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Atoms and molecules exposed to intense laser fields:
The numerical treatment of atoms or molecules exposed to intense fields
(comparable to the Coulombic binding forces within these systems) remains
a great challenge to theory. On the other hand, this research area is
not only of interest for atomic and molecular physics, but also for example
for astrophysics (strong magnetic fields in, e.g., white dwarfs), laser
physics (intense, short pulses), scanning tunneling microscopy (strong
electric fields due to short distances), or single-molecule conduction
(how does an electric current flows through an atom or molecule). Perturbative multiphoton regime:
In the case of not too high intensities but high photon frequencies, the
interaction of a laser with an atom or molecule can be described within
lowest-order perturbation theory. However, already on this level of
approximation an in principle infinite sum over all field-free states
of the atom or molecule is required. This includes also the corresponding
electronic (ionization) or vibrational (dissociation) continua. Special
techniques have to be developed and coded that allow for such a summation.
Presently, we are using two different techniques (the discretization
approach and the complex-scaling method) to achieve this goal. Quasi-static regime:
In the case of higher intensities but low frequencies the interaction
of a laser with atoms or molecules may be approximately described within
the so-called quasi-static approximation. The laser field is then
described as a slowly varying electric field. Simple expressions
for predicting the corresponding ionization rates were predicted long
time ago, and they are usually used when interpreting experiments.
However, the reliability of these expressions has not yet been carefully
investigated. The experimental verification is difficult, since the
knowledge about the laser-pulse parameters is usually too unprecise.
A theoretical check is difficult, since fully three-dimensional ab initio
calculations were for a long time only feasible for atomic hydrogen,
but the simplified expressions were derived for this system. Thus atomic
hydrogen is not a good test candidate. We have developed a code that
allows such an ab initio calculation for diatomic two-electron systems
like molecular hydrogen. This lead to the discovery of interesting
phenomena (bond softening and enhanced ionization) that were
predicted to occur only in molecular ions with an odd number of
electrons. We have shown that these phenomena occur also for neutral
molecules, but for different reasons than for the ions. Presently, we
are working on extending our calculations to laser pulses (instead of
considering static fields). Non-perturbative regime:
With the new laser sources intensity and frequency regimes can be
reached that do not allow the approximative treatments discussed
above (perturbation theory or quasi-static approximation). In this
case a full time-dependent treatment is required. This is computationally
extremely demanding. Two different approaches to this problem are
presently under development for molecular systems. The grid-method
expands the time-dependent wave function on a discretized
many-dimensional grid and solves the resulting discretized equations.
Based on our (good) experience with atomic systems, we are working on
an expansion in field-free eigenstates. Coherent control of (chemical) reactions:
The control of processes on the level of atoms or molecules is a
long-standing dream of chemists, but it becomes recently also an
increasing topic in physics and technology. The reason for this
becomes apparent, if one considers the physical lower limit of
nanotechnology. Here, manipulation on the atomic scale becomes
necessary. An efficient realization of control could be the coherent
(mostly optical) excitation. Different coherent-control schemes are
presently discussed and partly experimentally realized. (Coherent
manipulation is also a key ingredient of the presently hotly debated
quantum technologies like quantum cryptography and quantum computers.)
One possible scheme is based on the quantum mechanical interference
principle. If a final state can be reached simultaneously via two
different paths, an interference will occur in the case of coherent
excitation. We are investigating schemes in which for example
one and three photons are used for exciting the same final state.
In this context we have found a possible explanation for a
mysterious phenomenon called "molecular phase". In an experiment
on molecular HI (hydrogen iodide) using one- and three-photon
excitation a final state was excited that is metastable with respect
to both ionization and dissociation. Surprisingly, it was found that
the ionization and dissociation yields oscillate out-of-phase, if the
relative phase between the one- and the three-photon field is varied.
This experimental result has motivated a lively debate, since
first theoretical predictions seemed to proof the absence of
such a phase lag between the different yields. On the other hand,
such a phase lag would provide a perfect tuning knob to achieve
even better control than could be obtained for zero phase lag. Interactions in (ultra)cold atomic or molecular gases:
The research area of cold atomic and molecular collisions is
receiving a lot of attraction after the experimental realization of
Bose-Einstein condensates in dilute atomic gases. These systems
are of great interest, since they are quantum objects of macroscopic
dimension. They may also be of interest for lithography or highly
accurate atomic clocks. Despite the sensationally rapid experimental
progress of the recent years, there are still a number of challenges left.
So far, only a small number of atomic systems could be Bose-Einstein
condensed (mainly alkali atoms). Besides hard work on extending this
catalogue, the next big step is the generation of a molecular
Bose-Einstein condensate. One possible way could be to photoassociate
Bose-Einstein condensed atoms. Other groups work on buffer-gas
cooling or electrostatic deceleration. We are currently working
on different topics in this field. One project heads for a very
accurate description of cold collisions between alkali atoms.
Related to this, we are part of an international collaboration
that investigates the collision of cold excited hydrogen atoms.
This project is relevant for the hydrogen Bose-Einstein experiment
and also for planned intense Lyman-alpha radiation sources.
Another project investigates different manipulation schemes for
producing cold molecules from atoms and predicting spectroscopic
data. Finally, we are working on a more accurate numerical
description of atomic or molecular Bose-Einstein condensates, going
beyond the usually adopted mean-field theory. Matter-antimatter interaction:
Based on the solution of fundamental equations, Dirac predicted
the existence of antimatter. This strange form of matter should
be a perfect counterpart of the matter surrounding us, but with
an opposite charge. Thus every elementary particle should possess
its antiparticle counterpart. The later on experimentally proven
existence of antimatter has always inspired not only physicists,
but also the authors of science-fiction stories. In star trek the
space ship is driven by a matter-antimatter machine that gains
energy by the annihilation of matter with antimatter. The energy that
is set free in this process is immense, since all (anti)matter is
converted into energy (according to Einstein's famous E=mc2 equation).
In the 1980s the US governmental SDI project was even planned to be
run by antimatter fuel. Besides this, there are however also more
serious thoughts related to antimatter. If matter and antimatter are
perfect mirror images of each other, why is our universe dominated
by matter although the Big Bang should have created matter and
antimatter in same amounts? A possible explanation could be a (tiny)
asymmetry between matter and antimatter. The hunt for this possibly
existing asymmetry is, however, tough, since for a long time it was
only charged antiparticles that could be produced (or escape from
radioactive decays). The charge is masking possible asymmetries, and
thus the production of antihydrogen (a neutral antiatom formed from
an antiproton and an antielectron (the positron)) would be a big step
towards tests of the fundamental symmetries of physics (like the
so-called charge-parity-time (CPT) invariance or the weak-equivalence
principle (WEP)). The goal is therefore to produce a sufficient amount
of cold antihydrogen and use this for high-precison spectroscopy
(comparing it to the extremely accurately known hydrogen spectra).
However, producing (cold) antihydrogen is extremely difficult, and
it was only in the mid 1990s that a handful antiatoms were produced.
Very recently (end of 2002), two groups at CERN managed to produce
a much larger number of antihydrogen atoms, but only in very highly
excited states and not yet cool enough for high-precision spectroscopy.
Within an international collaboration we are studying the interaction of
hydrogen atoms with antihydrogen. This turned out to be not only
of interest for the on-going antihydrogen experiments, but also to
be a nice model system for quantum mechanics and collision theory. Tritium neutrino-mass experiment:
For a long time, the neutrino was declared to possess no rest mass.
However, the standard model of physics (and the textbooks) had recently
to be revised, since a phenomenon called neutrino oscillations
was experimentally shown to occur. This is, however, only possible,
if neutrinos have a rest mass. Unfortunately, those experiments do
not provide the neutrino rest mass itself, but only mass differences.
The experiment that was so far most successful in providing an upper
limit to the rest mass of the electronic (anti)neutrino is the
tritium neutrino-mass experiment. In this experiment the energy
spectrum of the electrons produced in nuclear \beta decay of tritium
is measured. The measured spectrum is then fitted to Fermi theory
using the neutrino mass as a fit parameter. This fit requires that
all other parameters influencing the shape of the \beta spectrum
are very accurately known. Since the experiments use molecular
tritium instead of atomic one, the so-called molecular final-state
distribution (the probability that a certain amount of the nuclear
decay energy leads to a rovibronic excitation of the generated
daughter molecule 3HeT+) has to be known. This distribution
could so far not be measured, and thus it has to be provided by
theory. We have been working on the precise calculation of this
molecular final-state distribution, including a careful analysis
of the underlying approximations. For this purpose, a fully
relativistic formalism was developed that allows to calculate
the first-order corrections to the usually adopted sudden
approximation for arbitrary molecular systems. These corrections
are also of interest for the precise determination of nuclear
$ft$ values. We have also collaborated with the experimentalists
in order to explain the energy loss of the \beta electrons due to
inelastic scattering by neighbour molecules. Photoabsorption and -ionization as well as electron scattering:
The accurate absolute cross-sections of small atoms and molecules
are of great interest not only for atomic and molecular physics, but
also for astrophysics where these cross-sections enter various
simulations about interstellar media. We are especially interested
in those processes that involve continua, like the dissociative
or the electronic (ionization) continuum. The accurate ab initio
treatment of these continua is far from trivial. We are using
the methods of box discretization or complex scaling in order
to handle those problems in a numerically stable form. |