Approximate dynamical symmetry of hydrogen atoms in circularly polarized microwave fields

Abstract

We report the discovery of an integrable three-dimensional Hamiltonian system with a velocity-dependent potential. A two-dimensional restriction of that system is (for low frequencies) a good approximation of the motion (in the polarization plane) of the hydrogen atom in circularly polarized microwave fields. An additional integral of motion of the integrable two-dimensional system (being approximate invariant for the hydrogen atom in a circular field) is used in the calculation of the classical ionization field threshold. The result is consistent with all available experimental observations.