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We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (ornoninteracting Bose-Einstein condensate) in a double-well potential withperiodically varying depths of the potential wells. The suppression oftunneling is possible for a single state and for superposition of two states,i.e. for a qbit. By varying spin-orbit coupling one can drastically increasethe range of modulation frequencies in which an atom remains localized in oneof the potential wells, the effect connected with crossing of energy levels.This range of frequencies is limited because temporal modulation may alsoexcite resonant transitions between lower and upper states in different wells.The resonant transitions enhance tunneling and are accompanied by pseudo-spinswitching. Since the frequencies of the resonant transitions are independent ofpotential modulation depth, in contrast to frequencies at which suppression oftunneling occurs, by varying this depth one can dynamically control bothspatial localization and pseudo-spin of the final state.

Dynamical suppression of tunneling and spin switching of a spin-orbit-coupled atom in a double-well trap