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

<sec>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 <inline-formula><tex-math id="M1">\begin{document}$ {\mathrm{H}}_{2}^{+} $\end{document}</tex-math></inline-formula>, 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.</sec><sec>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.</sec><sec>Moreover, for <inline-formula><tex-math id="M2">\begin{document}$ {\mathrm{H}}_{2}^{+} $\end{document}</tex-math></inline-formula> 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.</sec>