Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential - art. no. 023613

We study the quantum coherent tunneling between two Bose-Einstein condensat es separated through an oscillating trap potential. The cases of slow and r apid varying in the time trap potential are considered. In the case of a sl owly varying trap, we study the nonlinear resonances and chaos in the oscil lations of the relative atomic population. Using the Melnikov function appr oach, we find the conditions for chaotic macroscopic quantum-tunneling phen omena 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 oscill ations in the relative population for any given damping and the nonlinear a tomic interaction In the case of a rapidly varying trap, we use the multisc ale expansion method in the parameter epsilon = 1/Ohm, where Ohm is the fre quency of modulations, and we derive the averaged system of equations for t he modes. The analysis of this system shows that new macroscopic quantum se rf-trapping regions, in comparison with the constant trap case, exist.