Performance of the exact adiabatic density functional to describe Rabi physics

Through the exact solution of few-electron systems interacting with a monochromatic laser we study the performance of adiabatic density functionals within time-dependent density-functional theory (TDDFT) to reproduce Rabi oscillations. The non-linear dynamics of the Kohn-Sham (KS) system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We illustrate this effect by comparing the exact time-dependent many-body solution of a He-atom in one dimension and a few-site Hubbard model with the solution of TDDFT-KS equations for different adiabatic exchange-correlation functionals. Preventing the detuning introduces a new strong condition to be satisfied by approximate new xc-functionals.