Spin-orbit coupling induced displacement and hidden spin textures in spin-1 Bose-Einstein condensates

We analytically and numerically investigate the ground state of spin-orbit coupled spin-1 Bose-Einstein condensates in an external parabolic potential. When the spin-orbit coupling is introduced, spatial displacement exists between the atom densities of components with different magnetic quantum numbers. The analytical calculations show this displacement reaches a maximum when the spin-orbit coupling strength is comparable with that of the trapping potential. As the spin-orbit coupling strength gets larger and larger, the spatial displacement decreases at a rate inversely proportional to the spin-orbit coupling strength. Correspondingly, periphery half-skyrmion textures arise; this displacement can be reflected by the non-uniform magnetic moment in the z direction. With the manipulation of the external trap, the local magnitude of the non-uniform magnetic moment can be increased evidently. This kind of increase of the local magnetic moment is also observed in the square vortex lattice phase of the condensate.