The numerical method for computing the ground state of the two-component dipolar Bose-Einstein condensate

Si-Qi Li,Xiang-Gui Li,Dong-Ying Hua

doi:10.1186/1687-1847-2013-204

Abstract

A two-component Bose-Einstein condensate described by two coupled Gross-Pitaevskii (GP) equations in three dimensions is considered, where one equation has dipole-dipole interactions while the other one has only the usual s-wave contact interaction, in a harmonic trap. The singularity in the dipole-dipole interactions brings significant difficulties both in mathematical analysis and in numerical simulations. The backward Euler method in time and the sine spectral method in space are proposed to compute the ground states. Numerical results are given to show the efficiency of this method.

Highlights

Since, the Bose-Einstein condensation (BEC) of ultra-cold atomic and molecular gases has attracted much attention both theoretically and experimentally
The studies of the binary condensates were limited to the case of s-wave interactions, while recently the dipolar BEC has drawn a great deal of attention
4 Conclusion An efficient numerical method is presented for computing the ground states of dipolar Bose-Einstein condensates based on two coupled three-dimensional Gross-Pitaevskii equations, where one equation has a dipole-dipole interaction potential and the other one has only the usual s-wave contact interaction

Summary

Introduction

Since , the Bose-Einstein condensation (BEC) of ultra-cold atomic and molecular gases has attracted much attention both theoretically and experimentally. More detailed and controlled experimental results have been obtained, illustrating the effects of phase separation in a multi-component BEC [ – ] In these papers, the studies of the binary condensates were limited to the case of s-wave interactions, while recently the dipolar BEC has drawn a great deal of attention. A numerical method for computing the ground state of the two-component dipolar BEC is considered, where one equation has dipole-dipole interactions and the other has only the usual s-wave contact interaction. The inter-atomic and inter-component s-wave scattering interactions are described by Uj (j = , ) and U , respectively, with the following expressions [ ]: Uj π aj mj. Is the Planck constant, mj is the mass of the atom of component j, and Vj (j = , ) is the external trapping potential confining the gas.

Numerical method for computing the ground states

Conclusion