Isolating Attosecond Electron Dynamics in Molecules where Nuclei Move Fast

Capturing electronic dynamics in real time has been the ultimate goal of attosecond science since its beginning. While for atomic targets the existing measurement techniques have been thoroughly validated, in molecules there are open questions due to the inevitable copresence of moving nuclei, which are not always mere spectators of the phototriggered electron dynamics. Previous work has shown that not only can nuclear motion affect the way electrons move in a molecule, but it can also lead to contradictory interpretations depending on the chosen experimental approach. In this Letter we investigate how nuclear motion affects and eventually distorts the electronic dynamics measured by using two of the most popular attosecond techniques, reconstruction of attosecond beating by interference of two-photon transitions and attosecond streaking. Both methods are employed, in combination with ab initio theoretical calculations, to retrieve photoionization delays in the dissociative ionization of ${\mathrm{H}}_2$, ${\mathrm{H}}_2\to {\mathrm{H}}^{+}+\mathrm{H}+e^{-}$, in the region of the $Q_1$ series of autoionizing states, where nuclear motion plays a prominent role. We find that the experimental reconstruction of attosecond beating by interference of two-photon transitions results are very sensitive to bond softening around the $Q_1$ threshold (27.8 eV), even at relatively low infrared (IR) intensity ($I_0\sim 1.4\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$), due to the long duration of the probe pulse that is inherent to this technique. Streaking, on the other hand, seems to be a better choice to isolate attosecond electron dynamics, since shorter pulses can be used, thus reducing the role of bond softening. This conclusion is supported by very good agreement between our streaking measurements and the results of accurate theoretical calculations. Additionally, the streaking technique offers the necessary energy resolution to accurately retrieve the fast-oscillating phase of the photoionization matrix elements, an essential requirement for extending this technique to even more complicated molecular targets.

Figure 1

(a) Potential energy surfaces involved in the ionization of ${\mathrm{H}}_2$. Direct photoionization pathways into the dissociative state are indicated by the black curves. Indirect pathways bring the molecule to the dissociation via autoionizing DESs of the first series $Q_1$ (blue curves) and of the second series $Q_2$ (red curves). The Franck-Condon (FC) region is indicated by the gray area around the equilibrium distance of ${\mathrm{H}}_2$ of $R_{\mathrm{eq}}=1.4\mathrm{a}.\mathrm{u}.$ The inset sketches the passage from laboratory (LF) to molecular frame (MF) and involved angles considered in this Letter ($\alpha$ and $\beta$). (b) and (c) represent examples of attosecond streaking and RABBIT experimental traces when selecting on the $H^{+}$ fragments for $\beta =0\pm 20°$ and $\alpha =0\pm 30°$ with respect to the XUV polarization axis.

Figure 2

(a) The blue curve and the blue shaded area show the experimental dipole phase and its standard deviation of the dissociative reaction of the ${\mathrm{H}}_2$ and $\beta$ parallel reconstructed using the ACDC algorithm. The red, magenta, and green symbols are the experimental RABBIT results for the KER integrated, $E_k<1\mathrm{eV}$ and $E_k>1\mathrm{eV}$ cases, respectively. The black dashed line indicates the threshold of 27.8 eV above which the $Q_1$ DESs are populated. The parallel configuration corresponds to an angular selection of the photoemitted electrons of $\alpha =0\pm 30°$ and $\beta =0°-0°$ and $150°$ – $180°$ for the streaking case, and $\alpha =0\pm 30°$; $180\pm 30°$ and $\beta =0°–20°$ and $160°$ – $180°$, for the RABBIT case. The black squares and the orange curve are the theoretical contributions for the RABBIT and streaking case, respectively. (b) and (c) Experimental KER as a function of the streaking pump-probe delay for the parallel orientation. The black dash-dotted line represents the $E_k=1\mathrm{eV}$ while the red line shows the reconstructed IR streaking field from the Ne spectrogram. In detail (b) shows the integrated signal for $E_k\le 1\mathrm{eV}$ where a significant increase is observed after the $\sim 7\mathrm{fs}$ pump-probe delay.