Effected of Feshbach resonance on dynamics of matter waves in optical lattices

TL;DR

This paper investigates how Feshbach resonance-induced changes in scattering length affect the dynamics of Bose-Einstein condensates in optical lattices, focusing on soliton formation and wave evolution through analytical and numerical methods.

Contribution

It introduces a detailed analysis of BEC dynamics under Feshbach resonance using the Gross-Pitaevskii equation and explores soliton generation from periodic waves.

Findings

Identification of adiabatic evolution of periodic solutions

Numerical demonstration of soliton train formation

Impact of varying nonlinearity on condensate dynamics

Abstract

Mean-filed dynamics of a Bose-Einstein condensate (BEC) loaded in an optical lattice (OL), confined by a parabolic potentials, and subjected to change of a scattering length by means of the Feshbach resonance (FR), is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases can be reduced a one-dimensional perturbed nonlinear Schr\"{o}dinger (NLS) equation. A particular form of the last one depends on relations among BEC parameters. We describe periodic solutions of the NLS equation and their adiabatic dynamics due to varying nonlinearity; carry out numerical study of the dynamics of the NLS equation with periodic and parabolic trap potentials. We pay special attention to processes of generation of trains of bright and dark matter solitons from initially periodic waves.