  The dynamics of Rydberg states of atomic hydrogen illuminated by resonant elliptically polarized microwaves is investigated both semiclassically and quantum mechanically in a simplified two-dimensional model of an atom. Semiclassical predictions for quasienergies of the system are found to be in a very good agreement with exact quantum data enabling a classification of possible types of motion and their dynamics with the change of the ellipticity of the microwaves. Particular attention is paid to the dynamics of the nonspreading wave packet states which are found to exist for an arbitrary microwave polarization. 
H atom in elliptically polarized microwaves: Semiclassical versus   quantum resonant dynamics