Bifurcation of nonlinear Floquet states in a periodically driven Bose–Einstein condensate

We study Floquet states of a nonlinear two-state model which is associated with a Bose–Einstein condensate (BEC) held in a driven double-well trap on the mean-field level. We reveal that the system exhibits pitchfork bifurcation and saddle-node bifurcation for resonance and off-resonance driven cases. Such a feature provides a new method for quasienergy band engineering and for precise control of the nonlinear Floquet states.