Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasi-periodic potentials

TL;DR

This paper investigates how interactions influence the diffusion and localization of ultracold atomic gases in one-dimensional quasi-periodic potentials, revealing that initial conditions critically affect self-trapping and delocalization.

Contribution

It introduces a numerical study of an extended Aubry-Andr extbackslash e model including interactions, analyzing the effects of initial wavepacket shape on localization phenomena.

Findings

Self-trapping dominates when initial state is a single lattice site.

Gaussian initial wavepackets show suppressed self-trapping and enhanced delocalization.

Interaction effects depend strongly on initial conditions and lattice commensurability.

Abstract

We study the behaviour of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andr\`e model for particles in a quasi-periodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wavepacket as well as the interplay between two competing effects of the interaction, namely self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters, even for weak interaction. Conversely, if the diffusion starts from a Gaussian wavepacket, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.