Monitoring Atomic Cluster Expansion by High-Harmonic Generation

High-harmonic generation is shown to be capable of providing time-resolved information about the particle density of a complex system. As an example, we study numerically high-harmonic generation from expanding xenon clusters in a pump-probe laser scheme, where the pump laser pulse induces the cluster explosion and the probe pulse generates harmonics in the expanding cluster. We show that the high-harmonic spectra characterize the properties of the expanding cluster. Hence, measuring the dependence of the harmonic signal on the pump-probe delay suggests itself as an experimental tool to monitor many-particle dynamics with unique temporal resolution; based on optical measurements, this technique is naturally free from any spatial charge effects.

Figure 1

Harmonic spectra generated by the probe pulse in an expanding ${\mathrm{Xe}}_{135}$ cluster and scaled in units of the probe frequency ${\omega }_0$. The pump-probe delays (i.e., the expansion times) are $\tau =300\mathrm{fs}$ (a) (blue line) and 5 ps (b) (red line). For comparison we show the peak positions for the 5 ps probe as circles in (a) and, similarly, the one for 300 fs probe in (b). The expansion is pumped with a 780 nm, 25 fs-long laser pulse with a peak intensity of $1.3\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The wavelength of the probe pulse is 390 nm, its duration is 10 fs, and the intensity is $1.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The three insets show individual lines for the harmonic orders $n=3$ (c), $n=9$ (d), and $n=15$ (e) on a linear scale.

Figure 2

(a) Normalized harmonic signals ($n=7,9,11$) from ${\mathrm{Xe}}_{135}$ found with Eqs. (1, 2) as a function of the time delay $\tau$ between pump and probe pulses; the parameters are the same as in Fig. 1. (b) Comparison of the densities calculated in the cluster simulation (filled circles) for the times (gray vertical lines) when the 50% level is reached and the threshold densities (open circles) for these harmonics; see text for details.

Figure 3

(a) Normalized signal $J_{15}$ of the 15th harmonic (black line) emitted by the cluster ${\mathrm{Xe}}_{135}$ (same laser pulse parameters as in Fig. 1) as a function of the time delay $\tau$ between pump and probe pulse. Contributions from ${\mathrm{Xe}}^{2+}$ (dashed blue line) and ${\mathrm{Xe}}^{3+}$ (dot-dashed red line) ions are shown separately. Inset: Average electric field (due to the other ions in the cluster) seen by the ions as a function of time $\tau$. (b) Harmonic signal $I_{15}$ for ${\mathrm{Xe}}^{2+}$ (dashed blue line) and ${\mathrm{Xe}}^{3+}$ (dot-dashed red line) ions in the presence of a static electric field. The times at the vertical gray lines indicate at which time during the cluster expansion the corresponding electric field acts on the cluster ions, cf. the arrows in the inset of (a).

Figure 4

Normalized signal $J_n$ of the $n$th harmonic emitted by the cluster ${\mathrm{Xe}}_{135}$ at a time delay of 300 fs. Laser parameters are the same as in Fig. 1.