Restricted-Geometry Quantum Models Beyond Atoms: Application to NSDI in Diatomic Systems

TL;DR

The paper tackles NSDI in diatomic molecules under strong laser fields by extending a $1+1$-dimensional restricted-geometry quantum model from atoms to diatomics. It introduces three molecular configurations $V_{parallel}$, $V_{perp2}$, and $V_{perp3}$ within a hydrogen-like two-electron Hamiltonian and confines dynamics to symmetric subspaces, enabling efficient computation of ionization yields and momentum distributions. The results reproduce the characteristic knee in double ionization yields, reveal only modest orientation dependence in most cases (with stronger effects in certain molecules like $S_2$), and yield momentum distributions consistent with experiments, including RESI-like features and resonance-driven structures under longer pulses. The study demonstrates the utility and limits of restricted geometry for molecular NSDI, and outlines future directions to incorporate molecular orbital symmetry, nuclear motion, and higher-order ionization channels.

Abstract

We present a (1+1)-dimensional quantum model designed to describe nonsequential double ionization (NSDI) in homonuclear diatomic molecules exposed to strong linearly polarized laser fields. Extending the restricted-geometry framework previously developed for atomic systems, our approach captures key features of NSDI, including the characteristic knee structure in double ionization yields. Despite its simplifying assumptions, the model shows good agreement with experimental data and proves particularly suitable for systems with $σ$-type orbital symmetry. It offers a computationally efficient tool for exploring multi-electron dynamics in molecular systems.

Figures (10)

• Figure 1: (Color online) The three configurations leading to the model potentials $V_{\parallel}$ (a), $V_{\perp 2}$ (b), and $V_{\perp 3}$ (c). Black dots represent the protons, the gray shaded plane indicates the plane in which the electrons move, and $\bm{F}$ denotes the field polarization axis, which is aligned with the $Z$-axis in all cases. In panel (c), one proton is located in front of the gray plane, and the other behind it.
• Figure 2: (Color online) The saddle points (SPs) of the model potentials $V_{\parallel}$ (a), $V_{\perp 2}$ (b), and $V_{\perp 3}$ (c) for a diatomic molecule X$_2$ with internuclear distance $d = 2.28$ a.u. are shown in blue. For comparison, saddle points for the helium atom are shown in green. In the case of $V{\perp 3}$, solutions exist only for field amplitudes $|F| < 0.39$ a.u. The upper axis displays the absolute peak field amplitude $|F|$ corresponding to the molecular saddle positions.
• Figure 3: (Color online) Single ionization (SI) and double ionization (DI) yield curves of potentials $V_{\parallel}$ and $V_{\perp 2}$ at a frequency of $\omega = 0.075$ a.u. for N$_2$.
• Figure 4: (Color online) Single ionization (SI) and double ionization (DI) yield curves of potentials $V_{\parallel}$ and $V_{\perp 2}$ at a frequency of $\omega = 0.06$ a.u. for O$_2$.
• Figure 5: (Color online) Single ionization (SI) and double ionization (DI) yield curves of potentials $V_{\parallel}$ and $V_{\perp 2}$ at a frequency of $\omega = 0.045$ a.u. for S$_2$.