Dinamica nonlineare di condensati di Bose-Einstein in una doppia buca di potenziale

In this work we study the dynamical regimes of a Bose-Einstein condensate in a double-well potential. Experiments on this system are carried out in traps usually having dimension of order of tens of micrometers, then opening the possibility to observe quantum effects on a mesoscopic scale. The Gross-Pitaevskii equation is a nonlinear equation that describes the dynamical evolution of the condensate at zero temperature. For a large height of the barrier between the two wells this equation can be effectively described by a set of two equations, providing the so-called two-mode model. Nontrivial dynamical regimes arise as an effect of the nonlinearity of the system, such as the macroscopic self trapping of the condensate in the wells. In this work we test the validity of the two-mode model, comparing its results with those obtained by a direct simulation of the Gross-Pitaevskii equation. Motivated by experiments where the scattering length of the interatomic interaction can be tuned via an external magnetic field, we introduce a spatial dependence in the nonlinear coefficient of the Gross-Pitaevskii equation and study how it affects the dynamics. We show that the inhomogeneity of the interaction term acts like an effective energy offset which can be described by the two-mode model and is supported by the Gross-Pitaevskii numerical simulation.