Eur. Phys. J. D (2015) 69: 61
https://doi.org/10.1140/epjd/e2015-50863-7

Regular Article

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

¹ Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Campus Diadema, Rua Prof. Artur Riedel, 275, Jd. Eldorado, 09972-270 Diadema, SP, Brazil
² Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Rua Santa Adélia 166, 09210-170 Santo André, SP, Brazil
³ Instituto de Física, Universidade de São Paulo, CP 66318, 05315-970 São Paulo, SP, Brazil

^a e-mail: marcelo.pires@ufabc.edu.br

Received: 1 December 2014
Received in final form: 21 January 2015
Published online: 3 March 2015

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.