Localized Higgs modes of superfluid Bose gases in optical lattices: A Guzwiller mean-field study

TL;DR

This study investigates localized Higgs modes in superfluid Bose gases within optical lattices, revealing bound states near the Mott transition and their evolution into quasi-bound states away from it, using Gutzwiller mean-field and Ginzburg-Landau theories.

Contribution

It demonstrates the existence and behavior of Higgs bound states near the Mott transition, highlighting the limitations of Ginzburg-Landau theory and the effectiveness of Gutzwiller mean-field analysis.

Findings

Higgs bound states are localized near potential barriers close to the Mott transition.

These bound states become quasi-bound states as the system moves away from the Mott transition.

Gutzwiller mean-field results align with Ginzburg-Landau theory near the transition but differ far from it.

Abstract

We study effects of a potential barrier on collective modes of superfluid Bose gases in optical lattices. We assume that the barrier is created by local suppression of the hopping amplitude. When the system is in a close vicinity of the Mott transition at commensurate fillings, where an approximate particle-hole symmetry emerges, there exist bound states of Higgs amplitude mode that are localized around the barrier. By applying the Gutzwiller mean-field approximation to the Bose-Hubbard model, we analyze properties of normal modes of the system with a special focus on the Higgs bound states. We show that when the system becomes away from the Mott transition point, the Higgs bound states turn into quasi-bound states due to inevitable breaking of the particle-hole symmetry. We use a stabilization method to compute the resonance energy and line width of the quasi-bound states. We compare the results obtained by the Gutzwiller approach with those by the Ginzburg-Landau theory. We find that the Higgs bound states survive even in a parameter region far from the Mott transition, where the Ginzburg-Landau theory fails.