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

TL;DR

This paper develops an effective two-mode model for 3D Bose-Einstein condensates in double-well potentials, incorporating an effective on-site interaction parameter, and validates it against detailed simulations, improving understanding of condensate dynamics.

Contribution

It introduces a refined two-mode model with an effective interaction parameter that accurately captures condensate dynamics across different particle numbers, validated by numerical simulations.

Findings

The effective on-site interaction parameter varies with particle number.

The analytical formula accurately predicts self-trapping periods.

The two-mode model shows excellent agreement with 3D simulations.

Abstract

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.