Hydrogen atoms in circularly polarized microwave fields: Near-integrability and ionization

We have recently found that the hydrogen atom in a circularly polarized (CP) microwave field possesses an approximate dynamical symmetry and its bounded motion can be well described by a three-dimensional integrable (but nonseparable) Hamiltonian function with a velocity-dependent potential [Rakovi {c} \'{c}{} and Chu, Phys. Rev. A 50, 5077 (1994)]. This finding provides a theoretical foundation for the understanding of the origin of the regularity of Rydberg atom dynamics in CP fields. We describe here the phase space topology of the three-dimensional integrable system relevant to the microwave ionization of the hydrogen atoms in CP fields. Using the integrable system as an approximation to the real system and with the use of the two additional integrals of motion, we are able to trace the deformation of the tori up to the point of bifurcation (ionization). From this, we have determined the classical ionization-field threshold law fₜₕ{}1/cn₀⁴, where n₀ is the principal quantum number of the initial state of the hydrogen atom and c is almost a constant ({}6 a.u.). These results are in good accord with the existing experimental observations.