Attosecond Probing of Nuclear Dynamics with Trajectory-Resolved High-Harmonic Spectroscopy

We report attosecond-scale probing of the laser-induced dynamics in molecules. We apply the method of high-harmonic spectroscopy, where laser-driven recolliding electrons on various trajectories record the motion of their parent ion. Based on the transient phase-matching mechanism of high-order harmonic generation, short and long trajectories contributing to the same harmonic order are distinguishable in both the spatial and frequency domains, giving rise to a one-to-one map between time and photon energy for each trajectory. The short and long trajectories in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ are used simultaneously to retrieve the nuclear dynamics on the attosecond and ångström scale. Compared to using only short trajectories, this extends the temporal range of the measurement to one optical cycle. The experiment is also applied to methane and ammonia molecules.

Figure 1

(a) Normalized envelope of the laser pulse. [(b) and (c)] Time-dependent phase mismatch of 17th harmonic for the long and short trajectories. In the simulation, a 30-fs, 800-nm laser field with intensity $1.5\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$ is adopted.

Figure 2

Spatially resolved harmonic spectra from (a) ${\mathrm{D}}_2$ and (b) ${\mathrm{H}}_2$. (c) Spatially integrated HHG signals for the spectra in (a) and (b).

Figure 3

Ratio between harmonic intensities from ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ as a function of harmonic order. Circles and squares are for the long (peak $P_L$) and short (peak $P_S$) trajectories, respectively. The solid and dashed lines are the ratios $R_C(\omega )$, calculated with complex saddle-point times (see the text), for the measured and exact field-free Born-Oppenheimer (BO) potentials, respectively. The laser intensity is (a) $1.5\times 10^{14}$ and (b) $2\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 4

Vibrational dynamics for the 19th harmonic in the exact field-free (dashed lines) and measured (solid lines) BO potentials. (a) Stepwise time evolution of the internuclear distance $R$ from the ionization time $t^{\prime }$ to the recombination time $t$, for the short trajectory of ${\mathrm{H}}_2$. (b) Evolution of the internuclear distance after tunneling, i.e., from $\mathrm{Re}{t}^{\prime }$ to $\mathrm{Re}t$, for the short trajectory, for ${\mathrm{D}}_2$ (thick lines) and ${\mathrm{H}}_2$ (thin lines). The origin of the time axis is set to the moment after tunneling, i.e., to $\mathrm{Re}{t}^{\prime }$. The curves start at different $R$ because the tunneling dynamics is dependent on the isotope and BO potential. (c) Same as (b) for the long trajectory.

Figure 5

(a) Spatially integrated high harmonic spectra from ${\mathrm{CH}}_4$ and ${\mathrm{CD}}_4$. (b) Ratio between harmonic intensities from ${\mathrm{CD}}_4$ and ${\mathrm{CH}}_4$ as a function of harmonic order. Circles and squares are for the long and short trajectories, respectively. The dashed lines show the theoretical ratio from [50].