搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于非绝热半经典模型对氩原子近阈值光电子干涉的研究

陶建飞 金鑫 吴可非 刘小井

引用本文:
Citation:

基于非绝热半经典模型对氩原子近阈值光电子干涉的研究

陶建飞, 金鑫, 吴可非, 刘小井

Revisiting Near-Threshold Photoelectron Interference in Argon with a Non-Adiabatic Semiclassical Model

TAO Jianfei, JIN Xin, WU Kefei, LIU Xiaojing
Article Text (iFLYTEK Translation)
PDF
导出引用
  • 本文结合实验与理论研究,探索了在多光子区域(γ > 1)短脉冲激光作用下氩原子的光电离过程。通过建立包含隧穿出口处电子初始纵向动量的半经典模型,我们模拟了光电子动量分布。该方法基于费曼路径积分理论框架,为每条电子轨迹赋予动力学相位,从而实现了量子干涉效应的研究。模拟结果与含时薛定谔方程(TDSE)数值解高度吻合,同时我们发现,初始纵向动量的引入对于精确重现电离阈值附近观测到的光电子谱干涉结构至关重要,并揭示出离子实极化对低能谱影响甚微。我们的研究结果强调了超短脉冲光电离中非绝热势垒下动力学的重要性,并提供了基于量子轨道的清晰物理图像。
    Purpose : The interaction of intense, ultrashort laser pulses with atoms gives rise to a rich tapestry of non-perturbative phenomena, encoded within the final-state photoelectron momentum distribution (PMD). A particularly enigmatic feature, often observed in the multiphoton ionization regime (Keldysh parameter $\gamma \gtrsim 1$), is a complex, fan-like interference pattern in the near-threshold, low-energy region of the PMD. The physical origin of this structure has been the subject of extensive debate, with proposed mechanisms ranging from multipath interference in the Coulomb field to complex sub-barrier dynamics. This work aims to provide a physical explanation for this phenomenon. We hypothesize and demonstrate that this fan-like structure is not a mere consequence of Coulomb focusing but serves as a direct and sensitive signature of non-adiabatic dynamics occurring as the electron tunnels through the laser-dressed atomic potential barrier. Our goal is to unambiguously isolate the key physical ingredients responsible for shaping this quantum interference.
    Methodology : To achieve this, we employ a synergistic three-pronged approach that combines experiment, exact numerical simulation, and a sophisticated theoretical model.
    1. Experiment : We performed velocity-map imaging measurements on argon atoms ionized by a 798 nm, 35 fs laser pulse at a peak intensity of $6.3 \times 10^{13}$ W/cm$^2$. This provides the experimental result, clearly revealing the low-energy fan-like interference pattern.
    2. Quantum Benchmark : We solved the time-dependent Schrödinger equation (TDSE) within the single-active-electron (SAE) approximation, using a well-established model potential for argon that accurately reproduces its ionization potential and ground-state properties. After performing a focal-volume average to simulate experimental conditions, the TDSE results show excellent qualitative agreement with the measurements, establishing the TDSE as a reliable quantum benchmark for our investigation.
    3. Semiclassical Model (CTMC-p) : The core of our analysis relies on a custom-developed semiclassical trajectory model based on the Feynman path-integral formulation. In this framework, ionization is a two-step process: (i) an electron tunnels through the potential barrier at an initial time $t_0$ and position $\mathbf{r}_0$, and (ii) it propagates classically in the combined laser and ionic fields according to Newton's equations. Crucially, each trajectory is endowed with a quantum phase accumulated along its path, $\Phi_k$, allowing for the coherent summation of all trajectories ending with the same final momentum, $M_j = \sum_k e^{i\Phi_k}$. Our model incorporates two critical physical effects beyond standard treatments:
    Non-Adiabatic Tunneling : We introduce a non-zero initial longitudinal momentum, $v_{0\parallel} = -A(t_0)(\sqrt{1+\gamma_{\text{eff}}^2}-1)$, acquired by the electron at the tunnel exit. This term accounts for the non-instantaneous nature of the tunneling process, a key non-adiabatic effect.
    Core Polarization : We include an induced dipole potential, $U_{\text{ID}} = -\alpha^I \mathbf{E}(t) \cdot \mathbf{r}/r^3$, to model the dynamic polarization of the Ar$^+$ ionic core, a multi-electron effect.
    By selectively including or excluding these effects, we can unambiguously isolate their respective contributions to the final PMD.
    Results : Our central finding is that the non-adiabatic initial longitudinal momentum is the decisive factor for correctly describing the near-threshold interference. This is powerfully illustrated in Figure 6. The benchmark TDSE calculation [Fig. 6(a)] for a single intensity of $5 \times 10^{13}$ W/cm$^2$ ($\gamma \approx 1.6$) reveals a distinct 6-lobe interference pattern. A conventional semiclassical simulation based on the quasi-static tunneling approximation (i.e., setting $v_{0\parallel}=0$) qualitatively fails, predicting an incorrect 8-lobe structure [Fig. 6(c)]. However, upon including the non-zero initial longitudinal momentum ($v_{0\parallel} \neq 0$), our non-adiabatic semiclassical model quantitatively reproduces the correct 6-lobe structure in perfect agreement with the TDSE benchmark [Fig. 6(b)].
    To understand the underlying physics, we performed a quantum-orbit decomposition. This analysis reveals that the overall fan-like structure arises from the interference of multiple trajectory types, including 'direct' (Category I), 'forward-scattered' (Category II), and 'glory-scattered' (Category III) orbits. While the full structure results from the collective interference of these paths, we have pinpointed the origin of the lobe-count correction. The initial longitudinal momentum contributes a phase term, $\Delta\Phi_{\text{initial}} \approx -\mathbf{v}_{0\parallel} \cdot \mathbf{r}_0$, to the total accumulated action. We found that the relative phase between the 'direct' and 'glory' trajectories is exquisitely sensitive to this term due to their vastly different paths and birth conditions. It is this specific and dramatic change in the I-III interference channel that ultimately corrects the topology of the entire pattern, reducing the lobe count from 8 to 6. In contrast, other interference pairs, such as the holographic pair II-III, are largely robust against this effect as their nearly identical birth conditions cause the initial phase term to cancel in their relative phase. In parallel, our simulations show that the ionic core polarization has a negligible effect on this low-energy structure but is essential for accurately describing higher-energy rescattering features by smoothing unphysical caustics caused by a pure Coulomb potential.
    Conclusion : We have unequivocally demonstrated that the near-threshold fan-like interference pattern in the multiphoton regime is a direct manifestation of non-adiabatic dynamics during tunneling, specifically the acquisition of a longitudinal momentum component by the electron during its finite-time passage under the potential barrier. Our findings not only provide a clear, intuitive, and orbit-based physical picture for this complex quantum phenomenon but also highlight the predictive power of semiclassical methods when crucial non-adiabatic effects are properly incorporated. This understanding lays a foundation for future investigations, including the extension of this model to more complex molecular systems and its application in retrieving attosecond electron dynamics from holographic interference patterns.
  • [1]

    Krausz F, Ivanov M 2009 Rev. Mod. Phys. 81 163

    [2]

    Pazourek R, Nagele S, Burgdörfer J 2015 Rev. Mod. Phys. 87 765

    [3]

    Agostini P, Fabre F, Mainfray G, Petite G, Rahman N K 1979 Phys. Rev. Lett. 42 1127

    [4]

    Paulus G G, Nicklich W, Xu H, Lambropoulos P, Walther H 1994 Phys. Rev. Lett. 72 2851

    [5]

    Krause J L, Schafer K J, Kulander K C 1992 Phys. Rev. Lett. 68 3535

    [6]

    Walker B, Sheehy B, DiMauro L F, Agostini P, Schafer K J, Kulander K C 1994 Phys. Rev. Lett. 73 1227

    [7]

    Huismans Y, Rouzée A, Gijsbertsen A, Jungmann J H, Smolkowska A S, Logman P S W M, Lépine F, Cauchy C, Zamith S, Marchenko T, Bakker J M, Berden G, Redlich B, van der Meer A F G, Muller H G, Vermin W, Schafer K J, Spanner M, Ivanov M Y, Smirnova O, Bauer D, Popruzhenko S V, Vrakking M J J 2011 Science 331 61

    [8]

    He M, Li Y, Zhou Y, Li M, Cao W, Lu P 2018 Phys. Rev. Lett. 120 133204

    [9]

    Xie W, Yan J, Li M, Cao C, Guo K, Zhou Y, Lu P 2021 Phys. Rev. Lett. 127 263202

    [10]

    Li M, Xie H, Cao W, Luo S, Tan J, Feng Y, Du B, Zhang W, Li Y, Zhang Q, Lan P, Zhou Y, Lu P 2019 Phys. Rev. Lett. 122 183202

    [11]

    Tao J F, Cai J, Xia Q Z, Liu J 2020 Phys. Rev. A 101 043416

    [12]

    Tao J F, Xia Q Z, Liao L G, Liu J, Liu X J 2022 Acta Phys. Sin. 71 233206 (in Chinese) [陶建飞, 夏 勤智, 廖临谷, 刘杰, 刘小井 2022 物理学报 71 233206]

    [13]

    Huang X F, Su J, Liao J Y, Li Y B, Huang C 2022 Acta Phys. Sin. 71 093202 (in Chinese) [黄雪飞, 苏杰, 廖健颖, 李盈傧, 黄诚 2022 物理学报 71 093202]

    [14]

    He M, Fan Y, Zhou Y, Lu P 2021 Chinese Phys. B 30 123202

    [15]

    Muller H G 1999 Phys. Rev. A 60 1341

    [16]

    HuP B, Liu J, gang Chen S 1997 Phys. Lett. A 236 533

    [17]

    Liu J, Xia Q Z, Tao J F, Fu L B 2013 Phys. Rev. A 87 041403

    [18]

    Ding B, Xu W, Wu R, Feng Y, Tian L, Li X, Huang J, Liu Z, Liu X 2021 Appl. Sci. 11

    [19]

    Hickstein D D, Gibson S T, Yurchak R, Das D D, Ryazanov M 2019 Rev. Sci. Instrum. 90 065115

    [20]

    Tulsky V, Bauer D 2020 Comput. Phys. Comm. 251 107098

    [21]

    Tong X M, Lin C D 2005 J. Phys. B: At. Mol. Opt. Phys. 38 2593

    [22]

    Tao L, Scrinzi A 2012 New J. Phys. 14 013021

    [23]

    Shvetsov-Shilovski N I, Lein M, Madsen L B, Räsänen E, Lemell C, Burgdörfer J, Arbó D G, Tőkési K 2016 Phys. Rev. A 94 013415

    [24]

    Delone N B, Krainov V P 1991 J. Opt. Soc. Am. B 8 1207

    [25]

    Arissian L, Smeenk C, Turner F, Trallero C, Sokolov A V, Villeneuve D M, Staudte A, Corkum P B 2010 Phys. Rev. Lett. 105 133002

    [26]

    Dreissigacker I, Lein M 2013 Chem. Phys. 414 69

    [27]

    Shvetsov-Shilovski N I, Dimitrovski D, Madsen L B 2012 Phys. Rev. A 85 023428

    [28]

    Dimitrovski D, Maurer J, Stapelfeldt H, Madsen L B 2014 Phys. Rev. Lett. 113 103005

    [29]

    Kang H P, Xu S P, Wang Y L, Yu S G, Zhao X Y, Hao X L, Lai X Y, Pfeifer T, Liu X J, Chen J, Cheng Y, Xu Z Z 2018 J. Phys. B: At. Mol. Opt. Phys 51 105601

    [30]

    Etches A, Madsen L B 2010 J. Phys. B: At. Mol. Opt. Phys 43 155602

    [31]

    Bristow M P F, Glass I I 1972 Phys. Fluids 15 2066

    [32]

    Li M, Geng J W, Han M, Liu M M, Peng L Y, Gong Q, Liu Y 2016 Phys. Rev. A 93 013402

    [33]

    Tao J F, Xia Q Z, Cai J, Fu L B, Liu J 2017 Phys. Rev. A 95 011402

    [34]

    Xia Q Z, Tao J F, Cai J, Fu L B, Liu J 2018 Phys. Rev. Lett. 121 143201

    [35]

    Liao L G, Xia Q Z, Cai J, Liu J 2022 Phys. Rev. A 105 053115

    [36]

    Wang T, Dube Z, Mi Y, Vampa G, Villeneuve D M, Corkum P B, Liu X, Staudte A 2022 Phys. Rev. A 106 013106

    [37]

    Möller M, Meyer F, Sayler A M, Paulus G G, Kling M F, Schmidt B E, Becker W, Milošević D B 2014 Phys. Rev. A 90 023412

  • [1] 王胤, 王壬颍, 陈桥, 邓永和. 点间隧穿耦合对四能级三量子点电磁感应透明介质孤子动力学的影响. 物理学报, doi: 10.7498/aps.73.20231194
    [2] 孙震, 吕项, 李盛, 安忠. 绝热表象下非绝热分子动力学方法. 物理学报, doi: 10.7498/aps.73.20240401
    [3] 王雪梅, 张安琪, 赵生妹. 电路量子电动力学中基于超绝热捷径的控制相位门实现. 物理学报, doi: 10.7498/aps.71.20220248
    [4] 马赟娥, 乔鑫, 高瑞, 梁俊成, 张爱霞, 薛具奎. 可调自旋-轨道耦合玻色-爱因斯坦凝聚体的隧穿动力学. 物理学报, doi: 10.7498/aps.71.20220697
    [5] 王艳梅, 唐颖, 张嵩, 龙金友, 张冰. 飞秒时间分辨质谱和光电子影像对分子激发态动力学的研究. 物理学报, doi: 10.7498/aps.67.20181334
    [6] 李晓克, 冯伟. 非绝热分子动力学的量子路径模拟. 物理学报, doi: 10.7498/aps.66.153101
    [7] 林呈, 张华堂, 盛志浩, 余显环, 刘鹏, 徐竟文, 宋晓红, 胡师林, 陈京, 杨玮枫. 用推广的量子轨迹蒙特卡罗方法研究强场光电子全息. 物理学报, doi: 10.7498/aps.65.223207
    [8] 黄文逍, 张逸竹, 阎天民, 江玉海. 超快强场下低能光电子的研究进展解析R矩阵半经典轨迹理论. 物理学报, doi: 10.7498/aps.65.223204
    [9] 肖相如, 王慕雪, 黎敏, 耿基伟, 刘运全, 彭良友. 强激光场中原子单电离的半经典方法. 物理学报, doi: 10.7498/aps.65.220203
    [10] 刘祥龙, 朱满座, 路璐. 等腰直角三角形的二维量子谱和经典轨道. 物理学报, doi: 10.7498/aps.61.220301
    [11] 唐小锋, 牛铭理, 周晓国, 刘世林. 基于阈值光电子-光离子符合技术的分子离子光谱和解离动力学研究. 物理学报, doi: 10.7498/aps.59.6940
    [12] 高嵩, 徐学友, 周慧, 张延惠, 林圣路. 电场中里德伯原子动力学性质的半经典理论研究. 物理学报, doi: 10.7498/aps.58.1473
    [13] 陆 军, 杜孟利. 从量子谱到经典轨道:矩形腔中的弹子球. 物理学报, doi: 10.7498/aps.53.2450
    [14] 张飞舟, 王 矫, 顾 雁. 量子混沌系统本征态的统计非遍历性及其半经典极限. 物理学报, doi: 10.7498/aps.48.2169
    [15] 李治宽. Raman自由电子激光的半经典理论. 物理学报, doi: 10.7498/aps.45.1812
    [16] 左维, 王顺金. 量子辐射场与经典流的相互作用 hω(4)线性非自治量子系统的代数动力学求解. 物理学报, doi: 10.7498/aps.44.1363
    [17] 李国强, 徐躬耦. 用有限温度自洽半经典方法研究热核上巨共振的性质. 物理学报, doi: 10.7498/aps.38.1413
    [18] 吴柏枚, 陈兆甲, 鲍世宁, 鲍德松, 季振国, 刘古. 非晶Nb-Ni合金晶化过程中紫外光电子能谱研究. 物理学报, doi: 10.7498/aps.38.675
    [19] 陈天杰. 位相因子在光学量子拍的半经典解释中的作用. 物理学报, doi: 10.7498/aps.35.1652
    [20] 唐景昌, 唐叔贤. 光电子衍射谱Fourier变换分析方法的垂直单电子束模型. 物理学报, doi: 10.7498/aps.33.362
计量
  • 文章访问数:  180
  • PDF下载量:  1
  • 被引次数: 0
出版历程
  • 上网日期:  2025-09-05

/

返回文章
返回