Routes to chaos for driven Bose-Einstein condensates: from fast to slow crossing regimes

Experiments with ultracold atoms periodically kicked in a phase-modulated lattice have clearly shown the emergence of chaotic behaviour and realized the transition from classical to quantum chaos, in agreement with the predictions of numerical calculations. We turn our attention to Bose-Einstein condensates (BEC), presenting a systematic study of the signatures which define the dynamical transition of periodically kicked BECs to classical and quantum chaos, pointing out the role of coherence. The same type of numerical experiments are performed and analyzed for a BEC following a different route to chaos under slow, adiabatic periodical driving. Preliminary comments are then devoted to the consequences of the nonlinear atomic interactions on the phase decoherence. Our results can be relevant to current experiments with BECs. (C) 2002 Elsevier Science B.V. All rights reserved.