Strong-Field Molecular Ionization Beyond The Single Active Electron Approximation

TL;DR

This paper tackles the limits of the SAE approximation in strong-field molecular ionization by solving the TDSE for the two-electron molecule $H_2$ using a Time-Dependent Configuration Interaction (TDCI) approach with a Feshbach partitioning and an adiabatic switch of the electron-electron interaction $V_{ee}$. The method isolates bound and ionized channels via a $Q$-$P$ partition and allows controlled modulation of electron correlation to assess its impact on ionization dynamics. The key finding is a striking non-monotonic ionization probability at $R=5.0$ a.u. due to Resonance-Enhanced Multiphoton Ionization (REMPI) caused by overlapping excited-state resonances, a signature of non-SAE behavior; in contrast, equilibrium ($R=1.4$ a.u.) and dissociation-limit ($R=10.2$ a.u.) cases show predominantly TI or MPI-like behavior with minimal correlation effects. These results highlight correlation-driven pathways that modify ionization and suggest experimental schemes, such as vibrational excitation and channel-resolved photoelectron spectroscopy, to observe non-SAE dynamics in molecules under strong fields.

Abstract

The present work explores quantitative limits to the Single-Active Electron (SAE) approximation, often used to deal with strong-field ionization and subsequent attosecond dynamics. Using a time-dependent multi\-configuration approach, specifically a Time-Dependent Configuration Interaction (TDCI) method, we solve the time-dependent Schr{ö}dinger equation (TDSE) for the two-electron dihydrogen molecule, with the possibility of tuning at will the electron-electron interaction by an adiabatic switch-on/switch-off function. We focus on signals of the single ionization of $H_2$ under a strong near-infrared (NIR) four-cycle, linearly-polarized laser pulse of varying intensity, and within a vibrationally frozen molecule model. The observables we address are post-pulse total ionization probability profiles as a function of the laser peak intensity. Three values of the internuclear distance R taken as a parameter are considered, R = R$_{eq}$ = 1.4 a.u, the equilibrium geometry of the molecule, R = 5.0 a.u for an elongated molecule and R = 10.2 a.u for a dissociating molecule. The most striking observation is the non-monotonous behavior of the ionization probability profiles at intermediate elongation distances with an instance of enhanced ionization and one of partial ionization quenching. We give an interpretation of this in terms of a Resonance-Enhanced-Multiphoton Ionization (REMPI) mechanism with interfering overlapping resonances resulting from excited electronic states.

Figures (7)

• Figure 1: Total ionization probability profiles given as a function of the laser pulse leading intensity, for three excitation frequencies: $\lambda=790$ nm blue line, $\lambda=750$ nm orange line, and $\lambda=700$ nm green line. The first column [panels (a) and (b)] is for $R=1.4$ a.u., the second [panels (c) and (d)] for $R=5.0$ a.u., and the third [panels (e) and (f)] for $R=10.2$ a.u. The upper row [panels (a), (c) and (e)] corresponds to the adiabatic switch-off of $V_{ee}$, while the lower one [panels (b), (d) and (f)] is for the full dynamical calculation including the electron correlation.
• Figure 2: Field-free eigenenergies of H$_2$ with (right side labeled as $\eta=1$) and without (left side labeled as $\eta=0$) the electronic interaction potential $V_{ee}$, at the equilibrium $R=1.4$ a.u. and extended $R=5.0$ a.u. geometries. The origin of energies is taken as the second ionization threshold. The gray rectangles correspond to ionization from the first $\sigma_g$ or $\sigma_u$ channels.
• Figure 3: Field-distorted Coulomb potential, as defined by Eq. (\ref{['Coulomb']}), with $R = 1.4$ a.u., $q_{eff} = 1$ and $\mathcal{F}_0$ corresponding to an intensity of $1.25\times10^{16}$ W/cm$^2$. The ground state level at $-I_p$ is indicated by the green dotted and the magenta dashed horizontal lines, respectively for the calculations with and without electron repulsion.
• Figure 4: Field-free eigenenergies of H$_2$ at $R=5.0$ au (solid thick black lines) and the ionization thresholds (thick blue rectangles and dashed black lines). The origin of energies is taken as the second ionization threshold. Indicated in thin red arrows are the number of ($\lambda=790$ nm) photons needed to ionize.
• Figure 5: Time evolution, during the $I=10^{15}$ W/cm$^2$, $\lambda=790$ nm laser pulse, of the populations of the energy eigenstates at (a) $R=1.4$ a.u., and (b) $R=5.0$ a.u.