Extracting sub-cycle electronic and nuclear dynamics from high harmonic spectra

Abstract

We present a new methodology for measuring few-femtosecond electronic and nuclear dynamics in both atoms and polyatomic molecules using multidimensional high harmonic generation (HHG) spectroscopy measurements, in which the spectra are recorded as a function of the laser intensity to form a two-dimensional data set. The method is applied to xenon atoms and to benzene molecules, the latter exhibiting significant fast nuclear dynamics following ionization. We uncover the signature of the sub-cycle evolution of the returning electron flux in strong-field ionized xenon atoms, implicit in the strong field approximation but not previously observed directly. We furthermore extract the nuclear autocorrelation function in strong field ionized benzene cations, which is determined to have a decay of [Formula: see text] fs, in good agreement with the [Formula: see text] fs obtained from direct dynamics variational multi-configuration Gaussian calculations. Our method requires minimal assumptions about the system, and is applicable even to un-aligned polyatomic molecules.

Figure 1

(a) Mapping of emitted photon energy to trajectory time for two different laser intensities, purple (higher) and yellow (lower). The “short” photoelectron trajectories recombining within 0.65 of the laser-cycle duration (solid lines) will contribute to the on-axis harmonic emission. Trajectories recombining at later times (dashed lines) do not contribute. The vertical dashed line shows two different evolution times being sampled at a single photon energy. (b) Low-to-high laser intensity ratios of harmonic yields in benzene (blue, 15 TW/${\text{cm}}^2$and 35 TW/${\text{cm}}^2$) and in xenon (red, 25 TW/${\text{cm}}^2$and 40 TW/${\text{cm}}^2$). The vertical shaded regions indicate the classical cutoffs corresponding to the lower intensities. Error bars reflect plus and minus one standard deviation of the ratio across six repetitions in benzene, restricted to positive values.

Figure 2

(a) An example of a two-dimensional intensity versus HHG spectrum recorded for benzene. Note the linear scaling of the cut-off with intensity in this non-saturated measurement regime. (b) Dynamical factor C obtained from fitting to experimental (red) and simulated (blue) HHG intensity scans in xenon. The experimental shaded area for xenon represents the mean plus/minus one standard deviation of the fits obtained by varying the numerical parameter $N_C$ (see SI sect. S2).

Figure 3

Dynamical factor C obtained from fitting to experimental (red) and simulated (blue-black) HHG intensity scans for benzene. The experimental shaded region for benzene represents 10–90% percentile intervals from bootstrapping the fit procedure using 6 independently recorded datasets and the simulated curves correspond to different decay constants $\tau$ as shown in the legend.