SU(3) spin-orbit-coupled Bose-Einstein condensate confined in a harmonic plus quartic trap

We consider a SU(3) spin-orbit coupled Bose-Einstein condensate confined in a harmonic plus quartic trap. The ground-state wave functions of such a system are obtained by minimizing the Gross-Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin-orbit coupling are investigated in detail. For the case of ferromagnetic spin interaction, the SU(3) spin-orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture. For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin-orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.