Ground-state phases of spin-orbit coupled spin-1 Bose-Einstein condensate in an optical lattice

We study the ground-state phases of two-dimensional (2D) spin-orbit coupled spin-1 Bose-Einstein condensates (BEC) in a one-dimensional (1D) optical lattice with polar and ferromagnetic interactions, respectively. Three types of the ground-state phases are found in polar and ferromagnetic BEC, respectively, i.e., the polar superfluid (PSF) phase, the polar stripe (PST) phase and the polar supersolid (PSS) phase in polar BEC and the ferromagnetic superfluid (FSF) phase, the ferromagnetic stripe (FST) phase and the ferromagnetic supersolid (FSS) phase in ferromagnetic BEC. Main different points between polar and ferromagnetic BECs are the stripe (ST) phase in polar BEC and the supersolid (SS) phase in ferromagnetic BEC for large spin-orbit coupling (SOC). We also investigate the ground-state phase diagrams of spin-orbit coupled spin-1 BEC in a 1D optical lattice with spin-dependent periodic disorder. The range of the SS phase increases and the range of the ST phase decreases with increasing the strength of the spin-dependent periodic disorder in both polar and ferromagnetic BECs, which shows the SS phase is obtained easily in spin-orbit coupled spin-1 BEC in a 1D optical lattice with spin-dependent periodic disorder.