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

By employing a nonlinear three-mode model, we study the band structure of Bose–Einstein condensates in Fourier-Synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In linear case, we present the band structure of the system. It is demonstrated that the energy band structure is strongly dependent on the value of relative phase of the two lattice harmonics. In the nonlinear case, we show that the eigenenergies as the functions of the quasi-momentum have a novel bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength at which the band structure will undergo interesting changes. Furthermore, the stability of the eigenstate is also investigated.