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

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.