Saddle-point ‘‘trapping’’ of Rydberg electrons in crossed electric and magnetic dc fields: A time-dependent approach

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Abstract
The possibility of a microscopic Penning trap [suggested by C. W. Clark, E. Korevaar, and M. G. Littman, Phys. Rev. Lett. 54, 320 (1985)] formed by the magnetic-field-induced stabilization of saddle-point motion of an atomic electron moving in the presence of combined internal Coulomb and externally applied electric and magnetic potentials is investigated using time-dependent methods. Photoeffect spectra are calculated as the Fourier transform of the dipole correlation function for propitiously chosen initial conditions, and these indeed show oscillations as predicted by Clark et al. However, it is shown that maximal trapping occurs for the case in which only the magnetic field is present (giving the usual Landau confined states for electrons with zero average mechanical momenta) and that the Stark-Coulomb saddle point simply destabilizes this simpler motion. Both the relationship of the calculated spectra to the propagation of wave packets in the combined fields and their relationship to the periodic classical orbits ‘‘quantized’’ by Clark et al. are discussed. The more difficult problem of predicting what might be observed in a photoeffect spectrum of an atomic ground state in the presence of crossed external fields is also discussed from the time-dependent perspective.