Static and rotating domain-wall cross patterns in Bose-Einstein condensates

For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by the intersection of two domain walls (DWs) separating immiscible species, with opposite signs of the wave functions in each pair of sectors filled by the same species. The cross pattern remains stable up to the zero value of the immiscibility parameter \Delta\, while simpler rectilinear (quasi-ID) DWs exist only for values of \Delta\ essentially exceeding those in BEC mixtures (two spin states of the same isotope) currently available to the experiment. Both symmetric and asymmetric cross configurations are investigated, with equal or different numbers N-1,N-2 of atoms in the two species. In rotating traps, propellers (stable revolving crosses) are found too. A full stability region for the crosses and propellers in the system's parameter space is identified, unstable crosses evolving into arrays of vortex-antivortex pairs. Stable rotating rectilinear DWs are found too, at larger values of \Delta\. All the patterns produced by the intersection of three or more DWs are unstable, rearranging themselves into ones with two DWs. Optical propellers are also predicted in a twisted nonlinear photonic-crystal fiber carrying two different wavelengths or circular polarizations, which can be used for applications to switching and routing.