Mode dynamics of Bose-Einstein condensates in a single-well potential

We investigate dynamics of Bose-Einstein condensates (BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.