Comparative study of quantum dynamics of a few bosons in a one-dimensional split hard-wall trap: exact results versus Bose-Hubbard-model approximations

TL;DR

This study compares exact and Bose-Hubbard-model approximations for the quantum dynamics of a few bosons in a one-dimensional split hard-wall trap, highlighting the limitations of one-band BHM in strongly interacting regimes and emphasizing the importance of correlated tunneling.

Contribution

It provides a detailed comparison between exact diagonalization and Bose-Hubbard models, demonstrating the need for multi-band BHM to accurately describe strongly interacting bosons.

Findings

One-band BHM accurately describes weakly interacting regimes.

Correlated tunneling is significant in strongly interacting regimes.

Multi-band BHM is necessary for quantitative accuracy in strong interactions.

Abstract

We study the dynamical properties of a few bosons confined in an one-dimensional split hard wall trap with the interaction strength varying from the weakly to strongly repulsive regime. The system is initially prepared in one side of the double well by setting the barrier strength of the split trap to be infinity and then the barrier strength is suddenly changed to a finite value. Both exact diagonalization method and Bose-Hubbard model (BHM) approximation are used to study the dynamical evolution of the initial system. The exact results based on exact diagonaliztion verify the enhancement of correlated tunneling in the strongly interacting regime. Comparing results obtained by two different methods, we conclude that one-band BHM approximation can well describe the dynamics in the weakly interacting regime, but is not efficient to give quantitatively consistent results in the strongly interacting regime. Despite of the quantitative discrepancy, we validate that the form of correlated tunneling gives an important contribution to tunneling in the large interaction regime. To get a quantitative description for the dynamics of bosons in the strongly interacting regime, we find that a multi-band BHM approximation is necessary.