Bose-Einstein Condensation Dynamics from the Numerical Solution of the Gross-Pitaevskii Equation by the Pseudospectral Method

TL;DR

This paper presents a pseudospectral numerical method using Laguerre polynomials to solve the time-dependent Gross-Pitaevskii equation for Bose-Einstein condensates, analyzing their dynamics under various conditions.

Contribution

It introduces a novel pseudospectral approach with Laguerre polynomials for solving the GP equation, enabling detailed study of condensate dynamics and responses to parameter changes.

Findings

Calculated radial wavefunctions and energies for different nonlinearities.

Analyzed condensate oscillation frequencies after parameter changes.

Demonstrated the effectiveness of the pseudospectral method for BEC simulations.

Abstract

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre polynomials to solve the time dependent GP for a spherically symmetric trap potential. The radial wavefunction and energy values have been calculated for different nonlinearities. Further, we study the effect of suddenly changing the interatomic scattering length or harmonic oscillator trap potential in the condensate. We also investigate the frequency of oscillation due to the variation in the strength of nonlinearity.