Spin structures of spin-1 bosonic atoms trapped in an optical lattice with harmonic confinement

We study the ground-state properties of spin-1 bosonic atoms trapped in a one-dimensional optical lattice with harmonic confinement. We have developed a highly efficient numerical method based on the Gutzwiller approximation to clarify the inhomogeneous magnetic phases induced by the harmonic confining potential. A quantum phase transition from a superfluid to a Mott insulator is examined for the respective cases with antiferromagnetic and ferromagnetic interactions. It is shown that the profile of local spins over the lattice sites changes as a function of the interaction strength forming the characteristic structures, which closely correlates with the average number of atoms at the sites. For antiferromagnetic cases, we find that there is a crossover from a superfluid polar condensate to Mott-insulator domains consisting of either a spin-singlet pair or a single spin at each site