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Electron correlation behaviors and recollision dynamics in nonsequential double ionization (NSDI) of Ar atoms in counter-rotating two-color elliptically polarized (TCEP) laser fields are investigated by using the classical ensemble model. The combined electric field in counter-rotating TCEP laser pulses traces out a trefoil pattern, i.e. the waveform in a period shows three leaves in different directions, and each leaf is called a lobe. Unlike counter-rotating two-color circularly polarized laser field, the combined electric field has no spatial symmetry. The amplitudes of the three field lobes and the angles between them are different. Thus, the returning electron mainly returns to the parent ion from one direction, and the electron momentum distributions show strong asymmetry. Numerical results show that the NSDI yield gradually decreases as the ellipticity increases, and the correlated behavior of the correlated electron momentum along the long axis of the laser polarization plane gradually evolves from correlation behavior mainly located in the first quadrant and the third quadrant to anti-correlation behavior mainly located in the second quadrant and fourth quadrant. In order to further understand the correlation behaviors of electron pairs, different characteristic times in the NSDI processes are discussed, respectively. It is found that single ionization events and recollision events gradually decrease, but single ionization time and recollision time change slightly. This may be the main reason for the decrease in NSDI yield. And as the ellipticity increases, the traveling time and the recollision energy gradually decrease, while the delay time increases. Therefore, we can conclude that ellipticity may be responsible for the NSDI process. In addition, further analysis finds that the shape of the trajectory becomes more and more triangular as the ellipticity increases due to the counter-rotating TCEP laser fields of the specific dynamical symmetries of the total net electric field. And it is found that whether it is a “short trajectory” or a “long trajectory”, more populations move to the second quadrant and the fourth quadrant as the ellipticity increases. The results show that increasing the ellipticity will gradually change the two electrons from emitting in the same direction to emitting in the opposite direction. This well demonstrates that both ellipticity and travelling time are responsible for the formation of the electron momentum distribution at the recollision time, meaning that both of them affect the emitted directions of both electrons.
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Keywords:
- counter-rotating two-color elliptically polarized laser fields /
- nonsequential double ionization /
- ellipticity /
- electron correlation
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图 1 (a)—(d)不同椭偏率下, 反旋TCEP激光场的电场结构和负矢势曲线, 三瓣代表电场结构, 三角形代表反旋TCEP激光场的负矢势; (e)对于不同椭偏率的反旋TCEP激光场下, Ar原子随激光强度变化的双电离产量曲线
Figure 1. (a)–(d) Electric field structure and negative vector potential curve of counter-rotating TCEP laser fields for different ellipticities. The three lobes represent the electric field structure, and the triangle structure represents the negative vector potential of the counter-rotating TCEP laser field. (e) The yield of NSDI for Ar as a function of laser intensity in counter-rotating TCEP laser fields for different ellipticities.
图 2 不同椭偏率的反旋TCEP激光场中电子动量分布(实线为反旋TCEP激光场的负矢势$ - A(t)$) (a) $\varepsilon = 0.2$; (b) $\varepsilon = 0.4$; (c) $\varepsilon = 0.6$—(d) $\varepsilon = 0.8$
Figure 2. Momentum distributions at different ellipticities in counter-rotating TCEP laser fields: (a) $\varepsilon = 0.2$; (b) $\varepsilon = 0.4$; (c) $\varepsilon = $$ 0.6$–(d) $\varepsilon = 0.8$. The solid line represents the negative vector potential $ - A(t)$of counter-rotating TCEP laser fields.
图 3 (a)—(d)不同椭偏率下, Ar原子单电离时刻${t_{{\text{SI}}}}$的分布; (e)—(h)不同椭偏率下, Ar原子重碰撞时刻${t_{{\text{RC}}}}$的分布
Figure 3. (a)—(d) Statistical distribution of the single ionization time ${t_{{\text{SI}}}}$for Ar atoms with different ellipticities; (e)–(h) statistical distribution of the electron recollision time ${t_{{\text{RC}}}}$for Ar atoms with different ellipticities.
图 4 (a)—(d)不同椭偏率下, 两个电子在x方向上的关联电子动量分布; (e)—(h)不同椭偏率下, 两个电子在y方向上的关联电子动量分布
Figure 4. (a)–(d) Correlated momentum distributions of the electrons in the x direction for different ellipticities; (e)–(h) correlated momentum distributions of the electrons in the y direction for different ellipticities.
图 5 (a)—(d)不同椭偏率下, Ar原子旅行时间(${t_{{\text{RC}}}} - {t_{{\text{SI}}}}$)的分布; (e)—(h)不同椭偏率下, 返回电子重碰撞能量的分布; (i)—(l)不同椭偏率下, Ar原子延迟时间(${t_{{\text{DI}}}} - {t_{{\text{RC}}}}$)的分布
Figure 5. (a)–(d) Statistical distribution of the traveling time (${t_{{\text{RC}}}} - {t_{{\text{SI}}}}$) for Ar atoms with different ellipticities; (e)–(h) distributions of the returning electron recollision energy with different ellipticities; (i)–(l) statistical distribution of the delay time $({t_{{\text{DI}}}} - {t_{{\text{RC}}}}$) for Ar atoms with different ellipticities.
图 6 不同椭偏率的反旋TCEP激光场中两个电子轨迹 (a)—(d) 上面一行是“短轨迹”( ${t_{{\text{RC}}}} - {t_{{\text{SI}}}} < 0.2 {\text{o}}{\text{.c}}{.}$)的电子轨迹; (e)—(h)下面一行是“长轨迹”( ${t_{{\text{RC}}}} - {t_{{\text{SI}}}} \geqslant 0.2 {\text{o}}{\text{.c}}{.}$)的电子轨迹
Figure 6. Trajectory of the two electrons at different ellipticities in counter-rotating TCEP laser fields: (a)–(d) The top row shows trajectories of the ionized electron coming back to the parent ion core with the “short trajectory” (${t_{{\text{RC}}}} - {t_{{\text{SI}}}} < 0.2 {\text{o}}{\text{.c}}{.}$); (e)–(h) the bottom row shows trajectories of the ionized electron coming back to the parent ion core with the “long trajectory” $({t_{{\text{RC}}}} - {t_{{\text{SI}}}} \geqslant 0.2 {\text{o}}{\text{.c}}{.}$).
图 7 不同椭偏率下, 两个电子在x方向上的关联电子动量分布 (a)—(d)上面一行是“短轨迹”( ${t_{{\text{RC}}}} - {t_{{\text{SI}}}} < 0.2 {\text{o}}{\text{.c}}{.}$)的关联电子动量分布; (e)—(h)下面一行是“长轨迹”( ${t_{{\text{RC}}}} - {t_{{\text{SI}}}} \geqslant 0.2 {\text{o}}{\text{.c}}{.}$)的关联电子动量分布
Figure 7. Correlated momentum distributions of the electrons in the x direction for different ellipticities: (a)–(d) The bottom row shows correlated momentum distributions with the “short trajectory”(${t_{{\text{RC}}}} - {t_{{\text{SI}}}} < 0.2 {\text{o}}{\text{.c}}{.}$); (e)–(h) the top row shows correlated momentum distributions with the “long trajectory”(${t_{{\text{RC}}}} - {t_{{\text{SI}}}} \geqslant 0.2 {\text{o}}{\text{.c}}{.}$).
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