  Nonlinear Floquet states associated with a symmetry-breaking driving field
are exploited to control the dynamics of a Bose-Einstein condensate in a
double-well potential. The population imbalance between the two wells is shown
to be controllable by slowly tuning system parameters along a closed path. The
results extend symmetry-breaking-based quantum control to many-body systems and
extend navigation of linear Floquet states to navigation of nonlinear Floquet
states.
