Two-mode effective interaction in a double-well condensate

TL;DR

This paper identifies and corrects a key source of discrepancy in the two-mode model for double-well Bose-Einstein condensates by incorporating a population imbalance-dependent on-site interaction energy, improving dynamic predictions.

Contribution

It introduces a population imbalance-dependent on-site interaction parameter into the two-mode model, enhancing its accuracy for double-well condensate dynamics.

Findings

Improved agreement between two-mode model and Gross-Pitaevskii dynamics.

More accurate estimates of the critical population imbalance.

Reduction of the discrepancy in predicted system dynamics.

Abstract

We investigate the origin of a disagreement between the two-mode model and the exact Gross-Pitaevskii dynamics applied to double-well systems. In general this model, even in its improved version, predicts a faster dynamics and underestimates the critical population imbalance separating Josephson and self-trapping regimes. We show that the source of this mismatch in the dynamics lies in the value of the on-site interaction energy parameter. Using simplified Thomas-Fermi densities, we find that the on-site energy parameter exhibits a linear dependence on the population imbalance, which is also confirmed by Gross-Pitaevskii simulations. When introducing this dependence in the two-mode equations of motion, we obtain a reduced interaction energy parameter which depends on the dimensionality of the system. The use of this new parameter significantly heals the disagreement in the dynamics and also produces better estimates of the critical imbalance.