Analysis of cluster dynamics

The basic dynamical property of a metal cluster is the optical absorption spectrum which has a pronounced collection of strength in the region of the Mie plasmon. TDLDA driven with small amplitude excitations allows to explore the optical response [9]. The figure beneath shows results for Na₈⁺ as example (taken from [???]) in comparison to experiment (upper panel) and CI calculations (???)(second from above). The overall position of the peak strength is nicely reproduced by all methods, even by the semiclassical approach. CI produces the most detailed spectrum. The green bars show the discrete spectrum as it emerges from the CI calculation, and the red curve results from Lorentzian smoothing which simulates to some extend the finite experimental resolution and thermal fluctuations. The enormous number of spectral lines (green) is due to electronic correlations which are absent in TDLDA. Nonetheless, the unavoidable smoothing overrules these details and makes TDLDA spectra competitive. It is noteworthy that also the semiclassical approximation (Vlasov-LDA) performs surprisingly well. This provides a good starting point for the subsequent applications in more energetic situations.

Laser induced direct photo-emission of electrons allows to conclude on the clusters single-electron states by measuring the photo-electron spectra (PES). TDLDA with appropriate self-interaction correction (SIC) [277] allows to simulate that process in detail [251] . The figure to the left shows two examples for two clusters which are nearly spherical (taken from [304]). The arrows indicate the level classification according to principal quantum number and angular momentum. The PES depend, of course, on the direction of emission (checked here are the case where the cluster axis is ``perpendicular'' or ``parallel'' to the laser polarization). Experiments take an average over all direction. The summed theoretical PES agree fairly well with the data.

Pump and probe (P&P) techniques are an extremely powerful tool for time-resolved analysis. The complexity of clusters allows an enormous manifold of P&P scenarios. The figure to the right sketches a simple and robust scenario for a nearly spherical cluster, actually Na₄₁⁺ [290]. The idea is to map the radius vibrations of the cluster by an off-resonant laser pulse. The pump pulse ionizes the Na₄₁⁺ within 50 fs by three more charge units, see second panel from top for dipole response (black line) and first panel for ionization. The generated Coulomb pressure drives oscillations of the radius R_ion, shown in the lowest panel.

The Mie plasmon frequency depends on the cluster extension as w_Mie~ R^-3/2 and oscillates with opposite phase, see third panel. Thus the changing distance to the off-resonant laser frequency (green horizontal line) modulates the dipole response to probe pulses accordingly (second panel) which, in turn, yields changing ionization through the probe pulse as function of delay time. The final ionization (upper panel) becomes then a direct map of the underlying breathing oscillations of the cluster.