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利用三维经典系综模型系统地研究了不同强度线偏振激光脉冲驱动下He原子的非次序双电离. 结果表明在非次序双电离中回碰电子的返回次数、两电子的碰撞距离和电子对的关联特性都强烈地依赖于激光强度. 对于750 nm, 随着激光强度的增加, 单次返回诱导的非次序双电离事件逐渐减少, 而多次返回事件的比例显著增加. 对于1500 nm, 随着激光强度的增加, 前三次返回诱导的非次序双电离事件都会减少, 返回次数大于3的轨道对非次序双电离的贡献逐渐增加. 这是因为在高强度下每次返回过程中母核的库仑吸引对返回电子横向偏离的补偿较弱, 所以需要更多次的返回来补偿电子的横向偏离以实现再碰撞. 轨道分析表明非次序双电离中两电子的碰撞距离随激光波长和强度的增加而逐渐减小. 最后讨论了非次序双电离中电子对的关联特性对返回次数的依赖.Using the three-dimensional classical ensemble model, we systematically investigate the strong-field nonsequential double ionization (NSDI) of He atom by intense linearly polarized laser pulses at different intensities for 750 nm and 1500 nm in wavelength. In the intensity range of 0.4−0.8 PW/cm2 considered in this work, for 750 nm wavelength the correlated electron pairs are always distributed mainly near the diagonal but for 1500 nm wavelength, with increasing laser intensity the population of electron pairs moves from the diagonal to the two axes, forming a near-axis V-shaped structure at 0.8 PW/cm2. The analysis indicates that for 750 nm with increasing laser intensity the contribution from the single-return events to NSDI decreases sharply and the contribution from the multiple-return events increases. For 1500 nm wavelength when the laser intensity increases, the contributions from one-, two- and three-return trajectories decrease and the contributions of other trajectories increase. It is because most of ionized electrons have a non-zero initial transverse momentum. After the excursion of the ionized electron, when it returns to the parent ion at the first time there is a distance in the transverse direction between the free electron and the parent ion, which hinders the recollision and NSDI from occurring. The transverse deviation can be significantly reduced by the Coulomb attraction from the parent ion to the free electron when it returns back to the parent ion in the longitudinal direction. Higher intensity results in larger returning velocity for the free electron. The free electron faster passes by the parent ion and the Coulomb attraction has less time to pull the free electron to the parent ion. For each return the compensation of the Coulomb attraction for the transverse deviation for high intensity is weaker than for low intensity. Thus for higher intensities more returns are required to compensate for the transverse deviation. Moreover, numerical results show the recollision distance in NSDI is smaller for the longer wavelength and higher intensity. It is attributed to the larger returning velocity of the free electron at the longer wavelength and higher intensity, which can more easily overcome the strong Coulomb repulsion between the two electrons and achieve a smaller recollision distance. Finally, electron correlation behaviors for those trajectories where recollision occurs with different return times are studied.
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图 1 He原子NSDI的关联电子动量分布 (a) 750 nm, 0.4 PW/cm2; (b) 750 nm, 0.6 PW/cm2; (c) 750 nm, 0.8 PW/cm2; (d) 1500 nm, 0.4 PW/cm2; (e) 1500 nm, 0.6 PW/cm2; (f) 1500 nm, 0.8 PW/cm2
Fig. 1. Correlated electron momentum distributions in NSDI of He: (a) 750 nm, 0.4 PW/cm2; (b) 750 nm, 0.6 PW/cm2; (c) 750 nm, 0.8 PW/cm2; (d) 1500 nm, 0.4 PW/cm2; (e) 1500 nm, 0.6 PW/cm2; (f) 1500 nm, 0.8 PW/cm2.
图 2 各次返回诱导的NSDI在总的NSDI中所占的百分比 (a) 750 nm; (b) 1500 nm
Fig. 2. Proportion of each return in the total NSDI yield: (a) 750 nm; (b) 1500 nm.
图 3 NSDI事件关于碰撞距离的概率分布 (a) 750 nm; (b) 1500 nm.
Fig. 3. Recollison distance in NSDI for (a) 750 nm and (b) 1500 nm at the laser intensities of 0.4, 0.6 and 0.8 PW/cm2.
图 4 750 nm 激光脉冲驱动He原子NSDI的关联电子动量分布 (a)—(e) 0.4 PW/cm2; (f)—(j) 0.6 PW/cm2; (k)—(o) 0.8 PW/cm2; 从左到右每列对应不同返回次数诱导的NSDI事件
Fig. 4. Correlated electron momentum distributions in NSDI of He for 750 nm at the laser intensities of 0.4 (the first row), 0.6 (the second row) and 0.8 PW/cm2 (the third row). The columns from left to right correspond to return numbers of 1 to 5.
图 5 1500 nm 激光脉冲驱动He原子NSDI的关联电子动量分布 (a)—(e) 0.4 PW/cm2; (f)—(j) 0.6 PW/cm2; (k)—(o) 0.8 PW/cm2; 从左到右每列对应不同返回次数诱导的NSDI事件
Fig. 5. Correlated electron momentum distributions in NSDI of He for 1500 nm at the laser intensities of 0.4 (the first row), 0.6 (the second row) and 0.8 PW/cm2 (the third row). The columns from left to right correspond to return numbers of 1 to 5.
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[1] L'Huillier A, Lompre L A, Mainfray G, Manus C 1983 Phys. Rev. A 27 2503
Google Scholar
[2] Figueira de Morisson Faria C, Liu X 2011 J. Mod. Opt. 58 1076
Google Scholar
[3] Becker W, Liu X, Jo Ho P, Eberly J H 2012 Rev. Mod. Phys. 84 1011
Google Scholar
[4] 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
[5] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[6] 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
[7] Lein M, Gross E K U, Engel V 2000 Phys. Rev. Lett. 85 4707
Google Scholar
[8] 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
[9] Wang X, Eberly J H 2010 Phys. Rev. Lett. 105 083001
Google Scholar
[10] Hao X L, Chen J, Li W D, Wang B B, Wang X D, Becker W 2014 Phys. Rev. Lett. 112 073002
Google Scholar
[11] 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
[12] Chen Y, Zhou Y, Li Y, Li M, Lan P, Lu P 2018 Phys. Rev. A 97 013428
Google Scholar
[13] 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
[14] Ye D, Li M, Fu L, Liu J, Gong Q, Liu Y, Ullrich J 2015 Phys. Rev. Lett. 115 123001
Google Scholar
[15] Liu Y, Tschuch S, Rudenko A, Dürr M, Siegel M, Morgner U, Moshammer R, Ullrich J 2008 Phys. Rev. Lett. 101 053001
Google Scholar
[16] Staudte A, Ruiz C, Schöffler M, Schössler S, Zeidler D, Weber Th, Meckel M, Villeneuve D M, Corkum P B, Becker A, Dörner R 2007 Phys. Rev. Lett. 99 263002
Google Scholar
[17] Rudenko A, Jesus V L B, Ergler Th, Zrost K, Feuerstein B, Schröter C D, Moshammer R, Ullrich J 2007 Phys. Rev. Lett. 99 263003
Google Scholar
[18] Chen Z J, Liang Y, Lin C D 2010 Phys. Rev. Lett. 104 253201
Google Scholar
[19] Ye D F, Liu X J, Liu J 2008 Phys. Rev. Lett. 101 233003
Google Scholar
[20] Zhou Y M, Liao Q, Lu P X 2010 Phys. Rev. A 82 053402
Google Scholar
[21] Camus N, Fischer B, Kremer M, Sharma V, Rudenko A, Bergues B, Kubel M, Johnson N G, Kling M F, Pfeifer T, Ullrich J, Moshammer R 2012 Phys. Rev. Lett. 108 073003
Google Scholar
[22] Huang C, Zhong M, Wu Z 2016 J. Chem. Phys. 145 044302
Google Scholar
[23] Liao Q, Winney A H, Lee S K, Lin Y F, Adhikari P, Li W 2017 Phys. Rev. A 96 023401
Google Scholar
[24] Bergues B, Kubel M, Johnson N G, Fischer B, Camus N, Betsch K J, Herrwerth O, Senftleben A, Sayler A M, Rathje T, Pfeifer T, Ben-Itzhak I, Jones R R, Paulus G G, Krausz F, Moshammer R, Ullrich J, Kling M F 2012 Nature Commun. 3 813
Google Scholar
[25] Liao Q, Lu P X 2010 Phys. Rev. A 82 021403(R)
Google Scholar
[26] Gong X, Song Q, Ji Q, Lin K, Pan H, Ding J, Zeng H, Wu J 2015 Phys. Rev. Lett. 114 163001
Google Scholar
[27] Liu K, Qin M, Li Q, Liao Q 2018 Opt. Quantum Electron. 50 364
Google Scholar
[28] Liao Q, Li Y, Qin M, Lu P 2017 Phys. Rev. A 96 063408
Google Scholar
[29] Winney A H, Lee S K, Lin Y F, Liao Q, Adhikari P, Basnayake G, Schlegel H B, Li W 2017 Phys. Rev. Lett. 119 123201
Google Scholar
[30] He M, Li Y, Zhou Y, Li M, Cao W, Lu P 2018 Phys. Rev. Lett. 120 133204
Google Scholar
[31] Liu X, Rottke H, Eremina E, Sandner W, Goulielmakis E, Keeffe K O, Lezius M, Krausz F, Lindner F, Schatzel M G, Paulus G G, Walther H 2004 Phys. Rev. Lett. 93 263001
Google Scholar
[32] He L, Zhang Q, Lan P, Cao W, Zhu X, Zhai C, Wang F, Shi W, Li M, Bian X, Lu P, Bandrauk A D 2018 Nat. Commun. 9 1108
Google Scholar
[33] 汤清彬, 张东玲, 余本海, 陈东 2010 物理学报 59 7775
Google Scholar
Tang Q B, Zhang D L, Yu B H, Chen D 2010 Acta Phys. Sin. 59 7775
Google Scholar
[34] 黄诚, 钟明敏, 吴正茂 2016 物理学报 65 083301
Google Scholar
Huang C, Zhong M, Wu Z 2016 Acta Phys. Sin. 65 083301
Google Scholar
[35] 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
[36] Wang J, He F 2018 Phys. Rev. A 97 043411
Google Scholar
[37] Ma X, Zhou Y, Li N, Li M, Lu P 2018 Opt. Laser Technol. 108 235
Google Scholar
[38] Zhou Y, Huang C, Tong A, Liao Q, Lu P 2011 Opt. Express 19 2301
Google Scholar
[39] Zhang L, Xie X H, Roither S, Zhou Y M, Lu P X, Kartashov D, Schoffler M, Shafir D, Corkum P B, Baltuska A, Staudte A, Kitzler M 2014 Phys. Rev. Lett. 112 193002
Google Scholar
[40] 童爱红, 冯国强, 邓永菊 2012 物理学报 61 093303
Google Scholar
Tong A H, Feng G Q, Deng Y J 2012 Acta Phys. Sin. 61 093303
Google Scholar
[41] Chaloupka J L, Hickstein D D 2016 Phys. Rev. Lett. 116 143005
Google Scholar
[42] Xu T, Zhu Q, Chen J, Ben S, Zhang J, Liu X 2018 Opt. Express 26 1645
Google Scholar
[43] Huang C, Zhong M, Wu Z 2018 Opt. Express 26 26045
Google Scholar
[44] Wolter B, Pullen M G, Baudisch M, Sclafani M, Hemmer M, Senftleben A, Schrter C D, Ullrich J 2015 Phys. Rev. X 5 021034
Google Scholar
[45] Huang C, Zhong M, Wu Z 2016 Opt. Express 24 28361
Google Scholar
[46] Li Y, Wang X, Yu B, Tang B, Wang G, Wan J 2016 Sci. Rep. 6 37413
Google Scholar
[47] Chen J, Nam C H 2002 Phys. Rev. A 66 053415
Google Scholar
[48] Panli R, Eberly J H, Haan S L 2001 Opt. Express 8 431
Google Scholar
[49] Haan S L, Breen L, Karim A, Eberly J H 2006 Phys. Rev. Lett. 97 103008
Google Scholar
[50] Dong S S, Zhang Z L, Bai L H, Zhang J T 2015 Phys. Rev. A 92 033409
Google Scholar
[51] Huang C, Zhong M, Wu Z 2018 Sci. Rep. 8 8772
Google Scholar
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