, Guangzhou 510006, China
4.
School of Life Sciences, Jiangxi Science and Technology Normal University, Nanchang 330038, China
5.
School of Physical Education, South China University of Technology, Guangzhou 510006, China

摘要

摘要: 电子竞技作为新兴体育运动项目之一，受到了越来越多的关注.电子竞技对健康的影响是研究者感兴趣的一个主题.近些年来，习惯性电子竞技与认知能力之间的关系成为研究热点.通过对该领域研究进展的综述发现，习惯性电子竞技可以增强认知功能，主要通过注意功能、视觉空间功能和认知控制功能的提高、认知负荷的增大、技能习得的加快以及奖赏加工的增强等方面来实现.研究结果证实了脑的可塑性，同时表明习惯性电子竞技可以帮助人们更加有效地学习与工作.
- 电子竞技 /
- 认知功能 /
- 习惯性行为 /
- 小脑 /
- 正则通路
Abstract: As one of the emerging sports, Esport has attracted more and more attention. The impact of Esport on health is a topic of interest to researchers. In recent years, the relationship between habitual Esport and cognitive abilities had become a hot topic of research. Through a review of research progress in this field, it was found that habitual Esport could enhance cognitive function, mainly through the improvement of attention function, visual space function and cognitive control function, the increase of cognitive load, the acceleration of skill acquisition, and rewards processing enhancement. The results confirm the plasticity of the brain and show that habitual Esport can help people learn and work more effectively.
- Esport /
- cognitive function /
- habitual behavior /
- cerebellum /
- normal function-specific signal transduction pathways

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复合脉冲是一组具有确定相位的脉冲序列，能够自动补偿操控误差，实现高效率高鲁棒性的量子态操控.复合脉冲是通用有效的量子态操控工具，主要被用于核磁共振^[1]、量子信息^[2-3]和量子光学^[4-7]中两能级系统的量子操控.近年来的研究开始将复合脉冲技术用于三态和多态量子系统中^[7-8].由于它在量子系统相干控制中的鲁棒性和精确性，复合脉冲序列已在原子物理^{[4, 6, 9]}、固态量子传感器的磁力测量^[10]、分子光谱^[11]和原子干涉测量^[12]中得到了应用.复合脉冲在多态量子系统中也有很多重要应用，例如，利用复合脉冲的鲁棒性，采用复合脉冲可构造对各种实验参数误差不敏感的高保真量子相位门^[13]; 利用复合脉冲结合受激拉曼绝热通道技术，可以在冷原子系统中实现无中间激发态布居的基态到里德堡态的高效率粒子数转移^[14]; 复合脉冲还可被应用于因补偿频率偏移、场的不均匀性等引起的系统性误差，提高量子操控的精确性，达到量子计算和量子模拟的要求^[15-25].

要实现精确的量子态操控，通常要求量子系统中的量子态和相互作用有明确的定义.但在实际多态量子系统中，由于偏振激光没有严格按照量子化轴设置、存在非共振耦合目标外的量子态、系统扰动易产生额外激发等因素，会在该量子系统中产生额外的量子转移通道，造成量子态操控的保真度下降.例如在超冷原子量子模拟实验中，装载于光阱或光晶格中的原子与圆偏振光相互作用时，形成光阱或光晶格的是聚焦的高斯光场，光场强度呈现不均匀性.这使得在束腰以外位置的原子感受到的相互作用与势阱中心的原子感受到的相互作用会有偏差.通过控制脉冲序列的相对相位，复合脉冲技术能够自动补偿脉冲面积、脉冲频率的偏差，有效抑制额外的量子转移通道，实现高效率的粒子数转移，保持高保真的量子态操控.

本文为解决阶梯型三态量子系统的粒子定向转移问题，采用改进的复合脉冲操控方法，对影响粒子数转移效率和保真度的参数进行了研究.

1. 三能级复合脉冲理论

三能级阶梯型系统如所示，利用耦合光操控粒子从初态|1〉转移到目标态|2〉上.由于耦合光偏振不纯等因素，在加入耦合光时，会产生干扰光将|2〉态和|3〉态耦合起来.粒子从初态|1〉转移到目标态|2〉的过程中，会因为耦合光的作用产生额外的干扰通道，使处于|2〉态的粒子跃迁到|3〉态上去，造成目标态转移效率降低.采用复合脉冲的方法，可以有效抑制干扰光产生的额外转移通道，保持初态|1〉到目标态|2〉的高转移效率.该过程用薛定谔方程 ${\rm{i}}\hbar {\partial _t}c(t) = H(t)c(t)$ 描述，其中态矢量 $c(t)=\left[c_{1}(t), c_{2}(t), c_{3}(t)\right]^{\mathrm{T}}$ .在旋波近似下，哈密顿量算符如下

$\begin{array}{l} H=(\hbar / 2) \Delta\left(\mathit{\Pi}_{11}-\mathit{\Pi}_{22}-\mathit{\Pi}_{33}\right)+(\bar{h} / 2)\left[\mathit{\Omega}_{12}(t) \mathrm{e}^{i \varphi_{12}} \mathit{\Pi}_{12}+\right. \\ \left.\mathit{\Omega}_{23}(t) \mathrm{e}^{\mathrm{i} \varphi_{23}} \mathit{\Pi}_{23}+\mathrm{h.c.}\right], \end{array}$

(1)

图 1 系统结构示意图

注：图A为三能级阶梯型量子系统, 图B为利用Morris-Shore转换后的二能级和孤立态的系统.

Figure 1. The schematic diagram of system structure

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其中, Δ=Ω₀-Ω是激光频率Ω相对原子跃迁频率Ω₀的失谐量， $\mathit{\Pi}_{j k}=|j\rangle\langle k|$ .拉比频率为 ${\mathit{\Omega} _{jk}}(t) = \left| {{d_{jk}} \cdot E(t)} \right|/\hbar$ ，表征原子和光场的耦合强度，式中E(t)是激光的电场强度，d_jk是电偶极矩，2束激光的相位分别为ϕ₁₂和ϕ₂₃.假设2束激光脉冲有相同的脉冲形状f(t)，用总拉比频率Ω和混合角θ定义2束激光的拉比频率分别为Ω₁₂(t)=Ωf(t)cos θ和Ω₂₃(t)=Ωf(t)sin θ.

对于阶梯型系统，在用复合脉冲将粒子数从|1〉态转移到|2〉态的过程中，可以通过控制脉冲序列的相对相位ϕ_1j来抑制从|1〉态到|3〉态的转移路径.采用复合脉冲技术，即使在额外干扰光的耦合强度未知的情况下，仍可实现高效率的粒子数转移.

利用Morris-Shore转换^[6]将三能级阶梯型系统变换为由1个二能级系统和1个孤立态构成的系统：

$\left\{ {\begin{array}{*{20}{l}} {|d\rangle = {{\rm{e}}^{ - {\rm{i}}{\phi _{12}}}}\cos \theta |3\rangle + {{\rm{e}}^{ - {\rm{i}}{\phi _{23}}}}\sin \theta |1\rangle }\\ {\begin{array}{*{20}{l}} {|2\rangle = |2\rangle }\\ {|c\rangle = {{\rm{e}}^{{\rm{i}}{\phi _{23}}}}\sin \theta |3\rangle + {{\rm{e}}^{{\rm{i}}{\phi _{12}}}}\cos \theta |1\rangle } \end{array}} \end{array}} \right.,$

(2)

这里|2〉态和|c〉态构成一个二能级系统，|d〉态为一个孤立态.该系统的传播算子为

$U=\left(\begin{array}{ccc} a & b & 0 \\ -b^{*} & a^{*} & 0 \\ 0 & 0 & 1 \end{array}\right),$

(3)

其中，Cayley-Klein参数a和b取决于脉冲面积

$A=\int_{t_{i}}^{t_{f}} \mathit{\Omega} f(t) \mathrm{d} t, a=\cos (A / 2), b=-\mathrm{i} \sin (A / 2).$

由此可得原基失上的传播算子

$U(\phi)=\left(\begin{array}{ccc} a^{*} \cos ^{2} \theta+\zeta \sin ^{2} \theta & -A^{*} & \left(a^{*}-\zeta\right) B^{*} \\ A & a & C \\ \left(a^{*}-\zeta\right) B & -C^{*} & \zeta \cos ^{2} \theta+a^{*} \sin ^{2} \theta \end{array}\right),$

(4)

其中，

$A=b \mathrm{e}^{\mathrm{i} \phi_{12}} \cos \theta, B=\mathrm{e}^{\mathrm{i} \phi} \sin \theta \cos \theta, C=b \mathrm{e}^{\mathrm{i} \phi 23} \sin \theta.$

当脉冲面积为π时，Cayley-Klein参数a=0和b=-i，代入式(4)可得

$U \pi(\phi)=\\ \left(\begin{array}{ccc} \zeta \sin ^{2} \theta & -\mathrm{ie}^{-\mathrm{i} \phi_{12}} \cos \theta & -\zeta \mathrm{e}^{-\mathrm{i} \phi} \sin \theta \cos \theta \\ -\mathrm{ie}^{\mathrm{i} \phi_{12}} \cos \theta & 0 & -\mathrm{ie}^{\mathrm{i} \phi_{23}} \sin \theta \\ -\zeta \mathrm{e}^{\mathrm{i} \phi} \sin \theta \cos \theta & -\mathrm{ie}^{-\mathrm{i} \phi_{23}} \sin \theta & \zeta \cos ^{2} \theta \end{array}\right),$

(5)

其中,

$\phi = {\phi _{12}} - {\phi _{23}}, \zeta = \exp \left[ {{\rm{i}}\int_{{t_i}}^{{t_f}} \Delta (t){\rm{d}}t/2} \right].$

$U^{(n)}=U\left(\phi_{n}\right) U\left(\phi_{n-1}\right) \cdots U\left(\phi_{2}\right) U\left(\phi_{1}\right),$

(6)

其中， $\phi_{k}=\left(\phi_{12}^{k}, \phi_{23}^{k}\right)$ 是第k个脉冲的相位，当θ=0时，有 $P_{1 \rightarrow 2}=\left|U_{21}^{(n)}\right|^{2}=1$ ，通过泰勒展开θ的函数P_1→2，选择合适的 $\phi _{12}^k$ 和 $\phi _{23}^k$ , 使θ高阶项的系数为0，由此确定脉冲序列的相位.

复合脉冲中第k个脉冲作用时的薛定谔方程为

$\left[\begin{array}{c} \dot{c}_{1 k}(t) \\ \dot{c}_{2 k}(t) \\ \dot{c}_{3 k}(t) \end{array}\right]=-\frac{\mathrm{i}}{2}\left(\begin{array}{ccc} 0 & D & 0 \\ D^{\prime} & 2 \Delta & E \\ 0 & E^{\prime} & 0 \end{array}\right)\left[\begin{array}{c} c_{1 k}(t) \\ c_{2 k}(t) \\ c_{3 k}(t) \end{array}\right],$

(7)

其中， $D = \mathit{\Omega} \cos \theta {{\rm{e}}^{ - {\rm{i}}{\phi ^{k12}}}}, {D^\prime } = \mathit{\Omega} \cos \theta {{\rm{e}}^{{\rm{i}}{\phi ^{k12}}}}, E = \mathit{\Omega} \sin \theta \times {{\rm{e}}^{ - {\rm{i}}{\phi ^{k23}}}}, {E^\prime } = \mathit{\Omega} \sin \theta {{\rm{e}}^{{\rm{i}}{\phi ^{k23}}}}$ .

求解由n个脉冲组成的复合脉冲作用后量子态演化的结果，是将第k-1个脉冲作用后的末态作为第k个脉冲的初态，并依次求解第1, 2, 3, …, n个脉冲作用时的薛定谔方程，最后得到n个脉冲作用后的结果.假设初始1个粒子处在初态|1〉上，即c₁₁(0)=1，n个脉冲作用后该粒子处在目标态|2〉上的概率 $P_{1 \rightarrow 2}=\left|c_{2 n}(t)\right|^{2}$ .

2. 数值计算与分析

2.1 脉冲序列数的影响

考虑共振情况，单光子失谐Δ=0，即ζ=1，矩形脉冲且脉冲面积A=π的情形.当单脉冲作用时，取相位ϕ₁₂=0和 ϕ₂₃=0，传播算子为

$U^{(1)}(\phi)=\left(\begin{array}{ccc} \sin ^{2} \theta & -\mathrm{i} \cos \theta & -\sin \theta \cos \theta \\ -\operatorname{icos} \theta & 0 & -\operatorname{isin} \theta \\ -\sin \theta \cos \theta & -\sin \theta & \cos ^{2} \theta \end{array}\right),$

(8)

当复合脉冲为三脉冲序列时，每个脉冲的传播算子分别为U₁(ϕ)、U₂(ϕ)、U₃(ϕ)，三脉冲复合脉冲作用的总传播算子为U⁽³⁾=U₃(ϕ) U₂(ϕ) U₁(ϕ).可得到3个脉冲的相位(ϕ₁₂，ϕ₂₃)分别为(0，0)、(2π/3，-2π/3)和(π/6，π/6).同样，当复合脉冲为五脉冲序列时，总传播算子U⁽⁵⁾=U₅(ϕ)U₄(ϕ)U₃(ϕ)U₂(ϕ)U₁(ϕ).每个脉冲的相位(ϕ₁₂，ϕ₂₃)分别为(0，0)、(-4π/10，4π/10)、(-π/10，3π/10)、(7π/10，3π/10)和(-4π/10，0).矩形复合脉冲的相位和形状如图 2所示.

图 2 复合脉冲的相位

Figure 2. The composite pulse phase

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将以上参数依次代入式(7)，通过数值求解得到|1〉态到|2〉态的转移效率(P_1→2)以及|1〉态到|3〉态的转移效率(P_1→3)与混合角θ的关系如图 2所示.当θ=0，在无额外转移通道时，粒子数全部从|1〉态转移到|2〉态.当θ偏离零点并逐渐增大时，干扰光的作用逐渐增强，额外的转移通道会逐渐开启，当复合脉冲为多脉冲序列时能有效抑制额外的转移通道，使P_1→2保持为1.由图 3可知，在单脉冲条件下，θ在开始偏离零点时，P_1→2立即下降; 在三脉冲序列条件下，只有当θ>0.36时P_1→2才开始下降; 在五脉冲序列条件下，只有当θ>0.59时P_1→2才开始下降.因此，随着脉冲序列数的增加，复合脉冲对混合角θ的鲁棒性越好，抵抗额外转移通道干扰的能力越强.

图 3 不同脉冲序列下转移概率P随混合角θ的变化

注：图中1、3、5分别代表单脉冲、三脉冲以及五脉冲的情况，下同.

Figure 3. The variation of transition probability P with mixing angle θ under different pulse sequences

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进一步计算转移效率P_1→2和P_1→3与拉比频率比值Ω₂₃/Ω₁₂的关系(图 4).在单脉冲条件下，只要干扰光的拉比频率大于0，P_1→2即可快速降低.在三脉冲条件下，当干扰光的拉比频率大于耦合光拉比频率的40%时，P_1→3才开始从1下降.而对于五脉冲，干扰光的拉比频率一直增加到耦合光拉比频率的60%时，P_1→3才开始从1下降到0.999.这说明即使干扰光较强(相当于耦合光的光强)，多脉冲的复合脉冲仍然能够很好地抑制额外的转移通道，保持高效率、高保真度的量子操控.在通常多态量子系统中，由于参数不完美或系统扰动产生的额外耦合强度一般远小于目标耦合的强度，即此时Ω₂₃/Ω₁₂ < 10%，采用多脉冲序列的复合脉冲能够完全抑制额外的转移通道，避免量子操控的保真度的降低.

图 4 不同脉冲序列下转移概率随拉比频率比的变化

Figure 4. The change of transfer probability with the ratio of Rabi frequency under different pulse sequences

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2.2 脉冲面积的影响

其他参数不变，只改变脉冲面积，得到转移效率P_1→2与混合角θ的关系(图 5).当脉冲面积偏离π时，单脉冲的P_1→2即使在混合角θ为0(即没有额外耦合)时，都会明显降低.而采用三脉冲序列的复合脉冲时，当脉冲面积减为原来的一半(即π/2)、混合角θ < 0.1时，P_1→2始终保持在90%以上.当脉冲面积为3π/4、混合角θ < 0.1时，P_1→2能够保持在98%以上.所以多脉冲序列的复合脉冲对于脉冲面积的参数扰动，也具有很好的抗干扰能力.

图 5 不同脉冲面积下转移概率随混合角的变化

注：图中π/2、3π/4、π分别代表脉冲面积.

Figure 5. The change of transition probability with mixing angle under different pulse areas

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2.3 失谐量的影响

最后改变单光子失谐量，分别取失谐量Δ为0.1/T、0.2/T、0.5/T，这里T是脉冲宽度，计算转移效率P_1→2与混合角θ的关系(图 6).在三脉冲条件下，当失谐量Δ=0.5/T、θ < 0.13时，转移效率可保持在90%以上.当失谐量较小、Δ=0.2/T、θ < 0.13时，转移效率可保持在0.98以上; 而当Δ=0.1/T、θ < 0.13时，转移效率可保持在0.99以上.由此可见，当单光子失谐量不为0、偏离共振点时，多脉冲序列的复合脉冲能够进行补偿并保持高效率的粒子数转移.

图 6 不同失谐量下转移概率随混合角的变化

注：黑线、红线、蓝线分别代表失谐量Δ=0.1/T、0.2/T、0.5/T的情况.

Figure 6. The change of transition probability with mixing angle under different detuning degrees

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3. 结论

复合脉冲操控量子态技术通常被用于二态量子系统，本文将该技术推广到阶梯型的三态量子系统.通过Morris-Shore变换，将三态量子系统等价转化为1个二态系统和1个孤立态，采用二态传播算子描述该量子系统的演化过程.求出n个脉冲序列复合脉冲的总传播算子U⁽ⁿ⁾，当θ=0时，令 ${P_{1 \to 2}} = {\left| {U_{21}^{(n)}} \right|^2} = 1$ ，通过泰勒展开θ的函数(P_1→2)，选择合适的第k个脉冲的相位( $\phi _{12}^k$ 和 $\phi _{23}^k$ )，使θ高阶项的系数为0，由此确定脉冲序列的相位.考虑共振时，面积为π的矩形脉冲序列与阶梯型三态量子系统的相互作用，求解含时薛定谔方程，结果表明：通过增加脉冲序列数并控制单个脉冲的相位，即可达到高效率、高鲁棒性的量子态操控和粒子数转移.即使存在额外的干扰光作用时，多脉冲序列的复合脉冲也可以很好地抑制额外的转移通道，实现高效率、高保真度的量子态操控和粒子数转移.

进一步通过数值模拟额外通道和转移通道的拉比频率比、脉冲面积的变化、单光子失谐偏离零点等因素对转移效率的影响，结果表明：增加脉冲序列数可有效抵抗相关参数的扰动，保持高效率的粒子数转移.多脉冲序列复合脉冲的技术可被用于解决实际实验中偏振不纯、激光频率不纯、控制参数扰动等造成的量子态操控效率不高的问题.该方法对构造量子门、量子模拟等相关研究具有重要意义.

图 1 习惯性玩家与非习惯性玩家在注意功能的比较^[4]

Figure 1. The comparison of attention functions between habitual player and non-habitual player^[4]

下载: 全尺寸图片幻灯片

图 2 电子竞技习惯回路的形成

Figure 2. The formation of Esport habit loop

下载: 全尺寸图片幻灯片

图 3 电子竞技与小脑活动的正则通路关系的可能机制^[80]

Figure 3. The possible mechanism of the relationship between Esports and the cerebellum's NSP

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1. 三能级复合脉冲理论
2. 数值计算与分析
2.1 脉冲序列数的影响
2.2 脉冲面积的影响
2.3 失谐量的影响
3. 结论

电子竞技影响认知功能的作用机制

通讯作者: 刘承宜, 教授, Email:liutcy@scnu.edu.cn

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