Effective two-mode model in Bose-Einstein condensates versus Gross-Pitaevskii simulations

We study the dynamics of three-dimensional Bose-Einstein condensates confined by double-well potentials using a two-mode (TM) model with an effective on-site interaction energy parameter. The effective on-site interaction energy parameter is evaluated for different numbers of particles ranging from a low experimental value to larger ones approaching the Thomas-Fermi limit, yielding important corrections to the dynamics. We analyze the time periods as functions of the initial imbalance and find a closed integral form that includes all interaction-driven parameters. A simple analytical formula for the self-trapping period is introduced and shown to accurately reproduce the exact values provided by the TM model. Systematic numerical simulations of the problem in 3D demonstrate the excellent agreement of the TM model for experimental parameters