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AUTHORS: M.
Dondera1), H.G. Muller2),
and M. Gavrila2)
1) Department of Physics,
University of Bucharest, Bucharest-Magurele
MG11, 76900,
Romania
2) FOM Institute for Atomic and Molecular Physics,Amsterdam,
1098 SJ, The Netherlands
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ABSTRACT:
Quasienergies (qe) are calculated traditionally by solving the
time-independent Floquet system of differential equations. A number of
such calculations have been carried out successfully in the past for
atomic hydrogen, albeit not at the frequencies of operation of current
superintense lasers. We now present a method for calculating qe based on
the evolution of a wave packet of the Schroedinger equation with a
time-periodic Hamiltonian, that is an extension of the well known
``spectral method'' for
obtaining (real) eigenenergies of a time-independent Hamiltonian.
The present method is based on propagating a wave packet
\Psi \(t)
with an appropriately chosen initial condition
\Psi \left( 0\right)
in a periodic field of constant amplitude, and then Fourier analyzing the
autocorrelation function
A\left( t\right) =\left\langle \Psi \left(0\right) \mid \Psi \left(
t\right) \right\rangle.
The Fourier transform of the autocorrelation function displays a set of
lines, whose location and widths are related to the complex qe of the
Floquet states present in the expansion of the wave packet. When these
lines are non-overlapping, standard fitting techniques allow the
extraction of the real and imaginary parts of the qe. For the case of
overlapping lines, we apply the more elaborate technique of ``filter
diagonalization''. Our method was tested by comparison with qe obtained
from other sources, e.g., the solution of the system of differential
equations.
We apply the method to 3D hydrogen in a laser field of linear
polarization, at the frequently used photon energy \omega =1.55 eV
(wavelength 800 nm).
We consider Floquet states belonging to several symmetry manifolds $m.$
The field amplitude is varied from zero to several a.u. We thus obtain a
``Floquet map'' for the real part of the qe of the lower states, and
separately, the imaginary parts (widths) of the qe. The Floquet map
displays interesting pseudo-crossings. We interpret the results in terms
of avoided crossings of trajectories of the qe in the complex energy
plane, and discuss their physical significance.
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