Excitation Spectra of Correlated Lattice Bosons in a Confining Trap

TL;DR

This paper introduces a time-dependent Gutzwiller approach to analyze excitation spectra of ultracold bosons in optical lattices with trapping potentials, focusing on superfluid and Mott insulator regimes.

Contribution

It develops a novel method for calculating excitation energies in trapped lattice bosons, extending previous homogeneous models to include trap effects and dynamics.

Findings

Excitation spectra near the superfluid-Mott insulator boundary are characterized.

Trap effects modify low-lying excitation energies compared to homogeneous systems.

The method successfully describes center of mass and breathing mode dynamics.

Abstract

We consider ultracold bosonic atoms in an optical lattice with an external trapping potential. To study the excitation energies of the resulting Bose-Hubbard model, we develop a method based on a time-dependent generalization of the Gutzwiller ansatz. We calculate the excitations of the homogeneous system both in insulating and superfluid regime, concentrating particularly on those near the superfluid-Mott insulator boundary. Low-lying excitation energies in presence of a static harmonic trap are obtained using this method and compared with the homogeneous case. Further, we explore the dynamics of the center of mass and the breathing mode in response to time-dependent perturbations of the trap.