Exotic Vortex Phases Of Two-Component Bose-Einstein Condensates In Spin-Dependent External Potentials

The rotating or spin-orbit coupled two-component Bose-Einstein condensates have rich ground-state structures. The spin-dependent physical quantities, such as the spin-dependent interaction, spin-orbit coupling and so on, play important roles in the formation of the ground-state structures of the condendates. In the present work, we investigate the ground-state vortex structures of two-component Bose-Eisntein condensates in the case that the real space potential or the gauge magnetic field is also spin-dependent.Firstly, we investigate the ground-state structure of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. We find that this system supports stable straight half-vortex sheets. We observe that the superfluid velocity always jumps across every sheet, and we give a quantitative description on this phenomenon both numerically and analytically. In the pseudospin representation, we investigate the response of the domain wall to rotation, and we find that in response to rotation, the spins on the domain walls twist and form spatially periodic "eyebrow-like" spin textures. We predict that the "eyebrow-like" spin textures widely exsits in the interfaces of the phase separated rotating two-component Bose-Einstein condensates. Under external disturbances, we observe some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession.Secondly, we investigate the ground-state properites of spin-orbit coupled two-component Bose-Einstein condensates in spin-dependent optical lattices. We find that the competition between the spin-orbit coupling strength and the depth of the optical lattice leads to a rich ground-state phase diagram. We demonstrate that the spin-orbit coupling locks the relative phase of the two-component condensates at±π/2, thus breaks the spin rotational symmetry in the x-y plane and restricts the type of the domain wall to Bloch wall. For sufficiently strong spin-orbit coupling, stable vortex lattices emerge spontaneously, corresponding to the formation of a meron-pair lattice in the pseudospin representation. Our research indicates that topological lattices, such as vortex lattices or spatially periodic spin textures can be stabilized in spin-orbit coupled systems by designing appropriate external potentials. Our findings deepen the understanding of spin-orbit coupling phenomena and provide thoughts on engineering new quantum states in spin-orbit coupled systems.Thirdly, we investigate the vortex lattice structures of two-component Bose-Einstein condensates in spin-dependent gauge magnetic fields. We find that the difference in the strength of the gauge magnetic fields experienced by different internal spin states will induce more exotic vortex phases, such as lattices composed of multi-quantum vortices, vortex dimers or trimers, and vortex bubbles. We show that different magnetic field strength ratios lead to different kinds of vortex lattices. We also demonstrate that the ratio c2/c0of the spin-exchange interaction and the density-density interaction plays a critical important role in the strucutre of the vorex lattice. In addition, we find that for a constant magnetic field strength ratio and constant c2/c0, the absolute magnetic field strength can also influence the structure of the vortex lattice.