Calculation of collective modes for the Bose-Hubbard model with confinement

TL;DR

This paper investigates the collective excitations in the one-dimensional Bose-Hubbard model with confinement, revealing distinct spectral behaviors in superfluid and Mott insulating regimes through numerical diagonalization.

Contribution

It provides a detailed numerical analysis of collective modes in trapped Bose-Hubbard systems, linking spectral features to superfluid and Mott insulating phases.

Findings

Superfluid regime exhibits a single dominant excitation frequency.

Mott insulating regions show multiple excited frequencies.

Results explain recent experimental observations involving Mott plateaus.

Abstract

The collective excitations in the Bose-Hubbard model in a trap are studied by means of numerical diagonalization in one dimension. The strength function is calculated for monopole and dipole perturbations, and moments of the strength function are utilized in order to obtain information about the collective behavior under external forces. In the superfluid regime, the spectrum is found to be exhausted by one single frequency, while in systems that contain a Mott insulating plateau several frequencies are excited. An explanation of recent experimental findings in terms of a Mott plateau is suggested.