Nonlinear energy spectrum of spin-1 spin-orbit-coupled Bose-Einstein condensates in an optical lattice

Abstract Employing the variational principle and the two-mode approximation, we have carried out a study on the nonlinear energy spectrum and current density of spin-1 spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in a one-dimensional shallow optical lattice. The energy spectrum structure diagrams in the momentum space are given. When certain conditions for the system parameters are satisfied, we find that the loop structure appears at the boundary of the Brillouin zone. Furthermore, we analyze the influence of the parameters in the system on the critical condition and width of the loop structure. It is revealed that the optical lattice and Raman coupling can suppress the emergence of the loop. On the contrary, the quadratic Zeeman strength, spin-orbit-coupling and atomic interactions are favorable for the generation of the loop, which leads to the complication of the energy band structure. Intriguingly, the change of the band structure is closely related to the current density distribution of the condensates. The spin-orbit-coupling leads to a strong asymmetry in the current density distribution of different spin states in the momentum space, so as to cause a separation phenomenon. However, the optical lattice and Raman coupling weaken this asymmetry and promote the current density distribution of different spin states to re-coincidence. Our results provide a theoretical basis for further understanding the nonlinear energy spectrum characteristics of this system.