Efficient numerical methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations

In this paper, we propose efficient numerical methods for computing ground states of spin-1 Bose-Einstein condensates (BECs) with/without the Ioffe-Pritchard magnetic field B(x). When B(x)≠0, a numerical method is introduced to compute the ground states and it is also applied to study properties of ground states. Numerical results suggest that the densities of mF=±1 components in ground states are identical for any nonzero B(x). In particular, if B(x)≡B≠0 is a constant, the ground states satisfy the single-mode approximation. When B(x)≡0, efficient and simpler numerical methods are presented to solve the ground states of spin-1 BECs based on their ferromagnetic/antiferromagnetic characterizations. Numerical simulations show that our methods are more efficient than those in the literature. In addition, some conjectures are made from our numerical observations.