Ground-state phase diagrams in spin–orbit coupled spin-3 Bose–Einstein condensates

We study the ground-state phases of spin–orbit coupled spin-3 Bose–Einstein condensates with the attractive and repulsive spin–singlet interactions, respectively. The competition between the interactions and spin–orbit coupling gives rise to abundant ground-state phases. For the system with the attractive spin–singlet interaction, a stripe phase is found with the weak spin–orbit coupling strength. The larger spin–orbit coupling drives the stripes to bend, which enhances the creation of the ring phase with the attractive spin–quintet interaction. Combining spin–orbit coupling and the repulsive spin–quintet interaction, two kinds of lattice phases are formed, namely the rectangular lattice and octagonal lattice phases. The system with the repulsive spin–singlet interaction possesses richer ground-state phases than the system dominated by the attractive spin–singlet interaction. Six distinct ground-state phases are identified, i.e., the stripe phase, the ring phase, the transition phase, the triangular lattice phase, the rectangular lattice phase and the octagonal lattice phase. These ground-state phase display a rich phase diagram. We compare the ground-state energies mutation point with the phase transition boundaries, and find that they are in good quantitative agreement.