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Soliton sheets which are formed by interference of Bose Einstein condensates occupying different single-particle states are observed in optical lattice potential. This structure consists of one-dimensional stationary solitons arranged periodically along the peaks of optical lattice (y direction) with the phase difference between the two sides of the soliton sheets is a linear function of y in each period, so we call it soliton sheet. A y component velocity difference exists between the two sides of the soliton sheet. Similar velocity distributions can be produced by the alignment of an infinite number of isotropic vortices along the peaks of the optical lattice. Their difference is that the soliton sheet structure is not limited by the number of phase singularities and can be generated even without phase singularities.

We demonstrate that a spin-orbit-coupled Bose-Einstein condensate can be effectively rotated by adding a real magnetic field to inputting gauge angular momentum, which is distinctly different from the traditional ways of rotation by stirring or Raman laser dressing to inputting canonical angular momentum. The gauge angular momentum is accompanied by the spontaneous generation of equal and opposite canonical angular momentum in the ground states, and it leads to the nucleation of quantized vortices. We explain this by indicating that the effective rotation with the vortex nucleation results from the effective magnetic flux induced by the gauge potential, which is essentially different from the previous scheme of creating vortices by synthetic magnetic fields. In the weakly interacting regime, symmetrically placed domains separated by vortex lines as well as half-integer giant vortices are discovered. With relatively strong interatomic interaction, we predict a structure of coaxially arranged annular vortex arrays, which is in stark contrast to the familiar Abrikosov vortex lattice. The developed way of rotation may be extended to a more general gauge system.

We investigate the ground-state properties of spin-orbit coupled Bose-Einstein condensates in spin-dependent optical lattices. The competition between the spin-orbit coupling strength and the depth of the optical lattice leads to a rich phase diagram. Without spin-orbit coupling, the spin-dependent optical lattices separate the condensates into alternating spin domains with opposite magnetization directions. With relatively weak spin-orbit coupling, the spin domain wall is dramatically changed from N\'{e}el wall to Bloch wall. For sufficiently strong spin-orbit coupling, vortex chains and antivortex chains are excited in the spin-up and spin-down domains respectively, corresponding to the formation of a lattice composed of meron-pairs and antimeron-pairs in the pseudospin representation. We also discuss how to observe these phenomena in real experiments.

We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternatively. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of novel domain walls, with spatially periodic "eyebrow-like" spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency and the period of the optical lattices., Comment: 8 pages, 9 figures