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利用三维经典系综模型, 研究空间非均匀激光场驱动的氙原子非次序双电离, 并对比了空间均匀激光场的情况. 结果显示, 波长较短时, 空间非均匀激光场与空间均匀激光场的非次序双电离的产率较为相近. 随着波长的增大, 较高激光强度时空间非均匀激光场下非次序双电离受到越来越明显的抑制. 相比于空间均匀激光场, 空间非均匀激光场下非次序双电离两电子的末态发射角表现出更强烈的关联特性, 特别在较大的激光波长下, 两电子的末态发射角几乎全部集中在
${0^\circ }$ 附近, 这意味着两电子往往是平行发射到相同方向. 此外, 波长由近红外增大到中红外时, 空间非均匀激光场下非次序双电离的有效再碰撞均由第1个电子的第1次返回主导, 而空间均匀激光场下则呈现由第1次返回主导到第2次返回主导的转变. 进一步, 通过反演分析非次序双电离的经典轨迹, 揭示了空间非均匀激光场下关联电子超快动力学过程的更多细节.Using a three-dimensional classical ensemble method, we investigate the nonsequential double ionization (NSDI) of xenon atoms from the near infrared wavelength to the mid-infrared wavelength in spatially inhomogeneous laser fields, and compare the results with those from spatially homogeneous laser fields. The results show that the NSDI probability curves from spatially inhomogeneous laser field and spatially homogeneous laser field at short wavelength are similar to each other. With the laser wavelength increasing, NSDI at the high intensities is more and more suppressed for spatially inhomogeneous laser field. Compared with the result from the spatially homogeneous laser field, the final emission angle of two electrons from the NSDI exhibits a very strongly correlated characteristic in the spatially inhomogeneous field, especially at a longer laser wavelength, the final emission angles of two electrons are almost both concentrated around ${0^\circ }$ , meaning that the two electrons are always emitted into the same direction parallelly. Moreover, effective recollision of the NSDI is always dominated by first return of the first electron from the near infrared to the mid-infrared inhomogeneous laser fields, however, the transition from the first return dominance to the second return dominance occurs in the spatially homogeneous laser fields. Further, we reveal the more details of the ultrafast dynamics of the correlated electrons in the spatially inhomogeneous laser field by back-tracing the classical trajectories of NSDI.-
Keywords:
- nonsequential double ionization /
- spatially inhomogeneous laser fields /
- electron correlation
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图 1 对于不同波长, 空间非均匀激光场 (蓝色方块) 和空间均匀激光场 (红色圆圈) 下DI产率随激光强度的变化 (a) 800 nm; (b) 1600 nm; (c) 3200 nm; (d) 4800 nm
Fig. 1. Probabilities of DI as a function of laser intensity for the spatially inhomogeneous (blue squares) and spatially homogeneous (red circles) laser fields at different wavelengths: (a) 800 nm; (b) 1600 nm; (c) 3200 nm; (d) 4800 nm.
图 2 空间非均匀激光场和空间均匀激光场中返回电子在碰撞前 0.03T 的动能与再碰撞时间的关系 (激光强度均为4×1013 W/cm2) (a)—(d) ε = 0.003; (e)—(h) ε = 0
Fig. 2. Kinetic energy of the returning electron before the recollision 0.03T vs. the recollision time for the spatially inhomogeneous and spatially homogeneous laser fields (Laser intensities are both 4×1013 W/cm2): (a)–(d) ε = 0.003; (e)–(h) ε = 0.
图 3 关联电子对在激光脉冲结束时的发射角分布 (a)—(d) 空间非均匀激光场; (e)—(h) 空间均匀激光场
Fig. 3. Distribution of the emitting angle between the correlated electron pairs at the end of the laser pulses: (a)–(d) Spatially inhomogeneous laser fields; (e)–(h) spatially homogeneous laser fields.
图 4 空间非均匀激光场和空间均匀激光场下末态电子的横向动量和纵向动量分布 (激光波长均为4800 nm) (a) ε = 0.003; (b) ε = 0
Fig. 4. Transverse and longitudinal momentum distributions of final state electrons for the spatially inhomogeneous and spatially homogeneous laser fields (Laser wavelengths are both 4800 nm): (a) ε = 0.003; (b) ε = 0.
图 5 空间非均匀激光场和空间均匀激光场下飞行时间 (a), (c)及时间延迟 (b), (d)的统计分布 (a), (b) ε = 0.003; (c), (d) ε = 0 (图(b), (d)中竖直实线对应0.25个光周期)
Fig. 5. Distributions of travel time (a), (c) and time delay (b), (d) for the spatially inhomogeneous and spatially homogeneous laser fields: (a), (b) ε = 0.003; (c), (d) ε = 0 (Vertical solid line in panels (b) and (d) corresponds to 0.25 cycles).
图 6 电子沿z轴正方向 (红线) 和负方向 (蓝线) 电离的演化轨迹. 1st, 2nd和3rd分别代表电子第1次、第2次和第3次返回母离子核, 黑色虚线代表原点处振荡的激光电场 (a), (b) 对应的激光波长分别为 800 nm和3200 nm, 激光强度均为4×1013 W/cm2
Fig. 6. Evolution trajectories of electron ionization along positive z direction (red lines) and the negative z direction (blue lines). 1st, 2nd and 3rd represent the first, second and third return of the electrons to the parent ion core. The black dashed lines show the oscillating laser electric field at the origin: (a), (b) Correspond to wavelengths of 800 nm and 3200 nm, respectively and the laser intensities are both 4×1013 W/cm2.
图 7 (a), (b)两个电子与母离子核的距离随时间的演化; (c), (d)两个电子沿z轴的速度随时间的演化; (a), (c) 沿z轴负方向电离并发生一次返回的电子运动轨迹; (b), (d) 沿z轴负方向电离发生二次返回的电子运动轨迹
Fig. 7. (a), (b) Distance of two electrons from the parent ion core as a function of time; (c), (d) velocity of two electrons along the z direction as a function of time; (a), (c) trajectory of electron ionization along negative z direction with one return; (b), (d) trajectory of electron ionization along negative z direction with secondary return.
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[1] Lein M, Hay N, Velotta R, Marangos J P, Knight P L 2002 Phys. Rev. Lett. 88 183903
Google Scholar
[2] Ghimire S, Reis D A 2019 Nat. Phys. 15 10
[3] Yang B, Schafer K J, Walker B, Kulander K C, Agostini P, DiMauro L F 1993 Phys. Rev. Lett. 71 3770
Google Scholar
[4] Milošević D B, Paulus G G, Becker W 2003 Opt. Express 11 1418
Google Scholar
[5] Busuladi M, Gazibegovi-Busuladi A, Miloevi D B, Becker W 2008 Phys. Rev. Lett. 100 203003
Google Scholar
[6] He M R, Li Y, Zhou Y M, Li M, Cao W, Lu P X 2018 Phys. Rev. Lett. 120 133204
Google Scholar
[7] Zhou Y, Tolstikhin O I, Morishita T 2016 Phys. Rev. Lett. 116 173001
Google Scholar
[8] Rudenko A, Jesus V, Ergler T, Zrost K, Ullrich J 2007 Phys. Rev. Lett. 99 263003
Google Scholar
[9] Quan W, Hao X L, Wang Y L, Chen Y J, Yu S G, Xu S P, Xiao Z L, Sun R P, Lai X Y, Hu S L, Liu M Q, Shu Z, Wang X D, Li W D, Becker W, Liu X J, Chen J 2017 Phys. Rev. A 96 032511
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[10] Huang C, Zhou Y M, Zhang Q B, Lu P X 2013 Opt. Express 21 11382
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[11] Tong A H, Liao Q, Zhou Y M, Lu P X 2010 Opt. Express 18 9064
Google Scholar
[12] Shaaran T, Augstein B B, Figueira D 2011 Phys. Rev. A 84 013429
Google Scholar
[13] Wang Y L, Xu S P, Chen Y J, Kang H P, Lai X Y, Quan W, Liu X J, Hao X L, Li W D, Hu S L, Chen J, Becker W, Chu W, Yao J P, Zeng B, Cheng Y, Xu Z Z 2017 Phys. Rev. A 95 063415
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[14] Corkum P B 1993 Phys. Rev. Lett. 71 1994
Google Scholar
[15] Feuerstein B, Moshammer R, Fischer D, Dorn A, Schroter C D, Deipenwisch J, Crespo Lopez-Urrutia J R, Hohr C, Neumayer P, Ullrich J, Rottke H, Trump C, Wittmann M, Korn G, Sandner W 2001 Phys. Rev. Lett. 87 043003
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Google Scholar
Su J, Liu Z C, Liao J Y, Li Y B, Huang C 2022 Acta Phys. Sin. 71 193201
Google Scholar
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Google Scholar
[20] Ortmann L, Landsman A S 2018 Phys. Rev. A 97 023420
Google Scholar
[21] Husakou A, Im S J, Herrmann J 2011 Phys. Rev. A 83 043839
Google Scholar
[22] Yavuz I, Bleda E A, Altun Z, Topcu T 2012 Phys. Rev. A 85 013416
Google Scholar
[23] Ciappina M F, Biegert J, Quidant R, Lewenstein M 2012 Phys. Rev. A 85 033828
Google Scholar
[24] Ortmann L, Pérez-Hernández J A, Ciappina M F, Schötz J, Chacón A, Zeraouli G, Kling M F, Roso L, Lewenstein M, Landsman A S 2017 Phys. Rev. Lett. 119 053204
Google Scholar
[25] Ciappina M F, Pérez-Hernández J, Shaaran T, Roso L, Lewenstein M 2014 Phys. Rev. A 89 013409
Google Scholar
[26] Chacón A, Ortmann L, Cucchietti F, Suárez N, Pérez-Hernández J A, Ciappina M F, Landsman A S, Lewenstein M 2017 Appl. Phys. B 123 116
Google Scholar
[27] Xu J K, Li Y B, Zhou Y B, Chen Y M, Li M, Yu B H, Lu P X 2022 Opt. Express 30 15951
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[41] Chen Y K, Zhou Y M, Tan J, Li M, Cao W, Lu P X 2021 Phys. Rev. A 104 043107
Google Scholar
[42] Li Y, Wang X, Yu B, Tang Q, Wang G, Wan J 2016 Sci. Rep. 6 37413
Google Scholar
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