同向旋转双色圆偏场中非次序双电离的频率比依赖

曾雪; 苏杰; 黄雪飞; 庞惠玲; 黄诚

doi:10.7498/aps.70.20211112

摘要

利用三维经典系综模型系统研究了不同频率比的两同向旋转圆偏场中Ar原子的非次序双电离. 数值结果显示, 非次序双电离的概率随两圆偏场频率比的增加而增加. 频率比为5时非次序双电离概率比频率比为2时的概率高出一个数量级. 非次序双电离的轨道分析表明, 再碰撞轨道主要以环形的短轨道为主, 并且随着频率比的增加, 电子碰前的旅行时间缩短. 进一步分析发现, 随着频率比的增加, 碰撞激发电离机制对非次序双电离的贡献逐渐增大, 而碰撞电离机制的贡献显著减小. 这是因为对于较大的频率比, 电子的返回能量更小, 且碰撞时两电子的碰撞距离更大.

关键词:

Abstract

Using a three-dimensional classical ensemble model, we investigate ultrafast dynamics in nonsequential double-ionization (NSDI) of Ar atom by co-rotating two-color circularly polarized laser fields with the frequency ratio varying between 2 and 5. Numerical results indicate that the NSDI probability gradually increases with the frequency ratio between the two components increasing. The probability for the frequency ratio 5 is one order of magnitude higher than for the frequency ratio 2. Back analysis of NSDI trajectories shows that recollision occurs mainly via a short looping trajectory. With the frequency ratio increasing, the traveling time of the free electron shortens. Furthermore, the relative contribution of recollision-induced excitation with subsequent field ionization mechanism in NSDI gradually increases as the frequency ratio increases. It is attributed to smaller recollision energy and larger recollision distance for larger frequency ratio.

Keywords:

作者及机构信息

西南大学物理科学与技术学院, 重庆　400715

通信作者: 黄诚, huangcheng@swu.edu.cn

基金项目: 国家自然科学基金(批准号: 11504302, 61475127, 12074329, 12004323)和国家级大学生创新创业训练计划(批准号: 202010635066)资助的课题

Authors and contacts

School of Physical Science and Technology, Southwest University, Chongqing 400715, China

Corresponding author: Huang Cheng, huangcheng@swu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11504302, 61475127, 12074329, 12004323) and the National Training Program of Innovation and Entrepreneurship for Undergraduates, China (Grant No. 202010635066)

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参考文献

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[2]	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
[3]	Chen Y, Zhou Y, Li Y, Li M, Lan P, Lu P 2018 Phys. Rev. A 97 013428 Google Scholar
[4]	Liu Y, Fu L, Ye D, Liu J, Li M, Wu C, Gong Q, Moshammer R, Ullrich J 2014 Phys. Rev. Lett. 112 013003 Google Scholar
[5]	Huang C, Guo W, Zhou Y, Wu Z 2016 Phys. Rev. A 93 013416 Google Scholar
[6]	Liao Q, Winney A H, Lee S K, Lin Y F, Adhikari P, Li W 2017 Phys. Rev. A 96 023401 Google Scholar
[7]	黄诚, 钟明敏, 吴正茂 2019 物理学报 68 033201 Google Scholar Huang C, Zhong M M, Wu Z M 2019 Acta Phys. Sin. 68 033201 Google Scholar
[8]	Fittinghoff D N, Bolton P R, Chang B, Kulander K C 1992 Phys. Rev. Lett. 69 2642 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, Xu S, Quan W, Gong C, Lai X, Hu S, Liu M, Chen J, Liu X 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 Y, Chen J, Jiang H B, Liu J, Fu P M, Gong Q H, Yan Z C, Wang B B 2009 J. Phys. B 42 125601 Google Scholar
[14]	Parker J S, Doherty B J S, Taylor K T, Schultz K D, Blaga C I, DiMauro L F 2006 Phys. Rev. Lett. 96 133001 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
[17]	Chen Z J, Liang Y, Lin C D 2010 Phys. Rev. Lett. 104 253201 Google Scholar
[18]	Ye D, Li M, Fu L, Liu J, Gong Q, Liu Y, Ullrich J 2015 Phys. Rev. Lett. 115 123001 Google Scholar
[19]	赵磊, 张琦, 董敬伟, 吕航, 徐海峰 2016 物理学报 65 223201 Google Scholar Zhao L, Zhang Q, Dong J W, Lü H, Xu H F 2016 Acta Phys. Sin. 65 223201 Google Scholar
[20]	Tan J, Xu S, Han X, Zhou Y, Li M, Cao W, Zhang Q, Lu P 2021 Adv. Photonics 3 035001 Google Scholar
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[22]	Fleischer A, Kfir O, Diskin T, Sidorenko P, Cohen O 2014 Nat. Photonics 8 543 Google Scholar
[23]	Eckart S, Kunitski M, Ivanov I, Richter M, Fehre K, Hartung A, Rist J, Henrichs K, Trabert D, Schlott N, Schmidt L P H, Jahnke T, Schoffler M S, Kheifets A, Dorner R 2018 Phys. Rev. A 97 041402 Google Scholar
[24]	Li M, Jiang W, Xie H, Luo S, Zhou Y, Lu P 2018 Phys. Rev. A 97 023415 Google Scholar
[25]	Ke Q, Zhou Y, Tan J, He M, Liang J, Zhao Y, Li M, Lu P 2019 Opt. Express 27 32193 Google Scholar
[26]	Chaloupka J L, Hickstein D D 2016 Phys. Rev. Lett. 116 143005 Google Scholar
[27]	Mancuso C A, Dorney K M, Hickstein D D, Chaloupka J L, Ellis J L, Dollar F J, Knut R, Grychtol P, Zusin D, Gentry C, Gopalakrishnan M, Kapteyn H C, Murnane M M 2016 Phys. Rev. Lett. 117 133201 Google Scholar
[28]	Eckart S, Richter M, Kunitski M, Hartung A, Rist J, Henrichs K, Schlott N, Kang H, Bauer T, Sann H, Schmidt L P H, Schoffler M, Jahnke T, Dorner R 2016 Phys. Rev. Lett. 117 133202 Google Scholar
[29]	Lin K, Jia X, Yu Z, He F, Ma J, Li H, Gong X, Song Q, Ji Q, Zhang W, Li H, Lu P, Zeng H, Chen J, Wu J 2017 Phys. Rev. Lett. 119 203202 Google Scholar
[30]	Li B, Yang X, Ren X, Zhang J 2019 Opt. Express 27 32700 Google Scholar
[31]	Xu T, Zhu Q, Chen J, Ben S, Zhang J, Liu X 2018 Opt. Express 26 1645 Google Scholar
[32]	Huang C, Zhong M, Wu Z 2018 Opt. Express 26 26045 Google Scholar
[33]	Ma X, Zhou Y, Chen Y, Li M, Li Y, Zhang Q, Lu P 2019 Opt. Express 27 1825 Google Scholar
[34]	Huang C, Pang H, Huang X, Zhong M, Wu Z 2020 Opt. Express 28 10505 Google Scholar
[35]	Pang H, Huang X, Huang C 2020 Int. J. Mod. Phys. B 34 2050304 Google Scholar
[36]	Peng M, Bai L H, Guo Z 2021 Commun. Theor. Phys. 73 075501 Google Scholar
[37]	Eichmann H, Egbert A, Nolte S, Momma C, Wellegehausen B 1995 Phys. Rev. A 51 R3414 Google Scholar
[38]	Qiao Y, Wu D, Chen J, Wang J, Guo F, Yang Y 2019 Phys. Rev. A 100 063428 Google Scholar
[39]	Huang C, Zhong M, Wu Z 2019 Opt. Express 27 7616 Google Scholar
[40]	Chaloupka J L 2020 J. Phys. B 53 185601 Google Scholar
[41]	Wu D, Guo F, Wang J, Chen J, Yang Y 2020 Commun. Theor. Phys. 72 055503 Google Scholar
[42]	Haan S L, Breen L, Karim A, and Eberly J H 2006 Phys. Rev. Lett. 97 103008 Google Scholar
[43]	Chen J, Nam C H 2002 Phys. Rev. A 66 053415 Google Scholar
[44]	Li Y, Xu J, Yu B, Wang X 2020 Opt. Express 28 7341 Google Scholar
[45]	Chen X, Ruiz C, He F, Zhang J 2020 Opt. Express 28 14884 Google Scholar
[46]	Huang C, Zhong M, Wu Z 2018 Sci. Rep. 8 8772 Google Scholar
[47]	Huang C, Zhong M, Wu Z 2016 J. Chem. Phys. 145 044302 Google Scholar

施引文献

图 1 不同频率比时同向旋转双色场的电场矢量(蓝虚线)和负矢势(红实线)　(a) 频率比为2; (b) 频率比为3; (c) 频率比为4; (d) 频率比为5. 箭头标出了时间演化的方向, 黑点标出了一个电场极大值及其对应的负矢势

Fig. 1. Combined laser electric field E(t) (dashed curves) and the corresponding negative vector potential A(t) (solid curves) for co-rotating two-color circularly polarized laser fields at different frequency ratios of (a) 2, (b) 3, (c) 4, (d) 5. The arrows indicate the time evolution direction. The black dots mark a field maximum and its negative vector potential.

下载: 全尺寸图片幻灯片

图 2 双电离与单电离的概率比对频率比的依赖

Fig. 2. Dependence of the ratio of double ionization probability to single ionization probability on frequency ratio.

下载: 全尺寸图片幻灯片

图 3 不同频率比时的电子动量分布　(a) 频率比为2; (b) 频率比为3; (c) 频率比为4; (d) 频率比为5

Fig. 3. Electron momentum distributions in the field plane at different frequency ratios of (a) 2, (b) 3, (c) 4, (d) 5.

下载: 全尺寸图片幻灯片

图 4 不同频率比时电子旅行时间的概率分布

Fig. 4. Distributions of electron traveling time at frequency ratios of 2, 3, 4 and 5.

下载: 全尺寸图片幻灯片

图 5 不同频率比时的再碰撞轨道　(a) 频率比为2; (b) 频率比为3; (c) 频率比为4; (d) 频率比为5

Fig. 5. Sample recollision trajectories at different frequency ratios of (a) 2, (b) 3, (c) 4, (d) 5.

下载: 全尺寸图片幻灯片

图 6 频率比分别为2 ((a), (b))和3 ((c), (d))时的两个长轨道　(a), (c)两电子能量的时间演化; (b), (d)两电子空间坐标演化

Fig. 6. Electron energies ((a), (c)) and positions in the field plane ((b), (d)) versus time for two sample long trajectories. Frequency ratios are 2 ((a), (b)) and 3 ((c), (d)), respectively.

下载: 全尺寸图片幻灯片

图 7 不同频率比时双电离延迟时间的概率分布

Fig. 7. Distributions of the delay time between double ionization and the recollision at frequency rations of 2, 3, 4 and 5.

下载: 全尺寸图片幻灯片

图 8 RESI和RII机制在NSDI中所占的比率对频率比的依赖

Fig. 8. Dependence of proportions of RESI and RII mechanism in NSDI on frequency ratio.

下载: 全尺寸图片幻灯片

图 9 频率比分别为2 ((a), (c)); 3 ((b), (d))时, RII机制((a), (b))和RESI机制((c), (d))对应的电子动量分布

Fig. 9. Electron momentum distributions in the field plane for RII ((a), (b)) and RESI ((c), (d)) mechanisms. Frequency ratios are 2 ((a), (c)) and 3 ((b), (d)), respectively.

下载: 全尺寸图片幻灯片

图 10 NSDI事件关于碰撞能量的概率分布

Fig. 10. Distributions of recollision energy at different frequency ratios of 2, 3, 4 and 5.

下载: 全尺寸图片幻灯片

图 11 NSDI事件关于碰撞距离的概率分布

Fig. 11. Recollison distance in NSDI at different frequency ratios.

下载: 全尺寸图片幻灯片

[1]	Corkum P B 1993 Phys. Rev. Lett. 71 1994 Google Scholar
[2]	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
[3]	Chen Y, Zhou Y, Li Y, Li M, Lan P, Lu P 2018 Phys. Rev. A 97 013428 Google Scholar
[4]	Liu Y, Fu L, Ye D, Liu J, Li M, Wu C, Gong Q, Moshammer R, Ullrich J 2014 Phys. Rev. Lett. 112 013003 Google Scholar
[5]	Huang C, Guo W, Zhou Y, Wu Z 2016 Phys. Rev. A 93 013416 Google Scholar
[6]	Liao Q, Winney A H, Lee S K, Lin Y F, Adhikari P, Li W 2017 Phys. Rev. A 96 023401 Google Scholar
[7]	黄诚, 钟明敏, 吴正茂 2019 物理学报 68 033201 Google Scholar Huang C, Zhong M M, Wu Z M 2019 Acta Phys. Sin. 68 033201 Google Scholar
[8]	Fittinghoff D N, Bolton P R, Chang B, Kulander K C 1992 Phys. Rev. Lett. 69 2642 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, Xu S, Quan W, Gong C, Lai X, Hu S, Liu M, Chen J, Liu X 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 Y, Chen J, Jiang H B, Liu J, Fu P M, Gong Q H, Yan Z C, Wang B B 2009 J. Phys. B 42 125601 Google Scholar
[14]	Parker J S, Doherty B J S, Taylor K T, Schultz K D, Blaga C I, DiMauro L F 2006 Phys. Rev. Lett. 96 133001 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
[17]	Chen Z J, Liang Y, Lin C D 2010 Phys. Rev. Lett. 104 253201 Google Scholar
[18]	Ye D, Li M, Fu L, Liu J, Gong Q, Liu Y, Ullrich J 2015 Phys. Rev. Lett. 115 123001 Google Scholar
[19]	赵磊, 张琦, 董敬伟, 吕航, 徐海峰 2016 物理学报 65 223201 Google Scholar Zhao L, Zhang Q, Dong J W, Lü H, Xu H F 2016 Acta Phys. Sin. 65 223201 Google Scholar
[20]	Tan J, Xu S, Han X, Zhou Y, Li M, Cao W, Zhang Q, Lu P 2021 Adv. Photonics 3 035001 Google Scholar
[21]	Zhou Y, Tan J, Li M, Lu P 2021 Sci. China, Ser. G 64 273011 Google Scholar
[22]	Fleischer A, Kfir O, Diskin T, Sidorenko P, Cohen O 2014 Nat. Photonics 8 543 Google Scholar
[23]	Eckart S, Kunitski M, Ivanov I, Richter M, Fehre K, Hartung A, Rist J, Henrichs K, Trabert D, Schlott N, Schmidt L P H, Jahnke T, Schoffler M S, Kheifets A, Dorner R 2018 Phys. Rev. A 97 041402 Google Scholar
[24]	Li M, Jiang W, Xie H, Luo S, Zhou Y, Lu P 2018 Phys. Rev. A 97 023415 Google Scholar
[25]	Ke Q, Zhou Y, Tan J, He M, Liang J, Zhao Y, Li M, Lu P 2019 Opt. Express 27 32193 Google Scholar
[26]	Chaloupka J L, Hickstein D D 2016 Phys. Rev. Lett. 116 143005 Google Scholar
[27]	Mancuso C A, Dorney K M, Hickstein D D, Chaloupka J L, Ellis J L, Dollar F J, Knut R, Grychtol P, Zusin D, Gentry C, Gopalakrishnan M, Kapteyn H C, Murnane M M 2016 Phys. Rev. Lett. 117 133201 Google Scholar
[28]	Eckart S, Richter M, Kunitski M, Hartung A, Rist J, Henrichs K, Schlott N, Kang H, Bauer T, Sann H, Schmidt L P H, Schoffler M, Jahnke T, Dorner R 2016 Phys. Rev. Lett. 117 133202 Google Scholar
[29]	Lin K, Jia X, Yu Z, He F, Ma J, Li H, Gong X, Song Q, Ji Q, Zhang W, Li H, Lu P, Zeng H, Chen J, Wu J 2017 Phys. Rev. Lett. 119 203202 Google Scholar
[30]	Li B, Yang X, Ren X, Zhang J 2019 Opt. Express 27 32700 Google Scholar
[31]	Xu T, Zhu Q, Chen J, Ben S, Zhang J, Liu X 2018 Opt. Express 26 1645 Google Scholar
[32]	Huang C, Zhong M, Wu Z 2018 Opt. Express 26 26045 Google Scholar
[33]	Ma X, Zhou Y, Chen Y, Li M, Li Y, Zhang Q, Lu P 2019 Opt. Express 27 1825 Google Scholar
[34]	Huang C, Pang H, Huang X, Zhong M, Wu Z 2020 Opt. Express 28 10505 Google Scholar
[35]	Pang H, Huang X, Huang C 2020 Int. J. Mod. Phys. B 34 2050304 Google Scholar
[36]	Peng M, Bai L H, Guo Z 2021 Commun. Theor. Phys. 73 075501 Google Scholar
[37]	Eichmann H, Egbert A, Nolte S, Momma C, Wellegehausen B 1995 Phys. Rev. A 51 R3414 Google Scholar
[38]	Qiao Y, Wu D, Chen J, Wang J, Guo F, Yang Y 2019 Phys. Rev. A 100 063428 Google Scholar
[39]	Huang C, Zhong M, Wu Z 2019 Opt. Express 27 7616 Google Scholar
[40]	Chaloupka J L 2020 J. Phys. B 53 185601 Google Scholar
[41]	Wu D, Guo F, Wang J, Chen J, Yang Y 2020 Commun. Theor. Phys. 72 055503 Google Scholar
[42]	Haan S L, Breen L, Karim A, and Eberly J H 2006 Phys. Rev. Lett. 97 103008 Google Scholar
[43]	Chen J, Nam C H 2002 Phys. Rev. A 66 053415 Google Scholar
[44]	Li Y, Xu J, Yu B, Wang X 2020 Opt. Express 28 7341 Google Scholar
[45]	Chen X, Ruiz C, He F, Zhang J 2020 Opt. Express 28 14884 Google Scholar
[46]	Huang C, Zhong M, Wu Z 2018 Sci. Rep. 8 8772 Google Scholar
[47]	Huang C, Zhong M, Wu Z 2016 J. Chem. Phys. 145 044302 Google Scholar

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同向旋转双色圆偏场中非次序双电离的频率比依赖