Dynamic behaviour of Bose-Einstein condensates in optical lattices with two- and three-body interactions

We study the dynamic behaviour of Bose-Einstein condensates with two- and three-atom interactions in optical lattices with analytical and numerical methods. It is found that the steady-state relative population displays tuning-fork bifurcation when the system parameters are changed to certain critical values. In particular, the existence of the three-body interaction not only transforms the bifurcation point of the system but also greatly affects the macroscopic quantum self-trapping behaviours associated with the critically stable steady-state solution. In addition, we investigated the influence of the initial conditions, three-body interaction, and the energy bias on the macroscopic quantum self-trapping. Finally, by applying the periodic modulation on the energy bias, we observed that the relative population oscillation exhibits a process from order to chaos, via a series of period-doubling bifurcations.