Ground states of the rotating SU(3) spin–orbit coupled spin 1 Bose–Einstein condensate in a two-dimensional harmonic trap

We investigated the effects of a novel SU(3) spin–orbit coupling (SOC) and rotation frequency on spin-1 Bose–Einstein condensates (BECs) in a two-dimensional harmonic trap. The interaction, spin–orbit coupling, and rotation frequency provide various phase diagrams for the ground state of BECs in an innovative artificial gauge field. In the antiferromagnetic state, the system underwent three novel phase transitions from the peculiar petal phase to the oblique fringe phase and then to the fringe lattice phase as the spin–orbit coupling increased. There are four types of phases in the ferromagnetic state: mixed petal-stripe phase, transverse stripe phase, reticular lattice phase, and transverse stripe lattice phase. Under the influence of the rotation frequency, BECs with weak spin–orbit coupling exhibit more vortices, such as triangular honeycomb, U-shaped vortex, and hexagonal honeycomb lattices. In the case of strong spin–orbit coupling, a square lattice forms and an annular vortex chain emerges with increasing rotation frequency.