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

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• Mean-field dynamics of a two-mode Bose-Einstein condensate subject to noise and dissipation
• Manipulation of matter waves using Bloch and Bloch-Zener oscillations
• Resonant tunneling of Bose-Einstein condensates in optical lattices
• Decay and fragmentation in an open Bose-Hubbard chain
• Spectral singularities in PT-symmetric Bose-Einstein condensates
• Nonlinear resonant tunneling of Bose-Einstein condensates in tilted 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
• Field-induced decay of quantum vacuum: visualizing pair production in a classical photonic system
• The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions
• Wave Function Renormalization Effects in Resonantly Enhanced Tunneling
• Exceptional points in bichromatic Wannier-Stark systems
• Exact numerical methods for a many-body Wannier Stark system
• Quantum versus classical effects in the chirped-drive discrete nonlinear Schrodinger equation
• Lifetimes of atoms trapped in an optical lattice in proximity of a surface
• Recent advances in the combination of nonlinearity and exceptional points
• Generation of robust entangled states in a non-hermitian periodically driven two-band Bose-Hubbard system