Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

TL;DR

This paper numerically investigates the dynamics of Bose-Einstein condensates by solving the Gross-Pitaevskii equation, focusing on oscillations caused by sudden changes in system parameters, using a stable split-step method.

Contribution

It introduces a highly accurate split-step numerical method for solving the time-dependent Gross-Pitaevskii equation with strong nonlinearities in BEC dynamics.

Findings

Accurate simulation of condensate oscillations after parameter changes

Stable long-time evolution with millions of iterations

Effective handling of strong nonlinearities in BEC modeling

Abstract

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii equation with both spherical and axial symmetries. We consider time-evolution problems initiated by changing the interatomic scattering length or harmonic trapping potential suddenly in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent Gross-Pitaevskii equation, where all nonlinear and linear nonderivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.