Spin texture in Bose–Einstein condensates confined in spin-dependent optical lattices

We investigate the ground state of rotating two-component Bose–Einstein condensates in the combined potential well of one-dimensional spin-dependent optical lattice potential and harmonic potential. The density distribution of the condensate is striped. By defining the generalized momentum operator, we derive the velocity distribution of the condensate. The velocity contours are concentric circles for each stripe, with different centers for different stripes. This velocity distribution corresponds to a specific spin texture structure. In this texture, the azimuthal angle of the magnetic moments varies along the y-direction, while the z-component of the magnetic moments varies along the x-direction. When the lattice period T₁=T₂ , the texture is divided into two regions. The magnetic moments reverse in a counterclockwise direction and in a clockwise direction as y increases in regions I and II, respectively. Furthermore, when the lattice period T₁=T₂/2 , the texture is divided into three regions. The magnetic moments reverse in a counterclockwise direction, do not reverse, and reverse in a clockwise direction as y increases in regions I, II, and III, respectively. Accurate manipulation of the texture can be achieved by adjusting the optical lattice periods T₁ and T₂ , the relative phase φ , and the rotational angular frequency Ω .