Electron and nuclear dynamics of a molecular ion in an intense laser field

The dynamics of a two-dimensional $\mathrm{H}_2{}^{+}$ molecule interacting with a strong laser pulse beyond the usual approximation of fixed nuclei is presented. The motion of the nuclei is studied by using the classical Newton laws while the electron is described with a full quantal treatment. The axis of the molecule, initially not aligned to the laser field, performs a long-period pendular motion around the laser polarization axis. Vibrational degrees of freedom are seen to be excited. The radiation emitted by the oscillating charges presents variations that are synchronous to the pendular motion. The possibility of monitoring the motion of the molecule through the emitted radiation is discussed.

Figure 1

Plots of the time evolution of the alignment angles $\Theta \left(t\right)$ of the molecular axis (solid lines) and of the internuclear distance $R\left(t\right)$ (dashed lines) for different values of the initial alignment angle: (a) ${\Theta }_0=30°$, (b) ${\Theta }_0=75°$. The alignment angles are expressed in degrees, the internuclear distances in a.u.

Figure 2

Plot of the maximum value of the angular velocity of the molecule ${\Omega }_{max}$ (solid line) and of the oscillation period (dashed line) as function of the initial alignment angle ${\Theta }_0$ in degrees. Here ${\Omega }_{max}$ is expressed in degrees per o.c.

Figure 3

The solid lines plot the time evolution of various electron quantities (all expressed in a.u.), for initial alignment angle ${\Theta }_0=30°$: (a) $⟨x⟩\left(t\right)$, (b) $⟨y⟩\left(t\right)$, (c) $x$ component, and (d) $y$ component, respectively, of the electron acceleration. Dashed lines plot the time evolution of the alignment angle $\Theta \left(t\right)$.

Figure 4

Same as Fig. 3, but for ${\Theta }_0=75°$.

Figure 5

Plot of the the emitted spectra associated with the $x$ component (solid line) and with the $y$ component (dotted line) of the acceleration for ${\Theta }_0=30°$.

Figure 6

Morlet spectra for the $x$ and $y$ electron acceleration components. In part (a) we plot the time evolution of the third harmonic (dashed line) of the $x$ component and the time evolution of the alignment angle $\Theta \left(t\right)$ in degrees (dotted line). The time evolution of the fundamental harmonic is not relevant since it is almost constant in time. In part (b) we plot the time evolution of the fundamental harmonic $\left(\omega ={\omega }_L\right)$ (solid line), of the third harmonic (dashed line) of the $y$ component of the electron acceleration, and of the alignment angle (dotted line). The initial alignment angle is ${\Theta }_0=30°$.

Figure 7

Same as Fig. 6 but for ${\Theta }_0=75°$.