Spin-orbit-coupled BEC in a double-well potential: Quantum energy spectrum and flat band

Spin-orbit-coupled Bose-Einstein condensates (BECs) provide a powerful platform for studies on physical problems in various fields. Here we study the energy spectrum of a tunable spin-orbit-coupled BEC in a double-well potential with adjustable Raman laser intensity. We find in the single-particle spectrum there is a highly degenerate flat band in the ground state of the BEC, which remains stable against changes of the Raman strength. Many-body interactions between atoms remove this high degeneracy. Analytical results for particular cases are obtained by using the perturbation theory, which are in good agreement with the numerical results.