Rabi-induced localization and resonant delocalization of a binary condensate in a spin-asymmetric quasiperiodic potential

We theoretically investigate the ground state and dynamics of a Rabi-coupled pseudospin-1/2 Bose-Einstein condensate, where only one spin component is subjected to an external potential. We show that in the quasiperiodic potential the Rabi coupling induces localization between the components as it is raised above the threshold value. Interestingly, the localization is mutually induced by both components for the quasiperiodic confinement, whereas for a harmonic trap the localization is induced in the potential-free component by interaction with that confined in the potential. Further, we explore the condensate dynamics by implementing a periodic driving of the Rabi frequency, where various frequency-dependent delocalization patterns, such as double- (triple)-minima, treelike (parquetlike), and frozen distributions with a correlated propagation of different spin populations are observed in the condensate density. These features pave the way to control the condensate mass and spin density patterns, both in the stationary and dynamical realizations.