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Through the exact solution of a two-electron system interacting with amonochromatic laser we prove that all adiabatic density functionals withintime-dependent density-functional theory are not able to discern betweenresonant and non-resonant (detuned) Rabi oscillations. This is rationalized interms of a fictitious dynamical exchange-correlation (xc) detuning of theresonance while the laser is acting. The non-linear dynamics of the Kohn-Shamsystem shows the characteristic features of detuned Rabi oscillations even ifthe exact resonant frequency is used. We identify the source of this error in acontribution from the xc-functional to the non-linear equations describing theelectron dynamics in an effective two-level system. The constraint ofpreventing the detuning introduces a new strong condition to be satisfied byapproximate xc-functionals.

Non-linear phenomena in time-dependent density-functional theory: What Rabi physics can teach us