The ground states of spin-orbit coupled Bose-Einstein condensates in spin-dependent potential

By exploring the Rashba spin-orbit (SO)-coupled pseudo-spin-1/2 Bose-Einstein condensates (BECs) with the Gross-Pitaevskii equations, we investigate the ground state properties of condensates in spin-dependent Gaussian potential. The condensates exhibit many rich density patterns due to competition among interparticle interaction, SO coupling and trapping potential. In the regime of fixed potential well spacing, with relatively weak SO coupling strength, a novel structure called skyrmion dipole can be observed. And the transition between skyrmion dipole, plane wave (PW) phase with vortex array, and stripe phase can be realized by changing the SO coupling strength. In the regime of fixed SO coupling strength, the non-overlap of two potential wells breaks the rotational symmetry of the potential well, and the spatial orientation of the stripe state and the PW state to be locked in a specific direction while each component replicates the same structure in the potential well of the other component. The orientation of the plane waves and stripes in both structures is same for small well spacing and independent for large well spacing. This work enriches the ground state phases of the ultracold atomic systems and deepens our understanding of topological excitation in cold atom physics and condensed matter physics.