Fundamental and multipole gap solitons in spin-orbit-coupled Bose-Einstein condensates with parity-time-symmetric Zeeman lattices

Our results demonstrate that fundamental and tripole matter-wave gap solitons can be stable in spin-orbit-coupled Bose-Einstein condensates (SOC-BECs) in one-dimensional (1D) parity-time (PT)-symmetric Zeeman lattices with attractive interactions. The solitons are found to be in a semi-infinite gap and both the components are complex. The real and imaginary parts of two components of these solitons respectively are even and odd functions. The peak numbers of the second component are twice that of the first component. We analyze the linear stability for the matter-wave gap solitons and the correctness is confirmed by the soliton evolutions. Moreover, the strength of spin-orbit (SO) coupling cannot change the critical threshold of the PT-symmetric Zeeman lattices.