Controlling the population imbalance of a Bose-Einstein condensate by a symmetry-breaking driving field

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 on the mean-field level and extend navigation of linear Floquet states to navigation of nonlinear Floquet states.