Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates

摘要

The dynamics of three coupled bosonic wells (trimer) containing $N$ bosons isinvestigated within a standard (mean-field) semiclassical picture based on thecoherent-state method. Various periodic solutions (configured as $\pi$-like,dimerlike and vortex states) representing collective modes are obtainedanalitically when the fixed points of trimer dynamics are identified on the$N$=const submanifold in the phase space. Hyperbolic, maximum and minimumpoints are recognized in the fixed-point set by studying the Hessian signatureof the trimer Hamiltonian. The system dynamics in the neighbourhood of periodic orbits (associated tofixed points) is studied via numeric integration of trimer motion equationsthus revealing a diffused chaotic behavior (not excluding the presence ofregular orbits), macroscopic effects of population-inversion and self-trapping.In particular, the behavior of orbits with initial conditions close to thedimerlike periodic orbits shows how the self-trapping effect of dimerlikeintegrable subregimes is destroyed by the presence of chaos.