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 [Cal97]. The
figure beneath shows results for Na8+ as
example (taken from [Leg06])
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) [Leg02]
allows to simulate that process in detail [Poh00]
. The figure to the left shows two examples for two clusters
which are nearly spherical (taken from [Poh03]).
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+
[And02]. 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 Rion, shown in the lowest
panel.
The Mie plasmon frequency depends on the cluster extension as
wMie~ 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.
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