Chaotic and frequency-locked atomic population oscillations between two coupled Bose-Einstein condensates

We have investigated the chaotic and frequency-locked population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric potential and damping. Under the deterministic perturbation, there exist stable oscillations close to the separatrix solution, which are Melnikov chaotic. Numerical results reveal that, in the nondissipative regime, regular oscillations gradually tend to chaotic with the increase of the trap asymmetry, the long-term localization disappears, and short-term localization can be changed from one of the Bose-Einstein condensates to the other through the route of Rabi oscillation. But in the dissipative regime, stationary chaos disappears and transient chaos is a common phenomenon before the regular stable frequency-locked oscillations, and a proper damping can keep the localization long lived.