Floquet formulation of time-dependent density functional theory

We present a generalized Floquet formulation of time-dependent density functional theory for nonperturbative treatment of both bound-bound and bound-free multiphoton transitions of many-electron systems in intense monochromatic laser fields. It is shown that the time-dependent Kohn-Sham equations can be converted into an equivalent time-independent infinite-dimensional non-Hermitian Floquet Hamiltonian eigenvalue problem. We introduce the notion of complex density and present a procedure for extracting the partial ionization rates from individual electron orbitals. The method is illustrated by a case study of multiphoton ionization of He in both weak and strong fields.