Nonperturbative treatments of level shifts of excited states and high-order harmonic generation in strong fields

In this paper we accomplish three goals. First, we present new nonperturbative results of complex quasi-energies (shifts and widths) for several low-lying excited states of atomic H in strong fields, using the L 2 non-Hermitian Floquet matrix technique. Second, we present a new nonperturbative L 2 technique for the treatment of ac Stark shifts of arbitrary excited states. We found that all the Rydberg states in weak fields are upshifted and closely follow the quadratic field dependence described by the ponderomotive potential e 2 F 2/4mW 2. Large deviation from the ponderomotive shift and intricate level-shift behaviors, however, occur in strong fields. Finally, we present a classical nonperturbative treatment of the electronic motion in intense laser fields. We show that the spectral analysis of classical trajectories can provide detailed insights regarding the mechanisms responsible for the multi- ple-harmonic generation recently observed in high-intensity experiments.