CHAOTIC DYNAMICS OF THE RELATIVE PHASE BETWEEN TWO COUPLED BOSE-EINSTEIN CONDENSATES

We investigate the chaotic dynamics of the relative phase between two coupled Bose-Einstein condensates with small fractional population imbalance. Based on the two-mode approximation, the system equation can be expressed as that of a Josephson junction with a ratchet potential. A general solution of the first order perturbed equation for the symmetric case is theoretically constructed. From the boundedness condition of the general solution we analytically obtain the Melnikov chaotic criterion predicting the onset of chaos in the system. Numerical simulations show that the relative phase can be a constant in some parameter spaces. That means the system is in a simple or regular state. It is also numerically demonstrated that adjusting the time-dependent nonlinear interaction for the symmetric case and the trap asymmetry parameters for the asymmetry case, respectively, can force the relative phase to step from periodic states into chaotic ones via period doubling route.