Contents - Max-Planck-Institut für Physik komplexer Systeme

2.1 Photo Activated Coulomb Complexes
CHRISTIAN GNODTKE, ALEXEI MIKABERIDZE, ULF SAALMANN, JAN M ROST
We introduce Coulomb complexes and investigate
their properties [1]. They offer analytical insight into
the highly non-linear dynamics of multiphoton absorption
by many electrons in a large molecule or
cluster as a result of irradiation with an intense laser
pulse. Coulomb Complexes explain the shape of the
photo electron spectrum for moderate laser intensity
as found in the experiment and deliver a transparent
understanding of high energy wings in the electron
spectrum observed in xenon clusters [2].
Multiphoton absorption occurs when matter is illuminated
by intense light fields. Historically, it was discovered
in atoms where one bound electrons can absorb
many photons giving rise to phenomena such as
high harmonic generation (HHG) and above threshold
ionization (ATI).
In extended systems, such as clusters or quantum dots,
a delocalized electron cloud can form a nanoplasma
which absorbs efficiently many photons through (classical)
resonant coupling [3]. For two-component systems
where the center material has lower ionization potential
than the hull (e.g, a xenon cluster embedded in
a helium droplet), dramatic “catalytic” effects can occur:
While the pristine helium cluster is transparent for
radiation of I = 7 × 10 14 Wcm −2 or less with photons
of 1.2 eV energy, a dozen xenon atoms in the center is
sufficient to remove all electrons from their bound orbitals
of up to 10 5 helium atoms. This happens since
(owing to the linear polarization of the light) a cigarshaped
electron plasma is formed as sketched in Fig. 1.
It remains resonant along the laser polarization with
the frequency of the light for a long time [4].
Figure 1: Schematic cut
through a xenon cluster
(blue) embedded in helium
(yellow and red), where
red indicates ionized
helium and therefore the
cigar-shaped nanoplasma.
The green line is the laser
polarization, after [4].
For higher photon frequencies of the order of the ionization
potential of atoms (∼ 12 eV), a new absorption
mechanism becomes relevant: inverse Bremsstrahlung
[5]. Increasing the photon energy even further to XUV
frequency (100 eV) and beyond up to X-rays, the multiphoton
light-matter coupling changes drastically its
character compared to 1.2 eV photons. Now, multiphoton
absorption is realized by different atoms absorbing
one photon each. During the short time when
the laser pulse rises a separation of positive (ions) and
negative charge (electrons) is realized. The latter remain
partially bound to the ion cloud as a relatively
cold plasma. The Coulomb forces among all charged
particles completely dominate the dynamics and induce
general properties to such “Coulomb Complexes”
(CC), irrespectively of the exact nature of their atomic
constituents.
Photo activation of Coulomb Complexes Since the
Coulomb forces dominate the dynamics we only need
to describe the number of electrons N(t) photo ionized
during a laser pulse. Assuming a Gaussian envelope
for the pulse with peak intensity I0, half width
T = 2τ(ln 2) 1/2 and atomic single ionization with a
cross section σω, we get N(t) = N∞/2[1 + erf(t/τ)],
where N∞ = NAσωI0τ/ω with NA atoms in the CC.
The separation of charges with N∞ negative electrons
leads to a positive background charge Q = N∞. For
simplicity we assume here a homogeneous charge distribution
and a spherical shape of the original cluster
of atoms with radius R so that the potential created
is that of sphere with constant charge density, trivially
Coulombic U(r > R) = −Q/r outside the cluster and
U(r ≤ R) = − Q
2R (3 − (r/R)2 ) (1)
inside. All N electrons eventually activated in a random
sequence at random atomic positions inside the
cluster exert their electrostatic (Coulomb) forces from
the beginning in order to avoid discontinuities upon
photo activation. The latter means operationally in
our approach that the electron to be activated switches
from infinite mass to its natural mass and starts to
move. For now, we also assume the laser pulse to be
such that the ions are static during the pulse so that the
background potential does not change. This restriction
can be lifted in future studies.
Analytical properties of Coulomb complexes The
main motivation behind our formulation of Coulomb
complexes is to work out analytical properties. They
remain buried in simulations which, of course, describe
specific situations more accurately. One of them is the
42 Selection of Research Results