Probing Time-Dependent Molecular Dipoles on the Attosecond Time Scale

Photoinduced molecular processes start with the interaction of the instantaneous electric field of the incident light with the electronic degrees of freedom. This early attosecond electronic motion impacts the fate of the photoinduced reactions. We report the first observation of attosecond time scale electron dynamics in a series of small- and medium-sized neutral molecules (${\mathrm{N}}_2$, ${\mathrm{CO}}_2$, and ${\mathrm{C}}_2{\mathrm{H}}_4$), monitoring time-dependent variations of the parent molecular ion yield in the ionization by an attosecond pulse, and thereby probing the time-dependent dipole induced by a moderately strong near-infrared laser field. This approach can be generalized to other molecular species and may be regarded as a first example of molecular attosecond Stark spectroscopy.

Figure 1

(a) Calculated molecular dipole $D$ (black curve) induced by a NIR femtosecond laser field $F$ (thin red curve), for the case of an aligned ${\mathrm{N}}_2$ molecule interacting with a 30 fs, 800 nm, ${10}^{12}\mathrm{W}/{\mathrm{cm}}^2$ laser pulse. The NIR field induces an adiabatic time-dependent dipole that corresponds to a displacement of the charge density distribution around the fixed nuclei. (b) Field-induced electronic density changes at three different time delays and, hence, field strengths [see (a)]. Times chosen are $t_a=t_0+75\mathrm{as}$, $t_b=t_0+334\mathrm{as}$, $t_c=t_0+667\mathrm{as}$), where $t_0$ corresponds to the time of a zero-crossing of the laser electric field. The color scale indicates an increase (light red) or decrease (dark blue) of the electron density around the nuclei. The red arrow indicates the direction of the light electric field. (c) Top: Kohn-Sham potential $V_{\mathrm{KS}}$ for an aligned ${\mathrm{N}}_2$ molecule, where the position of the nuclei are shown with red dashed lines; (down) variation of the Kohn-Sham potential when an electric field is present. The Kohn-Sham potential acts as a screening field when the polarized molecule interacts with an ionizing XUV laser pulse (see Fig. 2).

Figure 2

(a) Ionization probability σ plotted as a function of the NIR-XUV pump-probe delay (upper curve), along with the variation of the NIR electric field $F$ (lower curve). The latter time axis is plotted in such a way that the time axis corresponds to the instant where the APT is synchronized. The maximum ionization is observed when the APT is synchronized with the extrema of the NIR field. In this case, the calculation was performed in 2D in order to decrease the computational time. (b) Variation of the ionization probability σ, for two different cases of the molecular alignment (when the molecules are aligned along ($\alpha$) or perpendicular ($\beta$) to the laser polarization axis). Importantly, although showing a pronounced alignment dependence, the field-induced oscillation persists in the case of alignment-averaged calculations (middle, black curve).

Figure 3

(a) Experimentally measured ${\mathrm{N}}_2^{+}$, ${\mathrm{CO}}_2^{+}$, and ${\mathrm{C}}_2{\mathrm{H}}_4^{+}$ yields (black dashed curves) as a function of the delay between the NIR pump and the XUV APT probe generated in argon. These oscillations trace the IR induced time-dependent molecular dipole and therefore the attosecond electronic motion in the neutral molecule prior to ionization. The relative placement of the time-axis of the three measurements is undefined, and has been chosen in a manner where for all three molecules a zero crossing in the yield occurs at $T=0$. (b) Normalized Fourier transform (FT) power spectra of the experimental results. The shaded gray area was used in an inverse-FT, leading to the red solid curves in the left panel. The parent ionization yields oscillate with a period corresponding to half the period of the NIR field (dashed blue line). (c) Time-of-flight spectra obtained for ionization of ${\mathrm{N}}_2$, ${\mathrm{CO}}_2$, and ${\mathrm{C}}_2{\mathrm{H}}_4$ molecules by an APT generated by high harmonic generation in argon. In each molecule the abundance of the parent ion dominates over that of the ionic fragments. (d) TDDFT calculations of the amplitude of the oscillation of the XUV-induced ionization yield $\Delta \sigma$, of aligned molecules, as a function of the polarizability tensor component along the molecular axis ${\alpha }_z$. The NIR-induced charge displacement increases with the polarizability of the molecule, enhancing the screening effect that leads to the ionization yield variations. The induced change in the electron density at the maximum of the NIR electric field is shown above the data points, while the ground state chemical bonding structure is shown to the right.