Numerical simulations of single-photon double ionization of the helium dimer

We study the energy exchange via electron correlation upon photon absorption over large distances in double photoionization of the helium dimer. Results of numerical simulations of the interaction of a planar helium dimer model with a short light pulse are found to be in good agreement with recent experimental data for the angular distribution of the emitted electron. The double ionization probability is closely related to that of the photoemission of an electron from one of the helium atoms along the internuclear axis. Together with an analysis of the temporal evolution of the two-electron probability distribution this provides direct evidence for the knockoff mechanism by which the photon energy is shared between the electrons over distances of several Angstroms in the dimer.

Figure 1

Scheme of the numerical model for the helium dimer. One electron at each atom is considered active and restricted to the same plane, with coordinates $(x_1,z_1)$ and $(x_2,z_2)$, respectively. The internuclear distance $R$ and dimer orientation $\theta$ with respect to the laser polarization direction $\varepsilon$ ($z$ axis) are fixed during the simulations.

Figure 2

Spatial distributions (on a logarithmic scale) of the ground state [panels (a) and (c)] and first excited state [panels (b) and (d)] of the planar model helium dimer. The distributions in the upper row are integrated over $x_1$ and $x_2$ and shown as a function of $z_1$ and $z_2$. The distributions in the lower row are integrated over $x_1$, $x_2$, and $Z=\frac{z_1+z_2}{2}$ and shown as a function of $z=z_1-z_2$. Note the node at $z_1=z_2$ or $z=0$ in the distributions of the first excited state.

Figure 3

Molecular-frame angular distribution of one of the electrons following double ionization of the helium dimer model with internuclear distances of $R=5.6$ a.u. [panels (a), (c), and (e)] and $R=10$ a.u. [panels (b), (d), and (f)] by a 20-nm, 4-cycle XUV pulse with a peak intensity of $1\times {10}^{14}$ W/cm${}^2$. Shown is a comparison between the theoretical results [solid lines, full results in panels (a) and (b), singlet contributions in panels (c) and (d), and triplet contributions in panels (e) and (f)] and the experimental data [solid circles, integrated over $R=5.1-6.8$ a.u. in panels (a), (c), and (e), and $R=9.4-10.9$ a.u. in panels (b), (d), and (f)] (subset of data shown in Fig. 3(b) of Ref. [14]).

Figure 4

Comparison of the laboratory-frame dipole-transition angular distribution ${\cos }^2\delta$ (dashed-dotted line) with (a) the theoretical photoelectron angular distributions (AD) for single ionization (SI) of the dimer oriented either parallel (red [gray] solid line) or perpendicular (blue [gray] dashed line) to the polarization axis and (b) the probability of double photoionization (DI) as a function of the orientation of the dimer axis (theoretical prediction: red [gray] solid line, experimental data: solid circles, integrated over $R=4.5-6.8$ a.u. (subset of data shown in Fig. 3(a) of Ref. [14])). The polarization direction of the field is along the horizontal axis in both panels. The internuclear distance was chosen to be $R=5.6$ a.u. and the parameters of the XUV field are the same as in Fig. 3.

Figure 5

Double photoionization probability (open circles) as a function of internuclear distance $R$ for orientation of the dimer axis parallel to the polarization direction of the field. It scales as $1/R$ with the internuclear distance. The fitting parameters are $a=2.88\times {10}^{-5}$ and $b=-4.56\times {10}^{-7}$. The parameters of the XUV field are the same as in Fig. 3.

Figure 6

Temporal evolution of the two-electron probability distribution of the helium dimer in $z=z_1-z_2$ starting from the ground state [singlet, panel (a)] and the first excited state [triplet, panel (b)], which exhibit the differences between singlet and triplet scattering. In the simulation, the dimer axis is oriented parallel to the polarization axis.