Wavelength scaling of atomic nonsequential double ionization in intense laser fields

Experimental and theoretical investigations of the wavelength dependence of the nonsequential double ionization (NSDI) process of the xenon atom in intense laser fields are reported. The observed wavelength dependence of the ratio ${\mathrm{Xe}}^{2+}/{\mathrm{Xe}}^{+}$ deviates significantly from the prediction of the three-step model of ionization (sometimes called the “simple-man” model), both in the slope of the overall decrease with increasing wavelength and in the existence of some pronounced humps. A semiclassical model calculation reproduces the changing slope of the overall decrease, which is due to the interplay of wave-packet diffusion, Coulomb focusing, and a closely related Coulomb defocusing effect of the liberated electron. The hump is beyond the scope of the semiclassical model.

Figure 1

(a) Experimental ratios of ${\mathrm{Xe}}^{2+}/{\mathrm{Xe}}^{+}$ vs laser intensity for various wavelengths. (b) Experimental wavelength dependence of the ratio of ${\mathrm{Xe}}^{2+}/{\mathrm{Xe}}^{+}$ at a fixed $U_p$ of 14.9 eV. For visual convenience, a dashed curve is plotted to show the overall change of the experimental ratio. (c) The ratio ${\mathrm{Xe}}^{2+}/{\mathrm{Xe}}^{+}$ (multiplied by a factor of 10) according to the semiclassical model: the red diamonds represent the complete result including all recollisions, the blue up-triangles and the green down-triangles represent the SRC and the MRC contributions, respectively. Here, the experimental ratios (black squares) are also shown for comparison. (d) MRC contributions separated as resulting from the second return (2-RC, black diamonds) and third return (3-RC, red left-triangles). The red solid curves in (b) and (c) represent the ratio predicted by the three-step model. The error bars in (a) and (b) are the statistical uncertainty.

Figure 2

(a) The ratio ${\mathrm{Xe}}^{2+}/{\mathrm{Xe}}^{+}$ analyzed with respect to the time between the first ionization and the second ionizing recollision in multiples of the laser period for wavelengths of 800, 1500, and 2200 nm. The vertical dashed line specifies the transition from SRC to MRC contributions. (b) The ratio of the number of electrons with very small impact parameters and energies larger than the second ionization potential of xenon when they return to the ionic core at the first (SRC), second (2-RC), and third (3-RC) time with the Coulomb potential (CP) to that without the CP as a function of the wavelength. The $U_p$ is fixed at 14.9 eV.

Figure 3

In (a) and (b), two typical trajectories for 800 and 2200 nm, respectively, illustrate the Coulomb defocusing effect. The black dashed curves in the figures represent the field-distorted Coulomb potential. The positions of the first and second return to the plane $z=0$ are marked by 1R and 2R, respectively. (c) Relative distribution of the distance $R$ from the ion of the 2-RC trajectories at the time when the electron returns for the first time to the ion, for three different wavelengths. Plots (d) and (e) show the initial transverse-momentum distribution of the electrons with very small impact parameters and energies larger than the second ionization potential of xenon when they return to the ionic core at the first (SRC), second (2-RC), and third (3-RC) time for 800 and 2200 nm, respectively. (f) Overlaps between the normalized initial transverse-momentum distributions of the first-return trajectory with those of the second $\left({\mathrm{X}}_{12}\right)$ and third $\left({\mathrm{X}}_{13}\right)$ returns.

Figure 4

Comparison of the wavelength scaling for the NSDI related to direct electron impact ionization (DEI) $(\mathrm{\Delta }t<10$ a.u.) and the recollision excitation followed by tunneling (RET) $(\mathrm{\Delta }t\ge 10$ a.u.) mechanisms. The calculated total ratios are also shown for comparison.