Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach

TL;DR

This paper investigates the excitation dynamics of a lattice Bose gas at zero temperature using a time-dependent Gutzwiller mean-field approach, analyzing collective modes, sound velocity, and Bragg scattering effects.

Contribution

It applies the time-dependent Gutzwiller mean-field method to systematically study collective excitations across superfluid and Mott-insulator phases, including linear-response and scattering analyses.

Findings

Sound velocity matches hydrodynamic predictions.

Higher excitation modes significantly contribute to Bragg scattering.

Density perturbation propagation agrees with linear-response theory.

Abstract

The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov-de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes give significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.