Identifying Mechanism of Energy-Resolved Attoclock

Abstract

We study above-threshold ionization (ATI) of atoms in strong elliptical laser fields numerically and analytically. Recent benchmark experiments for H showed that the attoclock offset angle related to each ATI ring increases remarkably with energy and this characteristic phenomenon can be attributed to the laser-induced nonadiabatic initial velocity and position of the electron at the tunnel exit [PRL127, 273201 (2021)]. However, the specific mechanism of how the nonadiabatic effects influence this angle remains unclear. Here, by using a strong-field model that analytically and quantitatively decouples complex nonadiabatic effects and Coulomb effects, the detailed mechanism can be clearly identified. We show that due to nonadiabatic effects, the angles associated with lower (higher) energy rings are dominated by the main (minor) axis of the laser ellipse, jumping from $0^o$ to $90^o$. These field-related rigid effects are softened by Coulomb-induced exit velocity closely related to system symmetry, resulting in a significant but smooth increase in angle with energy.

Figures (3)

• Figure 1: Offset angles $\theta$ as a function of the radial momentum $p_r$ obtained by different methods for different targets and laser parameters. (a) The experimental, TDSE and model (NACTS) results for H from Trabert2021. (b) The experimental results for Ar from Xie2024. (c) The TDSE and model results for H from Trabert2021. In each panel, besides TRCM, results of SFA are also presented. In (a) and (b), the TRCM results are also vertically shifted to match the experimental data, represented by TRCM'. The laser parameters used in our calculations are $I=0.9\times10^{14}$W/cm$^2$, $\xi=0.85$ with $\lambda=390$ nm in (a) and $\lambda=780$ nm and $\lambda=1170$ nm in (c), and $I=0.9\times10^{14}$W/cm$^2$, $\xi=0.8$ with $\lambda=400$ nm in (b).
• Figure 2: Illustration of mechanism of energy-resolved attoclock. (a) and (b) PMDs of TDSE and TRCM for He. The inset shows the helicity of the EPL field and the orientation of the polarization ellipse. $\theta$ indicates the offset angle. (c) A sketch of ionization geometry. The color coding indicates the noncoherent PMD of TDSE in (a). The white concentric circles indicate some ATI rings of SFA predictions. The orange-solid dots indicate some typical momenta $\textbf{p}$ along the axes of $p_{x(y)}=0$ in the rings, denoted with $\textbf{p}(p_{x(y)}=0)$. The light-blue-solid dots indicate the corresponding Coulomb-shifted momenta $\textbf{p}'(p_{x(y)}=0)$ of Eq. (1). The pink dots indicate the LMPR abstracted from the noncoherent PMD of TRCM in (b) and show an elliptical structure. (d) Offset angles $\theta$ as a function of the radius momentum $p_r$, obtained from PMDs in (a) and (b). Offset angles from PMDs of SFA and TDSE with a short-range potential (SP) are also shown here. The gray-dot curve shows the results obtained by Eq. (2) for the Coulomb-shifted momenta $\textbf{p}'(p_{x}=0)$. (e) SFA predictions of initial positions $r_0(\textbf{p})$ and amplitudes $M(\textbf{p})$ for the momenta $\textbf{p}(p_{x(y)}=0)$. The corresponding TRCM predictions of amplitudes $M'(\textbf{p}')$ for $\textbf{p}'(p_{x(y)}=0)$ are also shown here. (f) Comparisons of $\textbf{p}(p_{x(y)}=0)$ and $\textbf{p}'(p_{x(y)}=0)$. The laser parameters are $I=5\times10^{14}$W/cm$^2$, $\lambda=800$ nm and $\xi=0.85$.
• Figure 3: Absolute differences of offset angles $\theta$ between TDSE and TRCM for He as a function of the radius momentum $p_r$, obtained for varied laser parameters. (a) $I=5\times10^{14}$W/cm$^2$, $\xi=0.85$ with different $\lambda$. (b) $\lambda=800$ nm, $\xi=0.85$ with different $I$. (c) $I=5\times10^{14}$W/cm$^2$, $\lambda=800$ nm with different $\xi$. The vertical arrows in (a-c) indicate the positions of MPR predicted by TRCM in each curve.