Intensity-dependent electron correlation in nonsequential double ionization of Ar atoms in counter-rotating two-color elliptically polarized laser fields

Su Jie; Liu Zi-Chao; Liao Jian-Ying; Li Ying-Bin; Huang Cheng

doi:10.7498/aps.71.20221044

Abstract

Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in a counter-rotating two-color elliptically polarized (TCEP) field are investigated by using a three-dimensional classical ensemble model. The numerical results show that the correlated momentum distribution of electron pairs in the x-axis direction evolves from a V-shaped structure in the first quadrant at the low intensity, to an arc-shaped structure mainly located in the second and fourth quadrants at moderate intensity, finally to a distribution near the origin located in the first quadrant in the high intensity. With the laser intensity increasing, the dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation. The combined electric field traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions. Each leaf is called a lobe. The electric field recursively evolves from lobe 1 to lobe 2 and to lobe 3. Unlike the counter-rotating two-color circularly polarized fields, the combined fields from two elliptical fields do not have the spatial symmetry. Amplitudes of the three field lobes and the angles between them are different. Furthermore, the back analysis of NSDI trajectories shows that the single ionization in NSDI events mainly occurs in lobe 1 and lobe 3, and the contribution from lobe 1 increases and that from lobe 3 decreases with the increase of the intensity. Correspondingly, the free electrons mainly return to the parent ion from 20° and 175°. With the laser intensity increasing, the electrons returning from 20° gradually increase and those returning from 175° gradually decrease. In order to further understand the correlation behaviors of electron pairs in the x-axis direction, the NSDI events triggered off by single ionization from different lobes are separately discussed. With the increase of laser intensity the correlation behavior of NSDI events triggered off by single ionization from field lobe 1 evolves from anti-correlation behavior to correlation behavior, but the correlation behavior of NSDI events induced by single ionization from field lobe 3 evolves from correlation behavior to anti-correlation behavior. With the laser intensity increasing, the NSDI events induced by single ionization from field lobe 1 increase gradually, but those from field lobe 3 decrease. This results in that the total dominant correlation behavior evolves from correlation to anti-correlation and finally reverts back to correlation as the laser intensity increases.

Keywords:

two-color elliptically polarized fields /
nonsequential double ionization /
electron correlation /
recollision

Authors and contacts

1.
Chongqing City Key Laboratory of Micro & Nano Structure Optoelectronics, School of Physical Science and Technology, Southwest University, Chongqing 400715, China
2.
College of physics and Electronic Engineering, Xinyang Normal University, Xinyang 464000, China

Corresponding author: Li Ying-Bin, liyingbin2008@163.com ; Huang Cheng, huangcheng@swu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11504302, 12074329, 12004323, 12104389), Southwest University Training Program of Innovation and Entrepreneurship for Undergraduates (Grant No. X202210635104), and Nanhu Scholars Program for Young Scholars of Xinyang Normal University.

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References

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Cited By

图 1 反向旋转TCEP复合激光电场 E(t) (虚线) 和相应的负矢势 –A(t) (实线) , 箭头表示时间演化方向, 激光强度为 2 × 10¹³ W/cm²

Figure 1. Combined laser electric field E(t) (dashed curve) and corresponding negative vector potential –A (t) (solid curve) at an intensity of 2 × 10¹³ W/cm², arrows indicate the direction of time evolution.

DownLoad: Full-Size Img PowerPoint

图 2 反向旋转 TCEP场中Ar原子双电离概率的强度依赖

Figure 2. Double ionization probability of Ar atoms in the counter-rotating TCEP laser field as a function of laser intensity.

DownLoad: Full-Size Img PowerPoint

图 3 不同强度下 x 方向上的相关电子动量谱　(a) 2 × 10¹³ W/cm²; (b) 4 × 10¹³ W/cm² ; (c) 6 × 10¹³ W/cm²; (d) 8 × 10¹³ W/cm²

Figure 3. Correlated electron momentum distributions in the x direction for different intensities: (a) 2 × 10¹³ W/cm²; (b) 4 × 10¹³ W/cm²; (c) 6 × 10¹³ W/cm²; (d) 8 × 10¹³ W/cm²

DownLoad: Full-Size Img PowerPoint

图 4 单电离时间(第1列) 、碰撞时间(第2列) 、碰撞后第1个(第3列)和第2个电子(第4列)的最终电离时间的统计分布. 为了更清楚显示碰撞和电离时刻的激光相位, 将碰撞时间和电离时间转换到一个激光周期, 其中彩色虚线给出了复合电场幅值的时间演化. 激光强度分别 2 × 10¹³ W/cm² (第1行)、4 × 10¹³ W/cm² (第2行) 、 6 × 10¹³ W/cm² (第3行) 和8 × 10¹³ W/cm² (第4行)

Figure 4. Distributions of single ionization time (the first column), recollision time (the second column) and final ionization times of the first (the third column) and second electron (the fourth column) after recollision for the intenstiies of 2 × 10¹³ W/cm² (the first row), 4 × 10¹³ W/cm² (the second row), 6 × 10¹³ W/cm² (the third row) and 8 × 10¹³ W/cm² (the fourth row). To more clearly show the laser phases of the recollision and ionization instants, the recollision and ionization times are transfered to one laser cycle. The dashed curve shows the combined electric field.

DownLoad: Full-Size Img PowerPoint

图 5 波瓣1 (第1行)和波瓣3 (第2行)处单电离诱导的NSDI事件在x方向的相关电子动量谱

Figure 5. Correlated electron momentum distributions in x direction for NSDI events induced by single ionizations at field lobe 1 (the first row) and field lobe 3 (the second row) for four different intensities.

DownLoad: Full-Size Img PowerPoint

图 6 波瓣1处单电离诱导的NSDI事件的单电离时间(第1列) 、碰撞时间(第2列) 、碰撞后第1个(第3列)和第2个电子(第4列)的最终电离时间的统计分布, 其他参数与图4相同

Figure 6. Distributions of single ionization time (the first column), recollision time (the second column) and final ionization times of the first (the third column) and second electron (the fourth column) after recollision for those NSDI events induced by single ionization at field lobe 1. Other parameters are the same as Fig. 4.

DownLoad: Full-Size Img PowerPoint

图 7 波瓣3处单电离诱导的NSDI事件的单电离时间(第1列) 、碰撞时间(第2列) 、碰撞后第1个(第3列)和第2个电子(第4列)的最终电离时间的统计分布, 其他参数与图4相同

Figure 7. Distributions of single ionization time (the first column), recollision time (the second column) and final ionization times of the first (the third column) and second electron (the fourth column) after recollision for those NSDI events induced by single ionization at field lobe 3, other parameters are the same as Fig. 4.

DownLoad: Full-Size Img PowerPoint

图 8 不同强度下电离电子返回方向的统计分布

Figure 8. Statistical distribution of return directions of ionized electrons for four intensities.

DownLoad: Full-Size Img PowerPoint

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[2]	Corkum P B 1993 Phys. Rev. Lett 71 1994 Google Scholar
[3]	Feuerstein B, Moshammer R, Fischer D, Dorn A, Schröter C D, Deipenwisch J, Crespo Lopez-Urrutia J R, Höhr C, Neumayer P, Ullrich J, Rottke H, Trump C, Wittmann M, Korn G, Sandner W 2001 Phys. Rev. Lett 87 043003 Google Scholar
[4]	Chen Y B, Zhou Y M, Li Y, Li M, Lan P F, Lu P X 2018 Phys. Rev. A 97 013428 Google Scholar
[5]	Liu Y Q, Fu L B, Ye D F, Liu J, Li M, Wu C Y, Gong Q H, Moshammer R, Ullrich J 2014 Phys. Rev. Lett 112 013003 Google Scholar
[6]	Huang C, Guo W L, Zhou Y M, Wu Z M 2016 Phys. Rev. A 93 013416 Google Scholar
[7]	Liao Q, Winney A H, Lee S K, Lin Y F, Adhikari P, Li W 2017 Phys. Rev. A 96 023401 Google Scholar
[8]	Ye D F, Li M, Fu L, Liu J, Gong Q H, Liu Y Q, Ullrich J 2015 Phys. Rev. Lett 115 123001 Google Scholar
[9]	Weber Th, Giessen H, Weckenbrock M, Urbasch G, Staudte A, Spielberger L, Jagutzki O, Mergel V, Vollmer M, Dörner R 2000 Nature 405 658 Google Scholar
[10]	Wang Y L, Xu S P, Quan W, Gong C, Lai X Y, Hu S L, Liu M Q, Chen J, Liu X J 2016 Phys. Rev. A 94 053412 Google Scholar
[11]	Figueira de Morisson Faria C, Liu X 2011 J. Mod. Opt 58 1076 Google Scholar
[12]	Becker W, Liu X, Jo Ho P, Eberly J H 2012 Rev. Mod. Phys 84 1011 Google Scholar
[13]	Li H, Chen J, Jiang H, Liu J, Fu P, Gong Q, Yan Z, Wang B 2009 J. Phys. B 42 125601 Google Scholar
[14]	Zhou Y M, Liao Q, Lu P X 2009 Phys. Rev. A 80 023412 Google Scholar
[15]	Wang X, Eberly J H 2010 Phys. Rev. Lett 105 083001 Google Scholar
[16]	Hao X L, Chen J, Li W D, Wang B B, Wang X D, Becker W 2014 Phys. Rev. Lett 112 073002 Google Scholar
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[18]	Huang C, Zhong M, Wu Z 2019 Opt. Express 27 7616 Google Scholar
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[30]	Peng M, Bai L, Guo Z 2021 Commun. Theor. Phys 73 075501 Google Scholar
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[32]	Chen Z, Su J, Zeng X, Huang X F, Li Y B, Huang C 2021 Opt. Express 29 29576 Google Scholar
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