Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances

Abstract

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 Schroedinger 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.

12 pages, 17 figures

References in corpus (3)

• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Nonlinearity induced destruction of resonant tunneling in the Wannier-Stark problem
• An analytical study of resonant transport of Bose-Einstein condensates

Cited by in corpus (5)

• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a two-mode Bose-Einstein condensate subject to noise and dissipation
• Resonant tunneling of Bose-Einstein condensates in optical lattices
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential
• Many-body Landau-Zener tunneling in the Bose-Hubbard model