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

TL;DR

This paper demonstrates that all adiabatic density functionals in time-dependent density-functional theory fail to distinguish between resonant and non-resonant Rabi oscillations, revealing a fundamental limitation in modeling electron dynamics under laser fields.

Contribution

It provides an exact solution showing the inability of adiabatic functionals to differentiate resonant from detuned Rabi oscillations and identifies the source of this error in the xc-functional's contribution.

Findings

Adiabatic functionals cannot distinguish resonant from detuned Rabi oscillations.

The error arises from a fictitious xc detuning in the effective two-level system.

Preventing this detuning imposes a new constraint on approximate xc-functionals.

Abstract

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.