Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutora: Montserrat Guilleumas MorellIn this work, we study the Josephson dynamics, a coherent tunneling of particles between two Bose-Einstein condensates, spatially confined in a double-well potential, at zero tem-perature. We have derived the dynamical equations of our system by using the Gross-Pitaevskii equation as theoretical framework, together with a two-mode approximation. We have investigated the tunneling dynamics within the Standard Two-Mode model, neglecting the overlap of nonlinear interaction terms, as well as within the Improved Two-Mode approximation, without neglecting them. We have obtained the interaction ranges where the Improved Two-Mode is necessary in order to accurately describe the dynamics of the syste
