New Development of Theoretical and Computational Methods for Probing Strong-Field Multiphoton Processes

The study of the strong-field multiphoton processes is a subject of much current significance in physics and chemistry. Recent progress of laser technology has triggered a burst of attosecond science where the electron dynamics plays a vital role in underlying physics. The nonlinear strong-field phenomena, such as multiphoton ionization, multiphoton resonance, high-order harmonic generation, etc, are beyond the perturbative regime and demand novel theoretical approaches for better understanding. This dissertation aims at developing new theoretical and computational methods with innovative spatial and temporal treatments, and delivering comprehensive studies of strong-field multiphoton processes explored by the proposed methods. The time-dependent Voronoi-cell finite difference method is a new grid-based method for electronic structure and dynamics calculations of polyatomic molecules. The spatial part is accurately treated by the Voronoi-cell finite difference method on multicenter molecular grids, featuring high adaptivity and simplicity. The temporal part is solved by the split-operator time propagation technique, allowing accurate and efficient non-perturbative treatment of electronic dynamics in strong fields. The method is applied to self-interaction-free time-dependent density-functional calculations to probe multiphoton processes of polyatomic molecules in intense ultrashort laser fields with arbitrary field-molecule orientation, highlighting the importance of multielectron effects. The generalized Floquet theory is extended for the investigations of an atom in intense frequency-comb laser fields and a qubit system driven by intense oscillating fields. For the frequency-comb laser generated by a temporal train of pulses, the many-mode Floquet theory is extended to treat the interaction of an atom and a series of comb frequencies, demonstrating coherent control of simultaneous multiphoton resonance processes. For the strongly driven qubit, the Floquet theory is extended and its analytic solution is derived to explore multiphoton quantum interference in the superconducting flux qubit