Identifying the Tunneling Site in Strong-Field Ionization of ${{\mathrm{H}}_2}^{+}$

The tunneling site of the electron in a molecule exposed to a strong laser field determines the initial position of the ionizing electron and, as a result, has a large impact on the subsequent ultrafast electron dynamics on the polyatomic Coulomb potential. Here, the tunneling site of the electron of ${{\mathrm{H}}_2}^{+}$ ionized by a strong circularly polarized (CP) laser pulse is studied by numerically solving the time-dependent Schrödinger equation. We show that the electron removed from the down-field site is directly driven away by the CP field and the lateral photoelectron momentum distribution (LPMD) exhibits a Gaussian-like distribution, whereas the corresponding LPMD of the electron removed from the up-field site differs from the Gaussian shape due to the Coulomb focusing and scattering by the down-field core. Our current study presents the direct evidence clarifying a long-standing controversy over the tunneling site in ${{\mathrm{H}}_2}^{+}$ and raises the important role of the tunneling site in strong-field molecular ionization.

Figure 1

The tunneling scenario in the field-dressed potential of ${{\mathrm{H}}_2}^{+}$ at the critical internuclear distance. In the presence of the external field, two barriers are formed for the bound electron localized on different nuclei.

Figure 2

Scheme for identifying the tunneling site of the electron in the ionization of ${{\mathrm{H}}_2}^{+}$ by a circularly polarized field. The blue curve shows the electric field with the arrow indicating its rotating direction. Trajectories 1 and 2 indicate the classical paths of the freed electron starting at different cores, as described in the text.

Figure 3

The CEP-averaged LPMDs (a)–(c) and 2D PMDs (d)–(f) for the ionization of ${{\mathrm{H}}_2}^{+}$ at the internuclear distances $R_0$, $R_1$, and $R_2$ by the 800-nm right CP pulse with the intensity $I_3=2.25\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The shapes of the laser-dressed potentials are illustrated inside (a)–(c). The Gaussian fit for the LPMD for $R_0$ is also shown in (a). The panel (g) shows the ionization probabilities under the fixed CEP $\varphi =0$ as a function of the internuclear distance.

Figure 4

(a)–(d) The LPMDs for the specific momentum regions indicated in Figs. 3 and 3, comparing with the Gaussian LPMD for $R_0$ (dashed curves). Panels (e) and (f) show the Coulomb potentials (contour curves) of ${{\mathrm{H}}_2}^{+}$ at $R_1$ and $R_2$ and the paths (thick curves with arrows) illustrating the underlying processes responsible for the corresponding LPMDs. The solid curves with dots in (c) and (d) indicate the LPMDs obtained from semiclassical simulations [35] and the corresponding averaged classical trajectories are depicted by the dash-dotted curves in (f).

Figure 5

The LPMDs for $R_0$ (dashed curves) and $R_2$ (shadows) and their absolute deviations (solid curves) under three pulse intensities $1.25\times {10}^{14}$, $2.25\times {10}^{14}$, and $3.25\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (from left to right) and $\varphi =0$.