Numerical solution to the time-dependent Gross-Pitaevskii equation

TL;DR

This paper presents a numerical method combining split-step and Legendre pseudospectral techniques to accurately and stably solve time-dependent Gross-Pitaevskii equations, enabling detailed simulations of Bose-Einstein condensate dynamics.

Contribution

The work introduces a novel numerical approach that improves accuracy and stability in solving GPEs for 1D and 2D systems, facilitating advanced condensate simulations.

Findings

High numerical accuracy demonstrated for 1D and 2D GPE solutions.

Stable simulations of condensate breathing modes with different interactions.

Effective modeling of Bose-Einstein condensate dynamics.

Abstract

In this work we employ the split-step technique combined with a Legendre pseudospectral representation to solve various time-dependent Gross-Pitaevskii equations (GPE). Our findings based on the numerical accuracy of this approach applied for one-dimensional (1D) and two-dimensional (2D) problems show that it can provide accurate and stable solutions. Moreover, this approach has been applied to study the dynamics of the Bose-Einstein condensate which is modeled with the GPE. The breathing of condensate with an repulsive and attractive interactions trapped in 1D and 2D harmonic potentials has been simulated as well.