We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schrödinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.
Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and crossing of resonances / Witthaut D.; Graefe E.M; Wimberger S.; Korsch H.J.. - In: PHYSICAL REVIEW A. - ISSN 1050-2947. - 75:1(2007), p. 013617. [10.1103/PhysRevA.75.013617]
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