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Physics Letters A

Nonlinear tunneling and chaos between two Bose–Einstein condensates trapped in time-dependent potential

B.-Y. Ou, Xingang Zhao, J. Liu, S. G. Chen

Published Nov 1, 2001• 10 citations
Publisher
DOI
10.1016/s0375-9601(01)00708-3

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We study the quantum coherent tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slow and rapid varying in the time trap potential are considered. In the case of a slowly varying trap, we study the nonlinear resonances and chaos in the oscillations of the relative atomic population. Using the Melnikov function approach, we find the conditions for chaotic macroscopic quantum-tunneling phenomena to exist. Criteria for the onset of chaos are also given. We find the values of frequency and modulation amplitude which lead to chaos on oscillations in the relative population, for any given damping and the nonlinear atomic interaction. In the case of a rapidly varying trap, we use the multiscale expansion method in the parameter $\ensuremath{\varepsilon}=1/\ensuremath{\Omega},$ where \ensuremath{\Omega} is the frequency of modulations, and we derive the averaged system of equations for the modes. The analysis of this system shows that new macroscopic quantum self-trapping regions, in comparison with the constant trap case, exist.
The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.
In this paper, we study the influence of the interatomic linear and nonlinear interactions on tunneling dynamics in two zerotemperature BoseEinstein condensates (BECs) when the two BECs are in coherent states. The shorttime behaviors of the tunneling dynamics are investigated in detail. It is found that the population difference between two BECs exhibits periodic Rabbi oscillations with a period, which depends upon not only interatomic linear and nonlinear interactions but also the initial state of two BECs. We show that the twoBEC system may reach a selftrapping stationary state through adjusting interatomic interactions and the initial state of the system under our consideration. We also investigate the coherent atomic tunneling current between BECs, and find that under certain conditions coherent atomic tunneling current may be a pure DC atom current.