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We investigate the dynamics of a Bose--Einstein condensate (BEC) in atriple-well trap in a three-level approximation. The inter-atomic interactionsare taken into account in a mean-field approximation (Gross-Pitaevskiiequation), leading to a nonlinear three-level model. New eigenstates emerge dueto the nonlinearity, depending on the system parameters. Adiabaticity breaksdown if such a nonlinear eigenstate disappears when the parameters are varied.The dynamical implications of this loss of adiabaticity are analyzed for twoimportant special cases: A three level Landau-Zener model and the STIRAPscheme. We discuss the emergence of looped levels for an equal-slopeLandau-Zener model. The Zener tunneling probability does not tend to zero inthe adiabatic limit and shows pronounced oscillations as a function of thevelocity of the parameter variation. Furthermore we generalize the STIRAPscheme for adiabatic coherent population transfer between atomic states to thenonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceedsthe detuning.Comment: RevTex4, 7 pages, 11 figures, content extended and title/abstract  change

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage