Rydberg state excitation of atoms and molecules in ultrafast intense laser field

Shen Xing-Chen; Liu Yang; Chen Qi; Lü Hang; Xu Hai-Feng

doi:10.7498/aps.71.20221258

Abstract

When atoms or molecules are irradiated by a strong laser field with pulse duration of tens of femtoseconds and intensity larger than 10¹³ W/cm², they will generally undergo tunneling ionization, which will induce various non-perturbative and highly nonlinear phenomena. Investigations into the strong field physical processes is of significance in studying attosecond physics, molecular orbital imaging, ultrafast electron diffraction and advanced short ultraviolet light sources. While there is a relatively long history of the studies of tunneling ionization induced physics including high-order above threshold ionization (HATI), high-order harmonic generation (HHG) and non-sequential double ionization (NSDI), it is until recently to surprisedly find that in the tunneling ionization region, neutral atoms or molecules can survive in strong laser fields in highly excited Rydberg states. As a basic process of the interaction between ultrafast strong laser fields and atoms or molecules, such a Rydberg state excitation (RSE) has been viewed as an important supplement to the physical picture of the tunneling ionization. During the past several years, the extensive research attention has been paid to the RSE process in strong laser field. Various theoretical and experimental methods have been developed to investigate the strong field RSE of both atoms and molecules, to understand the underlying physical mechanism behind the recapture of the tunneling electrons and to reveal the quantum features and molecular structure effect in RSE. These advances have brought about an in-depth understanding and a systematic view of the atomic and molecular RSE in strong laser fields, as well as their relations to the other tunneling ionization induced physical processes such as ATI, HHG and NSDI. Here, we systematically review recent research progress of the atomic and molecular RSE in strong laser fields. We particularly focus on several aspects of this strong field process, i.e. the physical mechanism of the recapture, the quantum feature and the interference of different orbits, and the structure effect in molecular RSE. In addition, neutral particle acceleration and coherent radiation which can be induced by the strong field RSE, are also discussed. Finally, we provide a short summary and prospect of the future studies on the strong field RSE.

Keywords:

Authors and contacts

Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Corresponding author: Xu Hai-Feng, xuhf@jlu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2019YFA0307700) and the National Natural Science Foundation of China (Grant Nos. 12174148, 12074144, 11874179).

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图 1 强场RSE的实验测量方法示意图　(a) 中性激发态直接测量方法^[29]; (b) 脉冲静电场场致电离方法^[21]; (c) COLTRIMS^[64]方法

Figure 1. Schematic diagrams of experimental measurements of strong field RSE: (a) Direct measurement of neutral excited states^[29]; (b) pulsed electric field ionization^[21]; (c) COLTRIMS ^[64].

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图 2 强场RSE过程示意图　(a) 多光子图像; (b)隧穿后俘获图像的

Figure 2. Schematic diagrams of multiphoton image (a) and tunneling plus capture image (b) of strong field RSE process.

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图 3 (a) 800 nm飞秒强激光场中电离 (He⁺, 黑色方框)和RSE (He*, 红色圆圈)产率随激光椭偏率的变化关系^[20]; (b) 强激光场中不同I_p的原子里德伯态产率对激光椭偏率依赖的半高全宽(σ_χ)和相位窗口的宽度与横向速度的比值 ($\Delta /{\upsilon _{\text{d}}}$, 绿色星形)^[37]; (c) 800 nm飞秒强激光场Kr原子RSE (Kr*, 黑色方框)及NSDI (Kr²⁺, 蓝色菱形)产率随激光椭偏率的变化关系. 红色圆圈为三维半经典计算结果, 蓝色实线为忽略库仑势的SFA模型计算结果^[31]

Figure 3. (a) Dependence of ionization (He⁺, black squares) and RSE (He*, red circles) yields on the ellipticity of the 800 nm strong laser fields ^[20]; (b) dependence of Rydberg state yields of atoms with different I_P on the ellipticity of strong laser fields (σ_χ) and the ratio between the width of phase window and the drift velocity v_d for different atoms ($\Delta /{\upsilon _{\text{d}}}$, green star)^[37]; (c) yields of Kr RSE (Kr*, black squares) and NSDI (Kr²⁺, blue diamonds) on the ellipticity of the strong 800 nm laser fields. Red circles are the results from 3D semiclassical calculations. Blue solid lines are the SFA model analytical results without considering the Coulomb potential^[31].

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图 4 (a) H原子在800 nm激光场下电离率(红色实线)和激发率(蓝色虚线)随激光光强变化的TDSE数值模拟结果^[77]; (b), (c) Ar原子在400和800 nm强激光场下实验测量的电离率和激发率随激光光强变化^[30]; (d) Ar原子在1800 nm激光场下激发率与电离率比值的测量和计算结果^[79]

Figure 4. (a) Dependence of H ionization (red solid lines) and RSE (blue dotted lines) yields on the intensity of 800 nm strong laser fields based on TDSE numerical simulations ^[77]; (b), (c) experimentally measured Ar ionization and RSE yields in 400 and 800 nm strong laser fields^[30]; (d) measured and calculated yield ratios of Ar ionization and RSE in 1800 nm strong laser fields^[79].

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图 5 强场RSE的量子图像. 在激光不同半周期内电离的隧穿电子被俘获到特定的里德伯态, 不同轨道的干涉产生随激光强度变化的振荡峰结构^[43]

Figure 5. Quantum picture of strong field RSE process. The tunneling electrons ionized in different optical half cycles of the laser pulse are captured into a certain Rydberg state, and the interference of different orbits leads to the intensity dependence of peak structures^[43].

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图 6 (a) 800 nm强激光场中He*的主量子数n的布居. 蓝色圆圈和红色方框分别代表1.8×10¹⁵ W/cm²和2.9×10¹⁵ W/cm²下实验测量结果. 空心菱形和空心方框分别代表1×10¹⁵ W/cm²和1.4×10¹⁵ W/cm²下半经典理论计算结果. 空心圆圈和空心三角形分别代表1.8×10¹⁵ W/cm²和2.9×10¹⁵ W/cm²下量子单电子近似理论结果^[29]; (b) 上图为不同直流电场下Ar*产率随时间的变化关系, 下图为提取的量子态分布. 黑色方框、红色圆圈和蓝色三角分别表示COLTRIMS中直流电场为1.8, 3.9和5.7 V/cm下的实验测量结果数据和分别在1.8, 3.9和5.7 V/cm处提取的主量子数的布居, 实线曲线是拟合结果以及在800 nm激光场下提取的Ar*的主量子数的布居, 品红色菱形表示半经典模型计算的主量子数的布居结果^[66].

Figure 6. (a) Measured n-distributions in 800 nm strong laser fields for a laser intensity 1.8×10¹⁵W/cm² (blue circles) and 2.9×10¹⁵ W/cm² (red squares). Semiclassical calculations at a laser intensity 1×10¹⁵ W/cm²(open diamonds) and 1.4×10¹⁵ W/cm² (open squares), and quantum mechanical SAE calculations at 1.8×10¹⁵ W/cm² (open circles) and 2.9×10¹⁵ W/cm² (open triangles) ^[29]. (b) upper panel: time dependence of the yields of Ar* at a series of dc electric fields. Lower panel: extracted PQNDs for the data presented in the above figure^[66]. The black squares, red circles, and blue triangles indicate the experimental data and the extracted PQND at 1.8, 3.9, and 5.7 V/cm, respectively. The fitting results and the extracted PQNDs of Ar* in 800 nm strong laser fields are depicted by solid curves. The magenta diamonds in the lower panel indicate the calculated PQND by the semiclassical model^[66].

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图 7 (a) 中性激发态H*碎片(黑色曲线)和离子碎片H⁺(红色曲线)的动能分布^[22]; (b) 分子碎片的里德伯态激发机制的示意图^[22]

Figure 7. (a) Kinetic energy distribution of excited neutral fragments He* (red curve) and ionic fragments H⁺(black curve)^[22]; (b) schematic picture of Rydberg state excitation mechanism of molecular fragments^[22].

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图 8 (a) 强激光场中CO分子形成的原子激发态碎片产率依赖于激光场方向和分子取向^[73]; (b) Ar₂二聚体高阶库仑爆炸通道的平动能分布^[28]

Figure 8. (a) The yields of atomic excited fragments formed by CO molecules in strong laser fields depend on the direction of laser field and molecular orientation^[73]; (b) kinetic energy release distribution of multiple ionization-induced Coulomb explosion channels of the Ar dimer^[28].

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图 9 实验测量的800 nm强激光场下N₂ vs. Ar和O₂ vs Xe的单电离(黑色圆圈)以及里德伯态激发(红色方框)的比值随激光强度的变化关系^[26]

Figure 9. Experimentally measured yield ratios of N₂ vs. Ar and O₂ vs. Xe for both single ionization and RSE as a function of intensity of 800 nm strong laser fields^[26].

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图 10 在线偏光下O₂/Xe (光强为8×10¹³ W/cm²)和N₂/Ar (光强为1.2×10¹⁴ W/cm²)的光电子-光离子符合光谱. 红色虚线表示由于原子分子激发态的黑体辐射导致光电离和直流电场电离之间的分界线^[27]

Figure 10. Photoelectron-photoion-coincidence spectra obtained in linearly polarized femtosecond laser pulses for O₂/Xe (at the intensity of 8×10¹³ W/cm²) and for N₂/Ar (at the intensity of 1.2×10¹⁴ W/cm²). The red dashed curves in both figures indicate the separation between DC electric field ionization and photon ionization due to black body radiation of the Rydberg atoms and molecules^[27].

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