Generalized Floquet Formulation of Time‐Dependent Density Functional Theory for Multiphoton Processes in Intense Laser Fields

Abstract

AbstractWe present a short review article of recent new developments of Floquet formulations of time‐dependent density functional theory (TDDFT) for ab initio nonperturbative treatment of multiphoton and high‐order nonlinear optical processes of many‐electron quantum systems in intense laser fields. In the presence of monochromatic or polychromatic (multi‐color) time‐dependent fields, it is shown that the time‐dependent Kohn‐Sham equation can be exactly reformulated as a time‐independent generalized Floquet matrix eigenvalue problem. The theory has been extended to include the time‐dependent current density functional theory (TDCDFT) as well. In the case of bound‐free transition processes such as multiphoton ionization or dissociation, we show that the complex scaling transformation can be implemented into the Floquet formulation of TDDFT and TDCDFT, and the field‐induced complex quasienergy (dressed) states of many‐electron quantum systems can be determined by means of the solution of a time‐independent non‐Hermitian Floquet matrix eigenvalue problem. To facilitate the exploration of the constraints satisfied by the universal but unknown time‐dependent exchange‐correlation energy functionals, we develop several exact relations and theorems for the quasienergy functionals. Finally we present some initial applications of the Floquet‐TDDFT formalism for the study of multiphoton ionization of neutral atoms and electron angular distribution in multiphoton detachment of negative ions in intense laser fields. The Floquet‐TDDFT/TDCDFT formalism provides a powerful new theoretical foundation and feasible procedures for the exploration of many‐electron atomic and molecular physics in strong fields in the future.