A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as new topological structures of the spectrum. Possible applications, such as the suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting phenomenon, which we call deterministic symmetry-breaking trapping associated with separatrix crossing, is also found in an adiabatic process.
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