Control of Electron Excitation and Localization in the Dissociation of $\mathrm{H}_2{}^{+}$ and Its Isotopes Using Two Sequential Ultrashort Laser Pulses

We study the control of dissociation of the hydrogen molecular ion and its isotopes exposed to two ultrashort laser pulses by solving the time-dependent Schrödinger equation. While the first ultraviolet pulse is used to excite the electron wave packet on the dissociative $2p{\sigma }_u$ state, a second time-delayed near-infrared pulse steers the electron between the nuclei. Our results show that by adjusting the time delay between the pulses and the carrier-envelope phase of the near-infrared pulse, a high degree of control over the electron localization on one of the dissociating nuclei can be achieved (in about 85% of all fragmentation events). The results demonstrate that current (sub-)femtosecond technology can provide a control over both electron excitation and localization in the fragmentation of molecules.

Figure 1

Dissociation probabilities with an electron localization along the positive (proton side, circles) and the negative (second nucleus side, stars) $z$-axis as a function of the mass of the molecule due to the interaction with an ultrashort UV pulse at ${\lambda }_1=106\mathrm{nm}$, ${\tau }_1=0.425\mathrm{fs}$ and $I_{0,1}={10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

Electron localization probabilities along the positive (proton side, thick line) and the negative $z$-axis (second nucleus, thin line) for (a) $\mathrm{H}_2{}^{+}$, (b) ${\mathrm{HD}}^{+}$, and (c) ${\mathrm{HT}}^{+}$ as a function of time. Laser parameters are as in Fig. 1. The arrows mark the time when the interatomic barrier reaches the energy of the first excited state.

Figure 3

Dependence of the asymmetry parameter $A$ of electron localization on the two control parameters $\Delta t$ and ${\varphi }_2$. Left hand panels: $A$ as a function of the time delay $\Delta t$ with ${\varphi }_2=0$ for (a) $\mathrm{H}_2{}^{+}$ and (c) ${\mathrm{HD}}^{+}$. Right hand panels: $A$ as a function of the carrier-envelope-phase ${\varphi }_2$ for (b) $\mathrm{H}_2{}^{+}$ and $\Delta t=4.8\mathrm{fs}$ and (d) ${\mathrm{HD}}^{+}$ and $\Delta t=6.8\mathrm{fs}$.

Figure 4

Same as Figs. 2a, 2b but with a second time-delayed laser pulse. The electric field of the latter is shown by the dashed-dotted line. The time delay is (a) $\Delta t=6.9\mathrm{fs}$ and (b) $\Delta t=7.2\mathrm{fs}$, respectively.