Band structure and dynamic behaviors of Bose-Einstein condensates in Fourier-Synthesized optical lattices

► We find there exist four critical values by employing three-mode approximation. ► In critical values (c1=0.25,c2=0.6,c3=0.88,c4=1.23), the band structure presents a very novel loop structure (bowl structure at c3=0.88). ► Changing of the relative phase impacts greatly on the properties of the energy structure. ► We analysis the stability of the corresponding eigenstates by the eigenvalues of the Jacobian of the classical Hamiltonian.