Dipole and monopole modes in the Bose-Hubbard model in a trap

TL;DR

This paper investigates the collective excitations of a trapped Bose gas in an optical lattice using the Bose-Hubbard model, revealing how modes change from oscillatory to non-oscillatory under different interaction regimes.

Contribution

It provides an exact diagonalization analysis of the lowest collective modes in a 1D Bose-Hubbard system, highlighting the transition from dipole and breathing modes to non-oscillatory excitations.

Findings

Dipole and breathing modes are confirmed in the tunneling-dominated regime.

Under Mott-like conditions, excitations are non-oscillatory.

Exact eigenstates reveal mode character changes with interaction strength.

Abstract

The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. Dipole and breathing character of the eigenstates is confirmed in the limit where the tunneling dominates the dynamics, but under Mott-like conditions the excitations do not correspond to oscillatory modes.