Spectral properties of planar helium under periodic driving

We present an original method for the accurate quantum treatment of
the planar three body Coulomb problem under electromagnetic
driving. Our ab initio approach combines Floquet theory, complex
dilation, and the representation of the Hamiltonian in suitably
chosen coordinates without adjustable parameters. The resulting
complex-symmetric, sparse banded generalized eigenvalue problem of
rather high dimension is solved using advanced techniques of
parallel programming. In the present thesis, this
theoretical/numerical machinery is employed to provide a complete
description of the bound and of the doubly excited spectrum of the
field-free 2D helium atom. In particular, we report on frozen
planet quantum states in planar helium. For the driven atom, we
focus on the near resonantly driven frozen planet configuration,
and give evidence for the existence of nondispersive two-electron
wave packets which propagate along the associated periodic orbit.
This represents a highly nontrivial qualitative confirmation of
earlier calculations on a 1D model atom, though with important
enhancements of the decay rate of these atomic eigenstates in the
field, due to the transverse decay channel. The latter is already
found to enhance the decay rates of the unperturbed frozen planet
as compared to the 1D model, in surprisingly good quantitative
agreement with 3D results.