Trojan wave packets: Mathieu theory and generation from circular states

We present an analytic theory of three-dimensional Trojan (stable nonspreading) wave packets. The theory is valid beyond the harmonic approximation presented previously. We show that electron wave packets that are both radially and angularly well localized can be generated from an angularly completely delocalized state (a circular Rydberg state) by adiabatic switching of a circularly polarized electric field. Confinement of the Rydberg electron results from the suppression of the nonlinearity of the Coulomb spectrum, the same nonlinearity that is responsible for wave-packet spreading and revivals in the absence of the applied field. A comparison with the harmonic approach is also presented, as well as the results of numerical experiments based on integration of the time-dependent and field-dependent Schrödinger equation for the electron. © 1996 The American Physical Society.