Nonadiabatic theory for subcycle ionic dynamics in multielectron tunneling ionization

Abstract

Multielectron tunneling ionization creates ionic coherence crucial for lasing and driving electron motion in molecules. While tunneling is well understood as a single active electron process, less emphasis has been placed on theoretical descriptions of bound electrons during tunneling. This work systematically investigates multielectron tunneling ionization based on the strong field approximation, establishing a theoretical foundation and demonstrating the equivalence of wave function and density matrix approaches for subcycle ionic dynamics. An accurate subcycle nonadiabatic ionization rate is also derived and incorporated into the theory to improve its quantitative accuracy. Applying the theory to N$_{2}$ and CO$_{2}$, this work showcases how an intense laser field can induce ionic coherence in molecules as observed in previous experiments. These findings encourage future investigations into multielectron tunneling ionization and its applications in lasing and in controlling chemical reactions.

Figures (8)

• Figure 1: Subcycle adiabatic (blue line) and nonadiabatic ionization rate for the H $1s$ orbital for a sinusoidal laser field with a peak laser intensity of 1.00 $\times 10^{14}$ W/cm$^{2}$ and wavelength of 800 nm (orange line) and 1600 nm (green line).
• Figure 2: Top row: Ionization yield for the H $1s$ orbital for a 10 fs cosine-square envelope pulse with a wavelength of 800 nm, 1200 nm, and 1600 nm at different peak laser intensities. The time-dependent Schrödinger equation (TDSE) results are extracted from Ref. Li2014b. The vertical line marks the critical intensity for the H $1s$ orbital. Bottom row: The percentage difference of the yield calculated using the ADK rate and the rate in this work with the TDSE results.
• Figure 3: Top: Ratio of the absolute value of birth delay to the birth time uncertainty of orbital 2 (solid line). The normalized ionization rate of orbital 2 (dashed line) is plotted to identify the relevant time interval. Bottom: Longitudinal canonical momentum $p_{z}$ at $p_{\perp} = 0$ for orbitals 1 (blue line) and 2 (orange line), corresponding to Keldysh parameter $\gamma_{K}=$ 1.00 and 1.13. The shaded area of the same color is the possible $p_{z}$ within the birth time uncertainty. The laser wavelength is 800 nm with a peak intensity of $1 \times 10^{14}$ W/cm$^{2}$.
• Figure 4: Top: Under the barrier phase acquired by the active electron with $p_{\perp} = 0$ from orbitals 1 (blue line) and 2 (orange line), corresponding to Keldysh parameter $\gamma_{K}=$ 1.00 and 1.13. The longitudinal canonical momentum is approximated to be identical for the two orbitals. The dashed line is the phase difference Re$(S_{1} - S_{2})$. Bottom: Imaginary part of the action with $p_{\perp} = 0$ from orbitals 1 (blue line) and 2 (orange line). The laser parameters are identical to Fig. \ref{['fig:pz']}.
• Figure 5: Subcycle dynamics of the population of (a) $X^{2}\Sigma_{g}^{+}$, (b) $A^{2}\Pi_{u+}$, and (c) $B^{2}\Sigma_{u}^{+}$ state of N$_{2}^{+}$ at 45 degrees, calculated using the DM-SFI theory with ADK (blue lines) and nonadiabatic rates \ref{['eq:NA-gamma']} (orange lines) and Eqs. (5) and (8) in Ref. Yuen2024b (green dotted lines). The dashed line depicts the 3.7 fs FWHM Gaussian pulse at 900 nm, with a peak intensity of $2 \times 10^{14}$ W/cm$^{2}$ and a zero carrier-envelope phase.