Response time of electrons to light in strong-field ionization of polar molecules

TL;DR

Polar molecules exhibit PD-induced asymmetry in PMD during strong-field ionization, complicating attoclock interpretations. The authors combine TDSE simulations for HeH+ in strong elliptic fields with an analytical TRCM framework that includes PD effects and a laser-dressed two-center Coulomb potential to map ionization timing to photoelectron momentum. The analysis yields analytical expressions for the PD-induced lag and the corresponding offset angles, showing that PD lengthens the first-half-cycle response while shortening the second-half, with near-nucleus Coulomb structure and exit-position corrections further shaping the dynamics; the model reproduces TDSE PMDs across parameter ranges without requiring fully quantum-mechanical treatment of excited-state channels in the long-wavelength regime. This work provides a quantitative, analytically tractable framework for attosecond ionization dynamics in polar molecules and informs interpretation of attosecond experiments in these systems.

Abstract

We study tunneling ionization of HeH+ in strong elliptical laser fields numerically and analytically. The calculated photoelectron momentum distribution (PMD) show two different offset angles corresponding to ionization events occurring in the first and the second half cycles of one laser cycle. When the larger angle is greater than the angle of a model symmetric molecule with a similar ionization potential to the polar molecule, the smaller angle is smaller than the symmetric molecule. Using a developed strong-field model that consider effects of both the permanent dipole (PD) and the asymmetric Coulomb potential, we are able to quantitatively reproduce these phenomena. We show that the PD effect can increase (decrease) the response time of electrons within polar molecules to light in photoemission, thereby increasing (decreasing) the offset angle related to the first (second) half cycle of a laser cycle. The laser-dressed asymmetric Coulomb potential near the atomic nuclei also plays an important role in the sub-cycle-related response time and offset angle. This model may be useful for quantitatively studying attosecond ionization dynamics of polar molecules in strong laser fields.

Figures (6)

• Figure 1: (a): sketch of the laser-dressed Coulomb potential $V'(\textbf{r})=V(\textbf{r}) + E_{0} x$ (solid curves) and laser-free potential $V(\textbf{r})$ (dashed curves) for HeH$^{+}$ (black curves), symmetric molecule (red curves) and atom (gray curves) with similar ionization potentials for the first half cycle of laser fields at the peak time $t_0$ ($E(t_0)>0$). The horizontal green line indicates the ground state energy of $-I_{p0}=-1.44$ a.u.. (b): sketch for the second half cycle ($E(t_0)<0$) with $V'(\textbf{r})=V(\textbf{r}) - E_{0} x$. The laser amplitude $E_0$ used is $E_0=0.19$ a.u., and the internuclear distances of model molecules are all fixed at $R=2$ a.u.. The vertical purple arrows are used to guide the eyes. Embedded graph is the ground state wave function of HeH$^{+}$.
• Figure 2: PMDs of model molecules and atom obtained by TDSE (left column) and TRCM (right column). (a): PMD of HeH$^+$ obtained by TDSE (Asym TDSE) at $R=2$ a.u., with permanent dipole $D=-0.7$ a.u.. (b): PMD of symmetric molecule obtained by TDSE (Sym TDSE) at $R=2$ a.u.. (c): PMD of atom obtained by TDSE (Atom TDSE). (d)-(f) are PMDs obtained by TRCM using the same laser and molecular parameters as TDSE. The offset angles $\theta$ are indicated by the white arrows. Model molecules and atom have the same ground state ionization potential $I_{p0}=1.44$ a.u.. Laser parameters used are $I=2.25\times10^{15}$ W/cm$^{2}$ (with $E_0=0.19$ a.u.), $\lambda=1000$ nm.
• Figure 3: Comparing the tunneling exit positions of asymmetric molecule, symmetric molecule, and atom at different laser parameters. The molecular and atomic parameters used are the same as in Fig. 2. For asymmetric molecule, the tunneling exit position $r"_0$ for the first (second) half of laser cycle is marked by "Asym-F" ("Asym-S"). The exit position for symmetric molecule $r'_0$ (atom $r_0$) is marked by "Sym" ("Atom"). The calculations for $r_0$, $r'_0$, and $r"_0$ can be found in discussions of Eqs. (7)-(9). In (a) [(b)], we change the laser wavelength (intensity), and fix the laser intensity (wavelength) at $I=2.25\times10^{15}$ W/cm$^{2}$ ($\lambda=1000$ nm).
• Figure 4: Comparing the PMD offset angles of asymmetric molecules obtained by TDSE and TRCM. The black (red) solid line marked "TDSE_F(S)" corresponds to the TDSE offset angles in the first (second) half cycle of the laser. The black (red) dashed line marked "TRCM_F(S)" corresponds to the TRCM results in the first (second) half cycle. The asymmetric molecules studied in the left (right) column have a ground state ionization potential $I_{p0}=1.44$ a.u. ($I_{p0}=1.11$ a.u.) at $R=2$ a.u., and the laser intensity used is $I=2.25\times10^{15}$ W/cm$^{2}$ ($I=1\times10^{15}$ W/cm$^{2}$). The values of the internuclear distances $R$ and permanent dipole $D$ are marked in the left corner of each figure.
• Figure 5: Comparing the PMD offset angles and response time $\tau$ of asymmetric molecules, symmetric molecules, and atoms obtained by TDSE and TRCM at different laser wavelengths. The ground state ionization potentials of molecules and atoms in the left (right) column are fixed at $I_{p0}=1.44$ a.u. ($I_{p0}=1.11$ a.u.), and the laser intensity used is $I=2.25\times10^{15}$ W/cm$^{2}$ with $E_0=0.19$ a.u. ($I=1\times10^{15}$ W/cm$^{2}$ with $E_0=0.127$ a.u.). The internuclear distances of model molecules are all fixed at $R=2$ a.u.. The first (last) two rows show the comparisons of offset angles (response time $\tau$). The results of asymmetric molecules in the first (second) half of laser cycle are marked as "Asym-F(S)". The results of symmetric molecules (atoms) are marked as "Sym" ("Atom").