Anticorrelation in nonsequential double ionization of helium

We calculate the correlated two-electron momentum distributions for nonsequential double ionization of helium in a 400-nm laser pulse with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$, which is below the recollision threshold, by using the quantitative rescattering model in which the lowering of the threshold due to the presence of the electric field at the instant of recollision is taken into account. While distinct correlated back-to-back emission of the electrons along the polarization direction is predicted in accord with other existing theoretical simulations, we suggest an alternative mechanism that is responsible for the anticorrelation. At intensities below the recollision threshold, recollision excitation can only take place when the barrier of the Coulomb potential is sufficiently suppressed by the electric field. The excited electron begins to ionize at a “delayed” recollision time after a crossing of the field and hence the probability of being tunnel-ionized after the subsequent peak of the field is increased. It is demonstrated that the “delayed” recollision time predominantly determines the parallel momentum distribution of the tunneling electron and plays a decisive role in forming anticorrelation.

Figure 1

Recolliding wave packet against the kinetic energy of the laser-induced returning electron in a 400-nm laser pulse with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$. The blue broken curve is the smoothed wave packet used in the numerical calculations. The arrow indicates the cutoff at $3.17U_p$.

Figure 2

Parallel momentum distributions for the active electron after recolliding with the ${\mathrm{He}}^{+}$ ion and exciting the residual ground-state electron to the excited states of (a) $2s$, (b) $2p_0$, (c) $2p_1$, (d) $3s$, (e) $3p_0$, and (f) $3p_1$ in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$. The recolliding electron returns to the origin along the $-\widehat{z}$ direction with energies of 45, 50, and 55 eV. The recollision times are chosen to be such that $\omega t_r={55}^{\circ }$ and ${70}^{\circ }$ after a crossing of the electric field for $n=2$ and 3, respectively.

Figure 3

Parallel momentum distributions for the electron ejected from ${\mathrm{He}}^{+}$ in the excited states of (a) $2s$, (b) $2p_0$, (c) $2p_1$, (d) $3s$, (e) $3p_0$, and (f) $3p_1$ by a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$. The recolliding electron returns to the origin along the $-\widehat{z}$ direction at $\omega t_r={55}^{\circ }$ and ${70}^{\circ }$ after a crossing of the electric field for $n=2$ and 3, respectively. Asymmetry parameters for the momentum distributions are also indicated. See text for details.

Figure 4

Right-side ($p_1^{\left|\right|}>0$) correlated parallel momentum spectra for excitation tunneling from (a) $2s$, (b) $2p_0$, (c) $2p_1$, (d) $3s$, (e) $3p_0$, and (f) $3p_1$ in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$ with $\omega t_r={55}^{\circ }$ and ${70}^{\circ }$ for $n=2$ and 3, respectively.

Figure 5

Symmetrized full-space correlated parallel momentum spectra for excitation tunneling from the excited states of (a) $2s$, (b) $2p_0$, (c) $2p_1$, (d) $3s$, (e) $3p_0$, and (f) $3p_1$ in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$.

Figure 6

Correlated parallel momentum spectra for excitation tunneling from all possible excited states of (a) $n=2$, (b) $n=3$, and (c) sum of $n=2$ and 3 in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$.

Figure 7

(a, b, c) Two-dimensional photoelectron momentum distributions parallel ($p_z$) and perpendicular ($p_{\perp }=\sqrt{{p_x^2+p_y^2}^{\phantom{\int }}}$) to the laser polarization direction from the TDSE for single ionization of ${\mathrm{He}}^{+}$ from the excited $2p_0$ state in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$. (d, e, f) Parallel momentum distributions for the ionized electron obtained from panels (a), (b), and (c), respectively. (g) Electric fields used in the TDSE calculations with the beginning times of $\omega t_r={20}^{\circ }$, ${40}^{\circ }$, and ${70}^{\circ }$ marked by points 1, 2, and 3, respectively. The red solid and black dotted lines represent the electric fields with $\omega t_r=0^{\circ }$ and ${70}^{\circ }$, respectively.

Figure 8

(a) ADK rate for ionization of ${\mathrm{He}}^{+}$ from $2p_0$ vs time in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$ with initial ionization times corresponding to $\omega t_r={20}^{\circ }$, ${40}^{\circ }$, and ${80}^{\circ }$, respectively. The electric field and vector potential of the laser field are also plotted. In the electric field the initial ionization times corresponding to $\omega t_r={20}^{\circ }$, ${40}^{\circ }$, and ${80}^{\circ }$ are marked by points 1, 2, and 3, respectively. (b) Parallel momentum distributions of the ionized electron corresponding to the ADK rates shown in panel (a). The asymmetry parameters are also indicated.

Figure 9

(a, b, c) Right-side ($p_1^{\left|\right|}>0$) correlated parallel momentum spectra for excitation tunneling from $2p_0$ in a 400-nm laser field with a peak intensity of $6.5\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$ for $E_i=45\mathrm{eV}$ and $\omega t_r={20}^{\circ }$, ${40}^{\circ }$, and ${70}^{\circ }$, respectively. (d, e, f) Symmetrized full-space correlated parallel momentum spectra obtained from panels (a), (b), and (c), respectively.