Time-resolved internal-electron-scattering effect of ${{\mathrm{H}}_2}^{+}$ in enhanced ionization regions

We theoretically investigate the electron interference dynamics of ${{\mathrm{H}}_2}^{+}$ in an intense infrared laser field. At intermediate internuclear distances, an interference fringe appears in the electron momentum distribution. By tracing the time evolution of the electron density, we identify an internal scattering channel of the electrons. The observed fringe is attributed to the interference between the internal scattered and direct photoelectrons. Our results reveal that the electron behaviors inside a molecule can be mapped onto the experimentally accessible photoelectron momentum spectra, suggesting a time-resolved way of probing the complex laser-driven electron dynamics on an attosecond time scale.

Figure 1

Photoelectron momentum distributions of ${{\mathrm{H}}_2}^{+}$ calculated from the 2D TDSE for different internuclear distances (a) $R=2$, (b) $R=4$, and (c) $R=8$ a.u. The color coding is on a logarithmic scale. The laser intensity is $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and the wavelength is 800 nm. The laser polarization direction is along the $x$ axis in parallel with the molecular axis, as indicated by the right arrow in (a).

Figure 2

(a) Electron density integrated over the $y$ direction as a function of time and coordinate $x$ at $R=8$ a.u., plotted on a logarithmic scale. The red solid curve is the laser field. (b) Electron population localized at the left (orange solid curve) and right (green solid curve) cores, respectively. (c) Electron probability flux at left $x_L=-R/2-10$ (orange solid curve) and right $x_R=R/2+10$ (green solid curve). We define right as the positive direction.

Figure 3

Photoelectron momentum distributions of ${{\mathrm{H}}_2}^{+}$ calculated from the 2D TDSE for different alignment angles (a) $0^{\circ }$, (b) ${30}^{\circ }$, (c) ${60}^{\circ }$, and (d) ${90}^{\circ }$ at internuclear distance $R=8$ a.u. in the laboratory frame. The color coding is on a logarithmic scale. Laser parameters are the same as in Fig. 1.

Figure 4

(a) Snapshot of the two-dimensional electron distribution in coordinate space at $t=2.7T$. The color coding is on a logarithmic scale. (b) Classical and SFA predictions of ionization and rescattering (revisiting) times for internal scattering (direct) electrons. The electric field is shown by the dark blue solid line. Ionization (red solid line) and revisiting (light blue dotted line) times for direct electrons and ionization (purple dashed line) and rescattering (light green dashed-dotted line) times for internal scattering electrons are extracted from the classical model. The corresponding SFA predictions are shown by squares and circles, respectively. (c) Sample electron trajectories for direct (light blue dotted lines) and internal scattering (light green solid lines) paths. (d) Interference pattern between direct and internal scattering channels predicted by the SFA model, plotted on a logarithmic scale.

Figure 5

Photoelectron momentum distributions of ${{\mathrm{H}}_2}^{+}$ calculated from the 2D TDSE for different internuclear distances (a) $R=8$, and (b) $R=10$ a.u. The color coding is on a logarithmic scale. Laser parameters are the same as in Fig. 1.

Figure 6

Sketch of interference between direct and internal scattering electrons.