Dissociation dynamic study of <inline-formula><tex-math id="M2">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> in time-delayed two-color femtosecond lasers

Abstract

In recent years, the rapid development of ultrashort pulse laser technology has made it possible to regulate the ionization and dissociation dynamics of atoms and molecules. Among them, the microscopic dynamics of molecular dissociation have always been a hot topic. The phenomenon of molecular dissociation, which is caused by the interaction between femtosecond intense laser fields and <inline-formula><tex-math id="M3">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> molecules, has attracted widespread attention. Previous theoretical studies on the dissociation of <inline-formula><tex-math id="M4">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> molecules mainly focused on studying its dissociation dynamics through numerical calculations, with relatively few theoretical models. This paper aims to establish a simple classical model to describe the dissociation dynamics. Firstly, this paper calculates the joint distribution of nuclear energy and electronic energy in the dissociation process of <inline-formula><tex-math id="M5">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> molecules under the action of pump lasers by numerically solving the Schrödinger equation. The results prove that <inline-formula><tex-math id="M6">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> molecules initially in the ground state are dissociated into <inline-formula><tex-math id="M7">\begin{document}$H^+ + H^*$\end{document}</tex-math></inline-formula> after absorbing a pump photon in the pump light field. Next, this paper studies the dissociation dynamics of <inline-formula><tex-math id="M8">\begin{document}$\text{H}_2^+$\end{document}</tex-math></inline-formula> molecules in time-delayed two-color femtosecond lasers. We find that it greatly depends on the specific forms of the pump light and the probe light. By utilizing the dependence of the dissociation kinetic energy release (KER) spectrum on the time delay of the two-color femtosecond lasers, we retrieve the sub-attosecond microscopic dynamic behaviors of electrons and atomic nuclei in the dissociation process. Furthermore, we establish a classical model based on the conservation of energy and momentum to describe the dissociation dynamics. This model can qualitatively predict the ion dissociation KER spectrum depending on the time delay of the two-color femtosecond lasers. The electronic resonant transition between the molecular ground state and the first excited state caused by the probe light will affect the ion kinetic energy spectrum in the dissociation process. Namely, the ion kinetic energy spectrum is dependent on the frequency of the probe laser. By taking advantage of this characteristic, we propose a scheme to reconstruct the evolution of the internuclear distance with time. Our reconstruction results can qualitatively predict the trend of the numerical simulation results, and this scheme may provide some theoretical guidance for experiments.