Beyond the Floquet theorem: generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields

The advancement of high-power and short-pulse laser technology in the past two decades has generated considerable interest in the study of multiphoton and very high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields, leading to the discovery of a host of novel strong-field phenomena which cannot be understood by the conventional perturbation theory. The Floquet theorem and the time-independent Floquet Hamiltonian method are powerful theoretical framework for the study of bound-bound multiphoton transitions driven by periodically time-dependent fields. However, there are a number of significant strong-field processes cannot be directly treated by the conventional Floquet methods. In this review article, we discuss several recent developments of generalized Floquet theorems, formalisms, and quasienergy methods, beyond the conventional Floquet theorem, for accurate nonperturbative treatment of a broad range of strong-field atomic and molecular processes and phenomena of current interests. Topics covered include (a) artificial intelligence (AI)-most-probable-path approach (MPPA) for effective treatment of ultralarge Floquet matrix problem; (b) non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative treatment of bound-free and free-free processes such as multiphoton ionization (MPI) and above-threshold ionization (ATI) of atoms and molecules, multiphoton dissociation (MPD) and above-threshold dissociation (ATD) of molecules, chemical bond softening and hardening, charge-resonance enhanced ionization (CREI) of molecular ions, and multiple high-order harmonic generation (HHG), etc.; (c) many-mode Floquet theorem (MMFT) for exact treatment of multiphoton processes in multi-color laser fields with nonperiodic time-dependent Hamiltonian; (d) Floquet-Liouville supermatrix (FLSM) formalism for exact nonperturbative treatment of time-dependent Liouville equation (allowing for relaxations and dephasing mechanisms) and high-order nonlinear optical processes (such as intensity-dependent nonlinear optical susceptibilities and multiphoton resonance fluorescence, etc.); (e) generalized Floquet approaches for the treatment of nonadiabatic and complex geometric phases involving multiphoton transitions; (f) generalized Floquet techniques for the treatment of multiphoton processes in intense laser pulse fields with nonperiodic time-dependent Hamiltonians; (g) Floquet formulations of time-dependent density functional theory (DFT) and time-dependent current DFT for nonperturbative treatment of multiphoton processes of many-electron quantum systems in periodic or polychromatic (quasiperiodic) laser fields. For each generalized Floquet approach, we present also the corresponding development of new computational techniques for facilitating the study of strong-field processes and phenomena. The advancement of these generalized Floquet formalisms and quasienergy methods provides powerful new theoretical frameworks and accurate computational methods for nonperturbative and ab initio treatment of a wide range of interesting and challenging laser-induced chemical and physical processes and insightful exploration of strong-field atomic and molecular physics. (C) 2003 Elsevier B.V. All rights reserved.