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

半经典响应时间理论在强场分子电离中的应用

叶升 王赏 陈子玉 李卫艳 申诗琪 陈彦军

引用本文:
Citation:

半经典响应时间理论在强场分子电离中的应用

叶升, 王赏, 陈子玉, 李卫艳, 申诗琪, 陈彦军

Applications of semiclassical response time theory in strong-field molecular ionization

YE Sheng, WANG Shang, CHEN Ziyu, LI Weiyan, SHEN Shiqi, CHEN Yanjun
Article Text (iFLYTEK Translation)
PDF
HTML
导出引用
  • 阿秒钟技术为研究原子分子强场电离过程中电子超快动力学提供了强有力的工具. 该技术依赖定量理论模型从实验测量得到的光电子频谱反演电离过程中系统的超快时域信息, 而构建定量强场理论模型的关键问题之一是库仑效应的理论描述. 与原子相比, 分子具有多中心库仑势, 在外场中具有许多新的效应, 这为检验定量理论模型的适用性提供了更广阔平台. 本文针对拉伸到大核间距的分子的阿秒钟特征观测量, 比较了不同理论模型的预言, 指出最近提出的半经典响应时间理论预言与数值实验结果更一致. 该理论强调, 与具有经典性质的远核库仑效应相比, 具有量子性质的近核库仑效应对分子隧穿电离影响更显著. 本文进一步展望了该理论模型在具有电荷共振、固有偶极、取向效应以及复杂库仑势形式的分子强场电离中的应用.
    The attosecond technology provides a powerful tool for studying the ultrafast dynamics of electrons during the strong-field ionization of atoms and molecules. This technology relies on quantitative theoretical models to invert the ultrafast time-domain information of the system in the ionization process from the photoelectron spectra obtained through experimental measurements. One of the key issues in constructing quantitative strong-field theoretical models is the theoretical description of the Coulomb effect. The Coulomb potential of molecules, compared with the single-center Coulomb potential of atoms, exhibits a multi-center distribution. This fundamental geometric structure feature results in many new effects of molecules in the external field, such as orientation effect, charge resonance effect, intrinsic dipole effect, and vibration effect. Therefore, it can be expected that the tunneling ionization process of molecules contains more phenomena than that of atoms, which is worthy of in-depth study in experiment and theory. Especially for stretched molecular ions, such as $ {\mathrm{H}}_{2}^{+} $, those exhibiting charge resonance effects in external fields, the difference between near-nucleus and far-nucleus Coulomb effects, which is of great significance for constructing quantitative theoretical models, becomes more complex, providing a platform for testing the applicability of quantitative theoretical models.This work systematically compares the predictions of different theoretical models for the attoclock characteristic observables in molecular systems with large internuclear distances. Through comparative analysis, it is found that the recently proposed semiclassical response time theory, which incorporates near-nucleus Coulomb corrections, shows better agreement with numerical experimental results than the developed strong-field approximation models that consider far-nucleus Coulomb corrections. The semiclassical response time theory establishes a theoretical framework for describing strong-field ultrafast ionization dynamics of stretched molecular systems by considering dual-center Coulomb potential corrections and excited-state contributions. Specifically, it approximates the complex four-body interactions (electron-laser-dual nuclei) in stretched molecular systems to a three-body interaction (electron-laser-dressed-up barrier-proximal nucleus), while using the influence of the other nucleus on the potential barrier as a correction term for the tunnel-exit position. This framework highlights the significant influence of quantum-property-dominated near-nucleus Coulomb effects on molecular tunneling ionization. Furthermore, the theory provides an explicit formula for the response time determined by fundamental laser and molecular parameters. By calculating this response time, the values of attoclock observables are deduced from the theory, thus enabling a clear discussion of ionization time delays in stretched molecular tunneling ionization and revealing that such delays reflect the timescale of strong four-body interactions between the laser, electron, and molecular nucleus. In contrast, the developed strong-field approximation model that simultaneously considers excited-state effects and numerically solves Newton’s equations to describe far-nucleus Coulomb effects cannot fully describe the above-mentioned four-body interaction, making it difficult to quantitatively describe the complex tunneling ionization dynamics under the combined action of coulomb and excited states. Additionally, since this model cannot clearly define the ionization time, the related ionization time delay issues cannot be well discussed. Computational results show that the semi-classical response time theoretical model has improved in terms of calculation accuracy and efficiency, thereby verifying the applicability of this theoretical model in the study of molecular ultrafast ionization dynamics.Moreover, for $ {\mathrm{H}}_{2}^{+} $ with intermediate internuclear distances, the charge resonance effect induces a significant ionization enhancement effect. We present relevant numerical experimental attoclock results and explore the potential applications of the response time theory in such systems. We also envision the extension of this theory to strong-field tunneling ionization in polar molecules, multi-center linear molecules, planar and three-dimensional molecules, and oriented molecules, where interference and Coulomb-acceleration effects compete with each other.
  • 图 1  不同激光和分子参数下的势函数曲线[40] (a) 在$ y=0 $处$ R=2 $ a.u.的$ {\mathrm{H}}_{2}^{+} $(红线)和模型原子(黑线)的激光缀饰势$ V'\left(\boldsymbol{r}\right)=V\left(\boldsymbol{r}\right)-{E}_{0}x $(实线)和无激光势$ V\left(\boldsymbol{r}\right) $(虚线). 水平线表示$ -{I}_{p}=-1.11 $ a.u.的能量. 插图显示了分子和原子出口位置之间差异结果的放大图. (b) 在$ y=0 $处$ R=16 $ a.u.的$ {\mathrm{H}}_{2}^{+} $的激光缀饰势$ V'\left(\boldsymbol{r}\right)=V\left(\boldsymbol{r}\right)-{E}_{0}x $(实线)和无激光势$ V\left(\boldsymbol{r}\right) $(虚线). 两条水平线分别表示$ {E}_{1}'\approx -\left[{I}_{\mathrm{p}}-{E}_{0}\left(R/2\right)\right]=-0.09 $ a.u.和$ {E}_{2}'\approx -\left[{I}_{\mathrm{p}}+{E}_{0}\left(R/2\right)\right]=-2.13 $ a.u.的能量. 坐标$ {x}_{2}\left({x}_{4}\right) $对应于电子从左(右)核附近向上(向下)缀饰的势垒中隧穿的出口位置. 坐标$ {x}_{1} $和$ {x}_{3} $表示分子左边和右边原子核的位置. 水平的粉红色箭头表示隧穿的方向, $ {{r}_{0}''}_{}=\left|{x}_{2}-{x}_{1}\right|({r}_{0}''=\left|{x}_{4}-{x}_{3}\right|) $表示出口位置相对于左(右)核位置的绝对值. 这里使用的激光振幅为$ {E}_{0}=0.13 $ a.u.

    Fig. 1.  Potential function curves obtained at different laser and molecular parameters [40]. (a) Sketch of the laser-dressed potential $ V'\left(\boldsymbol{r}\right)=V\left(\boldsymbol{r}\right)-{E}_{0}x $ (solid curves) and laser-free potential $ V\left(\boldsymbol{r}\right) $ (dash-dotted line) for $ {\mathrm{H}}_{2}^{+} $ with $ R=2 $ a.u. (red curves) and the model atom (black curves) at $ y=0 $. The horizontal line indicates the energy of $ -{I}_{\mathrm{p}}=-1.11 $ a.u. The inset shows a close-up of the results for the difference in exit position between the molecule and the atom. (b) Sketch of the laser-dressed potential $ V'\left(\boldsymbol{r}\right)=V\left(\boldsymbol{r}\right)-{E}_{0}x $ (solid curves) and laser-free potential $ V\left(\boldsymbol{r}\right) $ (dash-dotted lines) $ {\mathrm{H}}_{2}^{+} $ with $ R=16 $ a.u. at $ y=0 $. Two horizontal lines represent the energy $ {E}_{1}'\approx -\left[{I}_{\mathrm{p}}-{E}_{0}\left(R/2\right)\right]=-0.09 $ a.u. and the energy $ {E}_{2}'\approx -\left[{I}_{\mathrm{p}}+{E}_{0}\left(R/2\right)\right]=-2.13 $ a.u., respectively. The coordinate $ {x}_{2}\left({x}_{4}\right) $ corresponds to the exit position of electrons tunneling out of the dressed-up (down) potential barrier neighboring the left (right) nucleus. The coordinates $ {x}_{1} $ and $ {x}_{3} $ represent the positions of the left and right nuclei of the molecule. The horizontal pink arrows indicate the direction of tunneling and $ {r}_{0}''=\left|{x}_{2}-{x}_{1}\right|({r}_{0}''=\left|{x}_{4}-{x}_{3}\right|) $ represents the absolute value of the exit position relative to the position of the left (right) nucleus. The laser amplitude used here is $ {E}_{0}=0.13 $ a.u..

    图 2  不同方法得到(a)—(d)模型原子、(e)—(h) $ R=2 $ a.u.的$ {\mathrm{H}}_{2}^{+} $、以及(i)—(l) $ R=16 $ a.u.的$ {\mathrm{H}}_{2}^{+} $的光电子动量分布[40] (a), (e), (i) TDSE; (b), (f) SFA; (j) DSFA; (c) A-TRCM方法; (g) S-TRCM方法; (k) L-TRCM方法; (d), (h) MSFA; (l) U'-MDSFA. 值得注意的是, (l)中的U'-MDSFA模型规定向上缀饰势垒附近原子核的位置为隧穿位置矢量的起点(该矢量终点为隧穿出口位置), 并将电子隧穿后演化的初始位置修正为$ \left|\boldsymbol{r}'\left({t}_{0}\right)\right|\equiv {r}_{0}'=\left|{\boldsymbol{r}}_{0}\right|-{r}_{\mathrm{d}} $, 其中$ {r}_{\mathrm{d}}={r}_{\mathrm{p}}-{r}_{0}'' $, $ {r}_{0}''=\left|{x}_{2}-{x}_{1}\right| $. PMD的非零偏移角$ \theta $也在每个面板中表示. 激光参数为$ I=1\times {10}^{15} $ W/cm2, $ \lambda =800 $ nm, $ \varepsilon =0.87 $

    Fig. 2.  PMDs of (a)–(d) the model atom, (e)–(h) $ {\mathrm{H}}_{2}^{+} $ with $ R=2 $ a.u., and (i)–(l) $ {\mathrm{H}}_{2}^{+} $ with $ R=16 $ a.u., obtained with different methods[40]: (a), (e), (i) The TDSE; (b), (f) the SFA; (j) the DSFA; (c) the TRCM method; (g) the S-TRCM method; (k) the L-TRCM method; (d), (h) the MSFA; (l) the U'-MDSFA. It is noteworthy that the U'-MDSFA simulation in (l) assumes taking the position of the atomic nucleus near the dressed-up potential barrier as the starting point of the tunneling position vector (the endpoint of this vector is the position of the tunnel exit), and modifies the initial position for post-tunneling electron evolution to $ \left|\boldsymbol{r}'\left({t}_{0}\right)\right|\equiv {r}_{0}'=\left|{\mathbf{r}}_{0}\right|-{r}_{\mathrm{d}} $, with $ {r}_{\mathrm{d}}={r}_{\mathrm{p}}-{r}_{0}'' $ and $ {r}_{0}''=\left|{x}_{2}-{x}_{1}\right| $. The nonzero offset angle $ \theta $ of the PMD is also indicated in each panel. The laser parameters are $ I=1\times {10}^{15} $ W/cm2, $ \lambda =800 $ nm and $ \varepsilon =0.87 $.

    图 3  MDSFA以及不同修正MDSFA模型预测$ R=16 $ a.u.的$ {\mathrm{H}}_{2}^{+} $的光电子动量分布 (a) MDSFA模型, 规定以坐标原点为隧穿位置矢量的起点(该矢量终点为隧穿出口位置); (b), (c) U(D)-MDSFA模型, 规定以向上(向下)缀饰势垒附近原子核所在的位置为隧穿位置矢量的起点; (d) D'-MDSFA模型, 该模型在D-MDSFA基础上将电子隧穿后演化的初始位置修正为$ \left|\boldsymbol{r}'\left({t}_{0}\right)\right|\equiv {r}_{0}'=\left|{\boldsymbol{r}}_{0}\right|-{r}_{\mathrm{d}} $, 其中$ {r}_{\mathrm{d}}={r}_{\mathrm{p}}-{r}_{0}'' $, $ {r}_{0}''=\left|{x}_{4}-{x}_{3}\right| $. PMD的非零偏移角$ \theta $也展示在每个面板中. 激光参数为$ I= $$ 1\times {10}^{15} $ W/cm2, $ \lambda =800 $nm, $ \varepsilon =0.87 $

    Fig. 3.  The PMDs of $ {\mathrm{H}}_{2}^{+} $ with $ R=16 $ a.u. calculated by MDSFA and different modified MDSFA models. (a) MDSFA model stipulates that the origin of the coordinate system is taken as the starting point of the tunneling position vector (the endpoint of this vector is the position of the tunnel exit). (b), (c) U(D)-MDSFA model stipulates that the position of the atomic nucleus near the dressed-up (dressed-down) barrier is defined as the starting point of the tunneling position vector. (d) D'-MDSFA model which modifies the initial position for post-tunneling electron evolution to $ \left|\boldsymbol{r}'\left({t}_{0}\right)\right|\equiv {r}_{0}'=\left|{\boldsymbol{r}}_{0}\right|-{r}_{\mathrm{d}} $, with $ {r}_{\mathrm{d}}={r}_{\mathrm{p}}-{r}_{0}'' $ and $ {r}_{0}''=\left|{x}_{4}-{x}_{3}\right| $, based on the D-MDSFA model. The nonzero offset angle $ \theta $ of the PMD is also indicated in each panel. The laser parameters are $ I=1\times {10}^{15} $ W/cm2, $ \lambda =800 $ nm and $ \varepsilon =0.87 $.

    图 4  TDSE、L-TRCM模型、U-MDSFA模型、U'-MDSFA模型、D-MDSFA模型和D'-MDSFA模型对于不同R预测的$ {\mathrm{H}}_{2}^{+} $的偏移角. 激光参数为$ I=1\times {10}^{15} $ W/cm2, $ \lambda =800 $nm, $ \varepsilon =0.87 $

    Fig. 4.  Offset angles of $ {\mathrm{H}}_{2}^{+} $ predicted by the TDSE, the L-TRCM model, the U-MDSFA model, the U'-MDSFA model, the D-MDSFA model, and the D'-MDSFA model for different R. The laser parameters are $ I=1\times {10}^{15} $W/cm2, $ \lambda =800 $ nm and $ \varepsilon =0.87 $.

    图 5  对中间核间距$ {\mathrm{H}}_{2}^{+} $隧穿电离的研究 (a) 在$ y=0 $处$ R=4 $ a.u.(绿线)和$ R=6 $ a.u.(红线)的$ {\mathrm{H}}_{2}^{+} $的激光缀饰势$ V'\left(\boldsymbol{r}\right)=V\left(\boldsymbol{r}\right)-{E}_{0}x $(实线)和无激光势$ V\left(\boldsymbol{r}\right) $(虚线). 水平线表示$ -{I}_{\mathrm{p}}=-1.11 $ a.u.的能量. (b), (c)分别是通过TDSE得到的$ R=4 $ a.u.和$ R=6 $ a.u.的$ {\mathrm{H}}_{2}^{+} $的光电子动量分布. PMD的非零偏移角$ \theta $也在每个面板中表示. 电离能均为$ {I}_{\mathrm{p}}=1.11 $ a.u.. 为满足不同系统对电离率的要求, (b)中电场强度为$ I=4\times {10}^{14} $ W/cm2, (c)中电场强度为$ I=3\times {10}^{14} $ W/cm2. 其他激光参数为$ \lambda =800 $ nm, $ \varepsilon =0.87 $

    Fig. 5.  Research on tunneling ionization of $ {\mathrm{H}}_{2}^{+} $ with intermediate $ R $. (a) Sketch of the laser-dressed potential $ V'\left(\boldsymbol{r}\right)= $$ V\left(\boldsymbol{r}\right)-{E}_{0}x $(solid curves) and laser-free potential $ V\left(\boldsymbol{r}\right) $ (dash-dotted line) for $ {\mathrm{H}}_{2}^{+} $ with $ R=4 $ a.u. at $ y=0 $. The horizontal line indicates the energy of $ -{I}_{\mathrm{p}}=-1.11 $ a.u.. PMDs of $ {\mathrm{H}}_{2}^{+} $ with (b) $ R=4 $ a.u. and (c) $ R=6 $ a.u.. The offset angle $ \theta $ of the PMD is also indicated in each panel. The ionization energy are both $ {I}_{\mathrm{p}}=1.11 $ a.u.. To satisfy the ionization rate requirements of different systems, the electric field strength used in (b) is $ I=4\times {10}^{14} $ W/cm2 and in (c) is $ I=3\times {10}^{14} $ W/cm2. Other laser parameters are $ \lambda =800 $ nm, $ \varepsilon =0.87 $.

  • [1]

    Li W, Zhou X B, Lock R, Patchkovskii S, Stolow A, Kapteyn H C, Murnane M M 2008 Science 322 1207Google Scholar

    [2]

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

    [3]

    Lépine F, Ivanov M Y, Vrakking M J J 2014 Nat. Photon 8 195Google Scholar

    [4]

    Garg M, Zhan M, Luu T T, Lakhotia H, Klostermann T, Guggenmos A, Goulielmakis E 2016 Nature 538 359Google Scholar

    [5]

    Lakhotia H, Kim H Y, Zhan M, Hu S, Meng S, Goulielmakis E 2020 Nature 583 55Google Scholar

    [6]

    MacColl L A 1932 Phys. Rev. 40 621Google Scholar

    [7]

    Wigner E P 1955 Phys. Rev. 98 145Google Scholar

    [8]

    Ranfagni A, Mugnai D, Fabeni P, Pazzi G P 1991 Appl. Phys. Lett. 58 774Google Scholar

    [9]

    Enders A, Nimtz G 1992 J. Phys. 12 1693

    [10]

    Steinberg A M, Kwiat P G, Chiao R Y 1993 Phys. Rev. Lett. 71 708Google Scholar

    [11]

    Spielmann C, Szipöcs R, Stingl A, Krausz F 1994 Phys. Rev. Lett. 73 2308Google Scholar

    [12]

    Muga J G, Sala Mayato R, Egusquiza I L (eds. ) 2002 Time in Quantum Mechanics (Vol. 1) (Berlin, Heidelberg: Springer) pp5, 6

    [13]

    Ramos R, Spierings D, Racicot I, Steinberg A M 2020 Nature 583 529Google Scholar

    [14]

    Eckle P, Smolarski M, Schlup P, Biegert J, Staudte A, Schöffler M, Muller H G, Dörner R, Keller U 2008 Nat. Phys. 4 565Google Scholar

    [15]

    Eckle P, Pfeiffer A N, Cirelli C, Staudte A, Dörner R, Muller H G, Buttiker M, Keller U 2008 Science 322 1525Google Scholar

    [16]

    Pfeiffer A N, Cirelli C, Smolarski M, Dimitrovski D, Abu-samha M, Madsen L B, Keller U 2012 Nat. Phys. 8 76Google Scholar

    [17]

    Pfeiffer A N, Cirelli C, Smolarski M, Keller U 2013 Chem. Phys. 414 84Google Scholar

    [18]

    Landsman A S, Weger M, Maurer J, Boge R, Ludwig A, Heuser S, Cirelli C, Gallmann L, Keller U 2014 Optica 1 343Google Scholar

    [19]

    Klaiber M, Hatsagortsyan K Z, Keitel C H 2015 Phys. Rev. Lett. 114 083001Google Scholar

    [20]

    Hofmann C, Landsman A S, Kelle U 2019 J. Mod. Optic. 66 1052Google Scholar

    [21]

    Serov V V, Bray A W, Kheifets A S 2019 Phys. Rev. A 99 063428Google Scholar

    [22]

    Sainadh U S, Xu H, Wang X, Atia-Tul-Noor A, Wallace W C, Douguet N, Bray A W, Ivanov I, Bartschat K, Kheifets A, Sang R T, Litvinyuk I V 2019 Nature 568 75Google Scholar

    [23]

    Chen C, Che J Y, Xie X J, Wang S, Xin G G, Chen Y J 2022 Chin. Phys. B 31 033201Google Scholar

    [24]

    车佳殷, 陈超, 李卫艳, 李维, 陈彦军 2023 物理学报 72 193301Google Scholar

    Che J Y, Chen C, Li W Y, Li W, Chen Y J 2023 Acta Phys. Sin. 72 193301Google Scholar

    [25]

    Yan T M, Popruzhenko S V, Vrakking M J J, Bauer D 2010 Phys. Rev. Lett. 105 253002Google Scholar

    [26]

    Li M, Geng J, Liu H, Deng Y K, Wu C Y, Peng L Y, Gong Q H, Liu Y Q 2014 Phys. Rev. Lett. 112 113002Google Scholar

    [27]

    Lai X Y, Poli C, Schomerus H, Figueira de Morisson Faria C 2015 Phys. Rev. Lett. 92 043407

    [28]

    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 013415Google Scholar

    [29]

    Xie X J, Chen C, Xin G G, Liu J, Chen Y J 2020 Opt. Express 28 33228Google Scholar

    [30]

    Che J Y, Chen C, Li W Y, Wang S, Xie X J, Huang J Y, Peng Y G, Xin G G, Chen Y J 2022 arXiv: 2111.08491

    [31]

    Camus N, Yakaboylu E, Fechner L, Klaiber M, Laux M, Mi Y, Hatsagortsyan K Z, Pfeifer T, Keitel C H, Moshammer R 2017 Phys. Rev. Lett. 119 023201Google Scholar

    [32]

    Chen Y J, Liu J, Hu B 2009 Phys. Rev. A 79 033405Google Scholar

    [33]

    Frumker E, Hebeisen C T, Kajumba N, Bertrand J B, Wörner H J, Spanner M, Villeneuve D M, Naumov A, Corkum P B 2012 Phys. Rev. Lett. 109 233904Google Scholar

    [34]

    Chen Y J, Zhang B 2012 J. Phys. B 45 215601Google Scholar

    [35]

    Li W Y, Dong F L, Yu S J, Wang S, Yang S P, Chen Y J 2015 Opt. Express 23 031010Google Scholar

    [36]

    Li W Y, Wang S, Shi Y Z, Yang S P, Chen Y J 2017 J. Phys. B 50 085003Google Scholar

    [37]

    Wang S, Che J Y, Chen C, Xin G G, Chen Y J 2020 Phys. Rev. A 102 053103Google Scholar

    [38]

    Etches A, Gaarde M B, Madsen L B 2012 Phys. Rev. A 86 023818Google Scholar

    [39]

    Li W Y, Yu S J, Wang S, Chen Y J 2016 Phys. Rev. A 94 053407Google Scholar

    [40]

    Shen S Q, Chen Z Y, Wang S, Che J Y, Chen Y J 2024 Phys. Rev. A 110 033106Google Scholar

    [41]

    Brabec T, Ivanov M Yu, Corkum P B 1996 Phys. Rev. A 54 R2551Google Scholar

    [42]

    Goreslavski S P, Paulus G G, Popruzhenko S V, Shvetsov-Shilovski N I 2004 Phys. Rev. Lett. 93 233002Google Scholar

    [43]

    Feit M D, Fleck J A, Steiger A 1982 J. Comput. Phys. 47 412Google Scholar

    [44]

    Lewenstein M, Kulander K C, Schafer K J, Bucksbaum P H 1995 Phys. Rev. A 51 1495Google Scholar

    [45]

    Corkum P B, Krausz F 2007 Nat. Phys. 3 381Google Scholar

    [46]

    Ren D X, Wang S, Chen C, Li X K, Yu X T, Zhao X N, Ma P, Wang C C, Luo S Z, Chen Y J, Ding D J 2022 J. Phys. B 55 175101Google Scholar

    [47]

    Becker W, Grasbon F, Kopold R, Milošević D B, Paulus G G, Walther H 2002 Adv. At. Mol. Opt. Phys. 48 35

    [48]

    Chen Y J, Hu B 2010 Phys. Rev. A 81 013411Google Scholar

    [49]

    Sun F J, Chen C, Li W Y, Liu X, Li W, Chen Y J 2021 Phys. Rev. A 103 053108Google Scholar

    [50]

    Zuo T, Bandrauk A D 1995 Phys. Rev. A 52 R2511Google Scholar

    [51]

    Becker W, Chen J, Chen S G, Milošević D B 2007 Phys. Rev. A 76 033403Google Scholar

    [52]

    Che J Y, Zhang F B, Li W Y, Chen C, Chen Y J 2023 New J. Phys. 25 083022Google Scholar

    [53]

    Chen J, Chen S G 2007 Phys. Rev. A 75 041402(R

    [54]

    Blaga C I, Catoire F, Colosimo P, Paulus G G, Muller H G, Agostini P, DiMauro L F 2009 Nat. Phys. 5 335Google Scholar

    [55]

    Corkum P B 1993 Phys. Rev. Lett. 71 1994Google Scholar

    [56]

    Yang B, Schafer K J, Walker B, Kulander K C, Agostini P, DiMauro L F 1993 Phys. Rev. Lett. 71 3770Google Scholar

    [57]

    Peng Y G, Che J Y, Zhang F B, Xie X J, Xin G G, Chen Y J 2024 Opt. Express 32 12734Google Scholar

    [58]

    Chen Z Y, Shen S Q, Li Y P, Yang Z Q, Che J Y, Chen Y J 2025 Phys. Rev. A 111 053118Google Scholar

    [59]

    Chen Y J, Chen J, Liu J 2006 Phys. Rev. A 74 063405Google Scholar

    [60]

    Kamta G L, Bandrauk A D 2005 Phys. Rev. Lett. 94 203003Google Scholar

    [61]

    Shi Y Z, Zhang B, Yu W Y, Chen Y J 2017 Phys. Rev. A 95 033406Google Scholar

    [62]

    Wang S, Cai J, Chen Y J 2017 Phys. Rev. A 96 043413Google Scholar

    [63]

    Su N, Yu S J, Li W Y, Yang S P, Chen Y J 2018 Chin. Phys. B 27 054213Google Scholar

    [64]

    Yu S J, Li W Y, Li Y P, Chen Y J 2017 Phys. Rev. A 96 013432Google Scholar

    [65]

    Chen Y J, Hu B 2009 J. Chem. Phys. 131 244109Google Scholar

    [66]

    Gao F, Chen Y J, Xin G G, Liu J, Fu L B 2017 Phys. Rev. A 96 063414Google Scholar

    [67]

    Chen C, Ren D X, Han X, Yang S P, Chen Y J 2018 Phys. Rev. A 98 063425Google Scholar

  • [1] 张一晨, 丁南南, 李加林, 付玉喜. 阿秒瞬态吸收光谱: 揭示电子动力学的超快光学探针. 物理学报, doi: 10.7498/aps.74.20250546
    [2] 杨旭, 冯红梅, 刘佳南, 张向群, 何为, 成昭华. 超快自旋动力学: 从飞秒磁学到阿秒磁学. 物理学报, doi: 10.7498/aps.73.20240646
    [3] 陶琛玉, 雷建廷, 余璇, 骆炎, 马新文, 张少锋. 阿秒脉冲的发展及其在原子分子超快动力学中的应用. 物理学报, doi: 10.7498/aps.72.20222436
    [4] 赵猛, 全威, 肖智磊, 许松坡, 王志强, 王明辉, 成思进, 吴文卓, 王艳兰, 赖炫扬, 柳晓军. 强激光场驱动Ar原子电离中的隧穿延时. 物理学报, doi: 10.7498/aps.71.20221295
    [5] 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
    [6] 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
    [7] 徐峰, 郑雨军. 量子相空间纠缠轨线力学. 物理学报, doi: 10.7498/aps.62.213401
    [8] 邓善红, 高嵩, 李永平, 裴云昌, 林圣路. 平行电磁场中锂原子自电离的半经典分析. 物理学报, doi: 10.7498/aps.59.826
    [9] 李钱光, 兰鹏飞, 洪伟毅, 张庆斌, 陆培祥. 阿秒电离门调控宽带超连续谱的传播特性. 物理学报, doi: 10.7498/aps.58.5679
    [10] 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
    [11] 王墨戈, 陆启生, 许晓军, 郭少锋. 宽谱染料激光器的数值模型及实验验证. 物理学报, doi: 10.7498/aps.57.1857
    [12] 何志红, 姚建铨, 时华峰, 黄 晓, 罗锡璋, 江绍基, 李建荣, 王 鹏. 抽运光强度对光学抽运重水气体产生THz激光的影响分析. 物理学报, doi: 10.7498/aps.56.6451
    [13] 何志红, 姚建铨, 时华锋, 黄 晓, 罗锡璋, 江绍基, 王 鹏. 光泵重水气体产生THz激光的半经典理论分析. 物理学报, doi: 10.7498/aps.56.5802
    [14] 欧阳世根, 关毅, 佘卫龙. 旋转超导体中的电流与电磁场. 物理学报, doi: 10.7498/aps.51.1596
    [15] 布 和, 刘 辽. 半经典Brans-Dicke理论中的闭合宇宙解. 物理学报, doi: 10.7498/aps.47.728
    [16] 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
    [17] 王海达. 氩气直流放电等离子体中三稳现象的半经典理论. 物理学报, doi: 10.7498/aps.39.1928
    [18] 张建平, 李玲, 叶培大. 电负反馈半导体激光器半经典理论. 物理学报, doi: 10.7498/aps.38.1436
    [19] 潘少华, 韩全生. 分布反馈染料激光器的半经典理论. 物理学报, doi: 10.7498/aps.31.318
    [20] 潘少华. 染料激光器模式耦合半经典理论. 物理学报, doi: 10.7498/aps.30.1067
计量
  • 文章访问数:  603
  • PDF下载量:  10
  • 被引次数: 0
出版历程
  • 收稿日期:  2025-04-08
  • 修回日期:  2025-05-08
  • 上网日期:  2025-05-20

/

返回文章
返回