Attosecond Probing of Vibrational Dynamics with High-Harmonic Generation

The numerical solution of the time-dependent Schrödinger equation for vibrating hydrogen molecules in few-cycle laser pulses shows that high-harmonic generation is sensitive to the laser-induced vibrational motion. More intense harmonics are generated in heavier isotopes, the difference increasing with the harmonic frequency. Analytical theory reveals a dependence of the harmonics on the vibrational autocorrelation function. With the help of a genetic algorithm, the nuclear motion can be reconstructed from the harmonic spectra with sub-fs time resolution.

Figure 1

Calculated harmonic spectra for ${\mathrm{H}}_2$ in a 780 nm pulse with $4\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$ intensity. The orientation of the molecule with respect to the field is (a) $\theta =0°$, (b) $\theta =30°$, (c) $\theta =60°$, (d) $\theta =90°$.

Figure 2

Ratio between harmonic intensities in different isotopes (aligned perpendicular to the field): ${\mathrm{D}}_2$ vs ${\mathrm{H}}_2$ (circles connected by solid lines), ${\mathrm{T}}_2$ vs ${\mathrm{H}}_2$ (squares connected by dashed lines). Shown are the ratios for odd harmonics at 780 nm wavelength [panel (a)] and 1200 nm wavelength [panel (b)]. Panel (a) includes also the ratio ${\mathrm{D}}_2$ vs ${\mathrm{H}}_2$ for randomly oriented molecules (stars). The laser intensity is $4\times {10}^{14}\mathrm{W}/{\mathrm{c}\mathrm{m}}^2$.

Figure 3

(a) Data points show the ratio between harmonics in ${\mathrm{D}}_2$ and ${\mathrm{H}}_2$ versus electron travel time for a 1200 nm laser pulse. Smooth lines are the autocorrelation ratio calculated from the vibrational wave-packet dynamics in potentials from the reconstruction procedure (solid, red) or in the exact ${\mathrm{H}}_2^{+}$ BO potential (dashed line). (b) Time evolution of the internuclear distance, as reconstructed from the ${\mathrm{D}}_2/{\mathrm{H}}_2$ harmonic spectra (solid, red) and time evolution in the exact potential (dashed lines).