Extremely asymmetric electron localization in H${}_2$${}^{+}$ controlled with a THz field

We propose a scheme to achieve extremely asymmetric electron localization during molecular dissociations. Hydrogen molecular ion (H${}_2$${}^{+}$) dissociation is investigated theoretically. A THz pulse is used to steer the electron motion after the molecular ion is excited by an ultrashort ultraviolet laser pulse. A high probability, as high as 99.3%, to localize electrons on one of the two nuclei is demonstrated, with a dissociation probability of 6.14% and almost no ionization, by optimizing the peak intensities and time delay of the two pulses. Even when the total dissociation probability is increased to 25.6%, more than 96.3% electrons can be localized in all dissociation events. These results represent a significant advancement in the electronic dynamics control in molecules.

Figure 1

(a) Asymmetry parameter $A$, total ionization $I$, and $P_{\pm }$ as functions of time delay Δ$t$. The intensities of the THz and UV pulses are 3.8 × 10${}^{12}$ and 5.0 × 10${}^{14}$ W/cm${}^2$, respectively. The solid yellow curve is the electric field of the THz pulse. (b) Asymmetry parameter A, I, and $P_{\pm }$ as functions of the electric-field strength of the THz pulse $E_{10}$. The intensity of the UV pulse is 5.0 × 10${}^{14}$ W/cm${}^2$ and Δ$t$ = 14.6 fs. (c) Asymmetry parameter A, I, and $P_{\pm }$ as functions of the electric-field strength of the UV pulse $E_{20}$. The intensity of the THz pulse is 4.4 × 10${}^{12}$ W/cm${}^2$ and time delay Δ$t$ = 14.6 fs. (d) Same as (a), but the CEP of the THz pulse is 0.5π.

Figure 2

Time-dependent electron probabilities of different parts.

Figure 3

(a) and (b) Snapshots of the common logarithm of the electron-nuclear probability density distribution taken at $t$ = 106.8 fs. (c) and (d) Time-dependent electron probabilities of PD${}_{\pm }$($t$), PI${}_{\pm }$($t$), PG($t$), and PGI${}_{\pm }$($t$) and the total ionization probability $I$, respectively. (a) and (c) Only the UV laser pulse is applied. (b) and (d) Both the UV and THz pulses are applied with intensities of 3.8 × 10${}^{12}$ and 5.0 × 10${}^{14}$ W/cm${}^2$, respectively, and time delay Δ$t$ = 14.6 fs.

Figure 4

(a) Calculated results with coupled equations (4). The probability of electron localization is stable after about 12 fs, although the probabilities of ${\psi }_g$ and ${\psi }_u$ are still being exchanged. After about 28 fs, the nuclear wave packet reaches the boundary and is absorbed by the mask function. (b) Asymmetry parameter changing with different wavelengths. The electron is excited at $t$ = 0. The pulse is a multicycle cosine function. From the figure we can see that, even though the pulse is very long, all the asymmetry parameters become stable at about 16 fs. The sine function pulse can obtain similar results.