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

摘要

We study the dynamical properties of a few bosons confined in a one-dimensional split hard-wall trap with the interaction strength varying from the weakly to strongly repulsive regime. The system is initially prepared on 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 the 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 diagonalization verify the enhancement of correlated tunnelling 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 the quantitative discrepancy, we validate that the form of correlated tunnelling gives an important contribution to tunnelling 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.