Band structure and tunnelling dynamics 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 the linear case, we present the band structure of the system. It is observed that the energy band structure is strongly dependent on the relative phase between the two lattice harmonics. In the nonlinear case, we show that the eigenenergy as a function of energy bias has a striking bowl structure in the middle energy level. It is found that there exist four critical values of interaction strength where the band structure undergoes interesting changes. Because of these topological distortions on the energy levels, we expect that the tunnelling dynamics make a dramatic change. The tunnelling probability is nonzero when the nonlinear term is very small and the energy levels keep the same topological structure as that in the linear case. Especially, the tunnelling probability as a function of the sweeping rate shows an irregular oscillation for the state on the middle level.