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 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 two-mode model. Systematic numerical simulations of the problem in 3D demonstrate the excellent agreement of the two-mode model for experimental parameters.