  We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (or
noninteracting Bose-Einstein condensate) in a double-well potential with
periodically varying depths of the potential wells. The suppression of
tunneling 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 increase
the range of modulation frequencies in which an atom remains localized in one
of the potential wells, the effect connected with crossing of energy levels.
This range of frequencies is limited because temporal modulation may also
excite resonant transitions between lower and upper states in different wells.
The resonant transitions enhance tunneling and are accompanied by pseudo-spin
switching. Since the frequencies of the resonant transitions are independent of
potential modulation depth, in contrast to frequencies at which suppression of
tunneling occurs, by varying this depth one can dynamically control both
spatial localization and pseudo-spin of the final state.
