  We investigate resonant strong field ionization of atomic hydrogen with
respect to the 1s-2p-transition. By "strong" we understand that Rabi-periods
are executed on a femtosecond time scale. Ionization and AC Stark shifts modify
the bound state dynamics severely, leading to nonperturbative signatures in the
photoelectron spectra. We introduce an analytical model, capable of predicting
qualitative features in the photoelectron spectra such as the positions of the
Autler-Townes peaks for modest field strengths. Ab initio solutions of the
time-dependent Schroedinger equation show a pronounced shift and broadening of
the left Autler-Townes peak as the field strength is increased. The right peak
remains rather narrow and shifts less. This result is analyzed and explained
with the help of exact AC Stark shifts and ionization rates obtained from
Floquet theory. Finally, it is demonstrated that in the case of finite pulses
as short as 20fs the Autler-Townes duplet can still be resolved. The fourth
generation light sources under construction worldwide will provide bright,
coherent radiation with photon energies ranging from a tenth of a meV up to
tens of keV, hence covering the regime studied in the paper so that
measurements of nonperturbative, relative AC Stark shifts should become
feasible with these new light sources.
