  Through the exact solution of a two-electron system interacting with a
monochromatic laser we prove that all adiabatic density functionals within
time-dependent density-functional theory are not able to discern between
resonant and non-resonant (detuned) Rabi oscillations. This is rationalized in
terms of a fictitious dynamical exchange-correlation (xc) detuning of the
resonance while the laser is acting. The non-linear dynamics of the Kohn-Sham
system shows the characteristic features of detuned Rabi oscillations even if
the exact resonant frequency is used. We identify the source of this error in a
contribution from the xc-functional to the non-linear equations describing the
electron dynamics in an effective two-level system. The constraint of
preventing the detuning introduces a new strong condition to be satisfied by
approximate xc-functionals.
