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

TL;DR

This paper investigates the behavior of Bose-Einstein condensates in accelerated double-periodic optical lattices, focusing on resonance coupling, crossing phenomena, and the effects of nonlinearity and decay in such systems.

Contribution

It introduces a detailed analysis of coupled resonances in nonlinear two-level systems with decay, specifically applied to BEC dynamics in tilted double-periodic optical lattices.

Findings

Decay properties are significantly altered by the addition of a period-doubled lattice.

Analytic results are supported by numerical computations of nonlinear resonance states.

The study provides insights relevant for ultracold atom experiments.

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.