Comparison between the numerical solutions and the Thomas-Fermi approximation for atomic-molecular Bose-Einstein condensates

TL;DR

This paper compares analytical Thomas-Fermi solutions with numerical solutions of coupled Gross-Pitaevskii equations for atomic-molecular Bose-Einstein condensates, revealing conditions where approximations are accurate or not.

Contribution

It provides a detailed comparison between the Thomas-Fermi approximation and numerical solutions for atomic-molecular BECs with various interspecies interactions.

Findings

Similar density profiles for out-of-phase wavefunctions with repulsive interactions.

Significant differences in density profiles for in-phase wavefunctions with repulsive interactions.

Some in-phase cases with attractive interactions match numerical solutions, others do not.

Abstract

We study the stationary solution of an atomic Bose-Einstein condensate coupled coherently to a molecular condensate with both repulsive and attractive interspecies interactions confined in an isotropic harmonic trap. We use the Thomas-Fermi approximation and find four kinds of analytical solution for the cases. These analytical solutions are adopted as trial function for the diffusive numerical solution of the Gross-Pitaevskii equations. For the repulsive interspecies interaction, the case in which the atomic and molecular wavefunctions are out-phase, the densities have similar profiles for both methods, however, the case where the wavefunctions are in-phase, there are considerable difference between the density profiles. For the attractive interspecies interaction, there are two cases in the Thomas Fermi approximation where the wavefunctions are in-phase. One of them has numerical solution that agree with the approximation and the other does not have corresponding numerical solution.