Linear and nonlinear dynamics of matter wave packets in periodic potentials

TL;DR

This paper explores the complex nonlinear behavior of matter wave packets in periodic potentials, combining experimental observations with theoretical modeling to understand phenomena like wave packet splitting and solitonic propagation in Bose-Einstein condensates.

Contribution

It introduces a model using effective mass to simplify 3D dynamics into a 1D framework, explaining complex wave packet behaviors in periodic potentials.

Findings

Wave packets exhibit slow spreading due to changing dispersion.

Splitting of wave packets is explained by transient solitonic effects.

The model accurately reproduces experimental observations.

Abstract

We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.