Time-resolved view on charge-resonance-enhanced ionization

We theoretically investigate the electronic dynamics in the hydrogen molecular ion at fixed intermediate internuclear distances in two-dimensional space for the electron in a linearly polarized laser field. Our results of numerical simulations confirm the predictions of multiple bursts of ionization within a half cycle of the laser field oscillation as recently reported for one-dimensional models. Based on the analysis of the Floquet states for a two-state model of the molecular ion, we discuss the relation of the multiple ionization bursts to the so-called charge-resonance-enhanced ionization phenomenon and the momentum gates.

Figure 1

Time evolution of the electron density along the molecular axis obtained by (a) 1D model and (b) 2D model with $R_0=7$ are plotted on logarithmic scale. Laser pulse of intensity $6\times {10}^{13}$ W/cm${}^2$, wavelength 800 nm, and FWHM duration of 10 laser cycles were used. (c) The electron density in the 2D model plotted on linear scale. (d) The vector potential $A\left(t\right)$ (black solid line) and the electric field $E\left(t\right)$ (blue dashed line) of the laser pulse.

Figure 2

Population analysis in the lowest CR pair. (a) Normalized populations $P_{\text{L}}$ (blue solid line) and $P_{\text{R}}$ (red dashed line) in the 1D model. (b) Same as in panel (a), except in 2D model. (c) Same as panels (a) and (b), except that the populations are obtained by Floquet analysis. (d) Vector potential (black solid line) and electric field (blue dashed line) of the applied laser pulse.

Figure 3

Quasienergies ${\epsilon }_1$ and ${\epsilon }_2$ calculated by numerically solving the eigenvalue Eq. (16) (black crosses) and from the formulas (17) and (18) (solid and dashed lines, respectively). The parameter values for the two-state model were taken from the 2D model. The laser wavelength was set at 800 nm.

Figure 4

Population transfer $\Delta P^{\left(1\right)}$ from $|\mathrm{R}\rangle$ to $|\mathrm{L}\rangle$ in the single Floquet state ($c_1=1$ and $c_2=0$). The ground-state and first excited-state energies as well as the transition dipole of the 2D model at $R=7$ were used to parametrize the two-level system. The laser wavelength was set equal to 800 nm.

Figure 5

Time evolution of the Wigner distribution over a quarter cycle of the laser field for the 1D model: (a) $t=-0.500$, (b) $-0.450$, (c) $-0.400$, (d) $-0.351$, (e) $-0.301$, and (f) $-0.251$ laser cycles.