Frequency dependence of nonsequential double ionization of atoms in strong laser fields

TL;DR

The paper investigates the frequency dependence of nonsequential double ionization (NSDI) using a fully quantum ab initio approach within a (1+1)-dimensional model atom. By solving the time-dependent Schrödinger equation and analyzing ionization yields and two-electron momentum distributions across multiple frequencies and pulse durations, the authors identify a knee structure in the double ionization yield and show that the knee shifts with pulse length rather than frequency alone. The study demonstrates that DI scales with frequency more robustly than SE DI and that longer pulses enhance NSDI before sequential processes dominate, with rate-equation comparisons corroborating the quantum results. Overall, the reduced-dimension quantum model captures the essential rescattering physics and momentum signatures observed experimentally, offering qualitative agreement and valuable mechanistic insight while acknowledging the limitations of a simplified geometry.

Abstract

The frequency dependence of (nonsequential) double ionization is studied in fully quantum mechanical calculations using a (1+1)-dimensional model atom. Other time-dependent effects such as the influence of the number of field cycles are also investigated. We present ionization yields and momentum distributions. The results are consistent with experimental and semi-classical data available in the literature, thus complementing them with a quantum mechanical description.

Figures (11)

• Figure 1: (color online) (a) Yields of single ionization (SI) and double ionization (DI) as a function of the peak field amplitude $F_0$ for $n_c=5$, $\varphi=0$ and different frequencies $\omega$. (b) Ratio of double to single ionization for the same parameters.
• Figure 2: (color online) Yields of consecutive double ionization (CE) and simultaneous double ionization (SE) as a function of the peak field amplitude $F_0$ for $n_c=5$, $\varphi=0$ and different frequencies $\omega$. The yields are artificially separated by a factor of 500.
• Figure 3: (color online) (a) Yields of single ionization (SI) and double ionization (DI) as a function of the peak field amplitude $F_0$ for $\omega=0.060$ a.u., $\varphi=0$ and different numbers of field cycles $n_c$. (b) Ratio of double to single ionization for the same parameters.
• Figure 4: (color online) Yields of single ionization (SI) and double ionization (DI) as a function of the peak field amplitude $F_0$ for $\varphi=0$ and a constant pulse duration of $T_p=13$ fs. All four single ionization yields saturate at $F_{sat}=0.25$ a.u. (dotted line) and exhibit a maximum at $F_{max}=0.34$ a.u. (dashed line).
• Figure 5: Comparison of the numerical ionization yields to the ones obtained by integrating the rate equations (\ref{['eq:rates']}) for $n_c=5$, $\omega = 0.060$ a.u. and $\varphi=0$. The sequential ionization rates ($W_{01}$ and $W_{12}$) are approximated by the ADK formula, the nonsequential one is approximated by $W_{02}=0.019\cdot W_{01}$ (solid lines) or set to zero (dashed lines).