Long-time expansion of a Bose-Einstein condensate: Can Anderson localization be observed?

TL;DR

This study uses numerical simulations to investigate whether Anderson localization can be observed in a long-time expanding Bose-Einstein condensate with interactions, finding that interactions tend to destroy localization over experimentally accessible times.

Contribution

The paper provides the first detailed numerical analysis of long-time dynamics of interacting BECs in disorder, highlighting the impact of interactions on localization.

Findings

Interactions lead to (sub)diffusive spreading of the wavepacket

Effective localization length increases over time

Anderson localization appears to be destroyed by interactions

Abstract

We numerically explore the long-time expansion of a one-dimensional Bose-Einstein condensate in a disorder potential employing the Gross-Pitaevskii equation. The goal is to search for unique signatures of Anderson localization in the presence of particle-particle interactions. Using typical experimental parameters we show that the time scale for which the non-equilibrium dynamics of the interacting system begins to diverge from the non-interacting system exceeds the observation times up to now accessible in the experiment. We find evidence that the long-time evolution of the wavepacket is characterized by (sub)diffusive spreading and a growing effective localization length suggesting that interactions destroy Anderson localization.