由动态Stark效应诱导的氢原子涡旋动量分布 
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1 引言
近年来,随着超强激光技术的飞速发展,其与原子或分子相互作用的强场过程引起了人们的广泛关注。处于强激光场中的原子或分子通常会被电离或解离,所产生的光电子动量谱或能量谱可被用于研究相关的强场过程,因此原子或分子中光电子的动量分布得到了广泛研究[1-22]。当原子或分子被两个具有时间延迟的中等强度圆偏振激光脉冲电离时,所产生的电子波包之间将发生Ramsey干涉,从而可以在激光偏振平面上观察到涡旋状或螺旋结构的光电子动量分布[23-26]。2016年,Ngoko Djiokap等[25]通过对圆偏振激光脉冲作用下氦原子的单电离过程进行数值研究发现,当激光脉冲载波频率为15 eV且强度为1×1012 W/cm2时,所产生的光电子动量分布会呈现奇重和偶重对称结构。此外,光电子的涡旋动量分布已经在钾原子实验中得到了证实[26]。
动态Stark效应,也被称为光学Stark效应,存在于几乎所有的强场过程中[27-30]。2012年,Demekhin等[31]在氢原子的光电子能谱中发现了一类新的干涉条纹,并证实这种新光谱特性是由动态Stark效应引起的。在一定条件下,动态Stark效应会引起原子能级随激光电场包络函数的平方移动,即该能级移动与时间有关,而与激光脉冲的载波频率无关[30-33]。值得注意的是,动态Stark效应会使氢原子的基态能级上移[34]。
20世纪中期,Keldysh[35]在研究原子与强激光场的相互作用时提出可忽略库仑势对电离原子的影响,之后Faisal[36]和Reiss[37]分别对Keldysh理论进行了改进,形成KFR理论,现已发展成强场近似(SFA)理论[1,38-39],成为相关领域常用的解析方法。
本文研究的原子中光电子动量分布的涡旋特性,与以往研究的氢原子的涡旋方向[40]不同。采用SFA方法,通过改变激光脉冲载波频率以及动态Stark效应的强度,对处于两个圆偏振激光场中的氢原子的顺时针涡旋状动量分布的产生、扭曲及机理进行了数值模拟,并研究了强光与原子相互作用的光谱表现。
2 数值方法
SFA方法是目前强场物理领域常用的解析计算手段,已被成功用于计算过阈电离(ATI)和高次谐波产生(HHG)等[1,41-45]。研究采用SFA方法,模拟计算光电离产生的氢原子的涡旋状动量分布。假定氢原子被两个具有时间延迟的圆偏振阿秒激光脉冲电离,则激光电场的分量
式中:
式中:
式中:
这种在SFA方法中利用有效电离势来模拟动态Stark效应的表达已经得到了验证[32-33,43],并且SFA理论也被大量应用于类似的强场过程研究中[46-51],其Keldysh参数
通过改变激光脉冲强度
3 结果与讨论
图 2. 氢原子动量涡旋图。(a)~(c) 两延时脉冲“右/左”圆偏振(第一个脉冲是右旋圆偏振,第二个脉冲是左旋圆偏振)的情况;(d)~(f) 两延时脉冲“左/右”圆偏振的情况
Fig. 2. Vortex-shaped momentum distributions of hydrogen atom. (a)-(c) ‘Right/left’ polarization for two time-delayed pulses (first is right circularly polarized and second is left circularly polarized); (d)-(f) ‘left/right’ polarization for two time-delayed pulses
如
图 3. 动态Stark效应作用下的氢原子动量涡旋图。(a)~(c)对应两延时脉冲“右/左”圆偏振的情况;(d)~(f)对应两延时脉冲“左/右”圆偏振的情况。激光脉冲参数与图2相同
Fig. 3. Vortex-shaped momentum distributions of hydrogen atom when dynamic Stark effect is considered. (a)-(c) ‘Right/left’ polarization for two time-delayed pulses; (d)-(f) ‘left/right’ polarization for two time-delayed pulses. Laser pulses parameters are same as in Fig. 2
图 4. α=0到α=0.04的动量涡旋变化图。(a) α=0(涡旋臂编号为1,2,3,4);(b) α=0.04(箭头指示臂2峰位置的移动);(c) 各臂峰值强度变化图;(d) 各臂极角变化图
Fig. 4. Transition of vortex-shaped momentum distributions from α=0 to α=0.04. (a) α=0 (vortex arms numbered as 1, 2, 3, 4); (b) α=0.04 (arrow illustrating corresponding shift of peak position of second vortex arm); (c) variation of peak intensity of each arm; (d) variation of polar angle of each arm
从
动态Stark效应会引入一个附加相位,即Stark相位,该附加相位在氢原子动量涡旋的扭曲过程中发挥着重要作用。在SFA 理论中,可以通过有效电离势的形式将该附加相位叠加到光电子半经典动作相位上。(4)式给出了总相位(即半经典动作相位
图 5. 相位随时间的变化图。(a)~(d) 附加Stark相位,分别对应α=0.01, 0.02, 0.03, 0.04; (e)~(h) 各臂总相位 (半经典动作相位+Stark相位);(i) 有(实线)、无(虚线)Stark效应情况下各臂总相位对比
Fig. 5. Time evolution of different kinds of phases. (a)-(d) Stark phases for α=0.01, 0.02, 0.03, 0.04; (e)-(h) total phase (semiclassical phase+Stark phase) for each vortex arm; (i) comparison of total phases with (solid line) and without (dashed line) Stark effect for each vortex arm
如
图 6. 2~8 o.c.间积分重现的动量涡旋图。(a) α=0.04; (b)脉冲包络函数F(t)为单位常数
Fig. 6. Vortex-shaped momentum distributions reproduced by integrating between 2 o.c and 8 o.c. (a) α=0.04; (b) pulse envelope function F(t) is unit constant
4 结论
利用SFA方法,对强激光脉冲作用下氢原子的光电子动量分布进行了大量的数值模拟。当两个具有时间延迟的反向圆偏振激光脉冲作用于氢原子时,会产生涡旋状的光电子动量分布。如果将动态Stark效应考虑在内,由于附加Stark相位对光电子总相位的影响,光电子动量涡旋会发生扭曲,并且扭曲程度会随着Stark效应的增强而加剧;这种扭曲是由附加Stark相位的时间非线性特性引起的。该研究利用了氢原子的光电子动量涡旋谱对动态Stark效应敏感的特点,可为研究强激光场特性提供一种新的手段。
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