Figure 1

Stick spectrum of the field-free energies of the band of 40 states used to carry out the computation.Reuse & Permissions

Figure 2

Adiabatic field-adjusted energies of the GS and excited states of LiH computed as a function of the strength [given in atomic units (a.u.)] of a static field polarized along the $z$ axis (a) and along the $x$ axis (b). The orientation of the molecule with respect to the Cartesian axis is shown as an inset in (b).Reuse & Permissions

Figure 3

Weights of the field-adapted GS on the field-free states ($y$ axis) as a function of the static field strength ($x$ axis). (Top) The field is applied along the $z$ direction, so the GS is a superposition of field-free Σ states only. The weights of the GS are shown on the six lowest field-free Σ states. The GS is mainly made of the third and the fourth field-free Σ for field strength stronger than –0.025 a.u., while there is a significant weight on the second Σ state in the range [–0.01,–0.02]. For positive field strength there is no weight on the second Σ state. (Bottom) The field is applied along $x$ and breaks the Σ and Π character. The weights of the GS are shown on the seven lowest Σ states and the three lowest Π ones. For field strength above |0.025| a.u., the GS is an equal mixture of Σ and Π states. Note that at the field strength considered, the field-adapted GS does not have weights on the field-free states that are above the IP.Reuse & Permissions

Figure 4

(a) Population dynamics for an intense, $E_z=-0.05$ a.u., pulse width $\sigma =\sqrt{2}$ fs at an IR frequency ${\omega }_0$ of 800 nm and (b) for a pulse with $E_z=+0.05$ a.u. The time profile of the pulse is shown as a black dotted line. Note how different excited states are dominant for different cycles in the pulse and how different is the population of the transient states when the pulse direction is reversed. Due to the Stark shifts (Fig. 2), the direction of the field along the molecular axis influences the population of the excited states. (c) and (d) The corresponding dipole $\mu (t)$, and the mean value of the energy, $H(t)=\langle \Psi (t)|\mathbf{H}(t)|\Psi (t)\rangle$.Reuse & Permissions

Figure 5

Weights of the field-free states for a pulse with ${\omega }_0$ $=$ 800 nm, $\sigma =1/1\sqrt{2}$ fs, and a carrier-envelope phase, CEP, ϕ $=$ 0 [see Eq. (2)]. The pulse is shown as black dotted lines. (Top) $E_z=+0.025$ a.u., (bottom) $E_z=-0.025$. For $\sigma =1/1\sqrt{2}$ fs pulse, there is essentially one frequency oscillation during the pulse. Only the second $\Sigma$ state is significantly accessed. Reversing the direction of the field reduces the population transfer because the second $\Sigma$ state has a dipole moment in the opposite direction compared to the GS (see Table ).Reuse & Permissions

Figure 6

(Top) Time evolution of the field-free states during the ultrashort excitation pulse ($E_z$ is $+$0.05 a.u., $\sigma =1/1\sqrt{2}$ fs, ${\omega }_0$ $=$ 0.133 a.u., $\varphi$ $=$ 0, the pulse profile is shown as a black dotted line). The final state is mainly made of the sixth $\Sigma$ state and of the autoionizing tenth state accessed by two-photon transitions. (Bottom) The dipole $\mu (t)$ and the mean value of the energy, $H(t)=\langle \Psi (t)|\mathbf{H}(t)|\Psi (t)\rangle$. Both exhibit a time dependence that is more complex than that of the pulse, especially as the pulse envelope declines. To reverse the direction of the field (not shown) leads to a different final state, which is a superposition of the GS and the sixth $\Sigma$ state with no significant population in autoionizing states.Reuse & Permissions

Figure 7

Transient spectrum computed for the dynamics shown in Fig. 4a. The value of ${\sigma }_W$ is 0.56 fs. The $y$ axis is the time τ for which the spectrum is computed, from 6 to 14 fs. Early in the excitation, at low τ values, the frequency is that of the unperturbed GS. Transient frequencies below that of the field-free GS appear when the field is high (see Fig. 2). After the end of the pulse, the spectrum is stationary; two frequencies dominate: that of the field-free GS and that of the field-free third, fourth, and sixth excited states that cannot not be resolved because the width ${\sigma }_W$ of the window function exceeds their spacings. (The field-free energy spectrum is shown in Fig. 1.)Reuse & Permissions

Figure 8

The value of the effective coupling parameter $\chi$ as a function of time during the pulse (black dotted lines) between the lowest adiabatic states, as indicated in the figure: (top) $E_x=-0.05$ a.u., (bottom) $E_z=+0.05$ a.u.; ${\omega }_0$ $=$ 0.133 a.u., $\sigma =1/1\sqrt{2}$ fs.Reuse & Permissions

Figure 9

The value of the effective coupling parameter $\chi$ as a function of time during the pulse (black dotted lines) between the lowest adiabatic states, (2,3) in dots, (5,6) in full line, and (1,2) in dashes, $E_z=-0.05$ a.u., ${\omega }_0$ $=$ 0.057 a.u., $\sigma =\sqrt{2}$ fs.Reuse & Permissions

Figure 10

One-electron densities of the three lowest Σ states and the lowest Π state. Note how the charge density reflects the orientation of the permanent dipole moment for the Σ states and how it is localized outside the bond axis for the Π state. See Table  for the values of the energies and permanent dipole moments.Reuse & Permissions