Vector gap solitons of spin-orbit-coupled Bose-Einstein condensate in square optical lattice

Vector gap solitons in quasi-two-dimensional Bose–Einstein condensate loaded in a square optical lattice with spin-orbit and Rabi coupling are investigated theoretically. The solitons are obtained by the Newton-Conjugate-Gradient method for various physical parameters. The stability properties of gap solitons are theoretically analyzed by direct nonlinear dynamical evolution. It is found that the existence of gap solitons is sensitive to the spin-orbit and Rabi coupling strength. Smaller Rabi coupling strength is beneficial for the excitation of solitons in the semi-infinite gap. Conversely, larger Rabi coupling strength is beneficial for the soliton excitation in the first gap. The dynamical stability of these gap solitons depends on the spin-orbit and Rabi coupling strength, and the location of the soliton in the bandgap. These findings may contribute to understanding the topological excitations in condensed matter systems.