Periodic orbits in atomic hydrogen exposed to circularly polarised laser light

Exact circular periodic orbits for a hydrogen atom in a strong circularly polarised laser field are derived. A stability analysis shows one orbit to be stable or unstable depending on the laser parameters, whereas the other orbit is always unstable. These orbits are expected to manifest themselves as resonances in laser assistede ^? ?H ⁺ scattering. The binding mechanism for these resonances is provided by the trapping of the quantum mechanical wave function onto the neighbourhood of a classical periodic orbit. This mechanism is analogous to that for a Wannier ridge resonance in a doubly excited two-electron atom.