Quasiclassical dynamics of resonantly driven Rydberg states

We present a semiclassical analysis of the dynamics of Rydberg states of at omic hydrogen driven by a resonant microwave field of linear polarization. The semiclassical quasienergies of the atom in the field are found to be in very good agreement with the exact quantum solutions. The ionization rates of individual eigenstates of the atom dressed by the field reflect their q uasiclassical dynamics along classical periodic orbits in the near integrab le regime, but exhibit a transition to nonspecific rates when global chaos takes over in phase space. We concentrate both on the principal resonance w here the unperturbed Kepler frequency omega(K) is equal to the driving fiel d frequency omega and on the higher primary resonance w = 2 omega(K). The l atter case allows for the construction of nondispersive wave packets which propagate along Kepler ellipses of intermediate eccentricity.