Abstract
The influence of a superposed offset field on the response of highly polarized (quasi-1D) very-high-$n$ Rydberg atoms to a periodic train of unidirectional half-cycle pulses (HCPs) is investigated, both experimentally and theoretically. It is observed that the presence of an offset field strongly influences the dynamics. The electronic states become transiently stabilized and trapped near the ionization threshold when the net average field they experience is near zero irrespective of whether the HCPs, applied parallel to the atomic axis, are directed towards or away from the nucleus. The nature of this stabilization is explored using Poincar\'e surfaces of section. In large offset fields, direct field ionization becomes possible but it is demonstrated that this can be suppressed by application of an oppositely directed HCP train. The use of such ``frustrated field ionization'' to measure the polarization of Rydberg atoms is discussed.
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