Damping of the Higgs and Nambu-Goldstone modes of superfluid Bose gases at finite temperatures

TL;DR

This paper investigates how finite temperatures affect the damping of Higgs and Nambu-Goldstone collective modes in superfluid Bose gases near the Mott insulator transition, revealing temperature-dependent damping behaviors.

Contribution

It introduces a finite-temperature analysis of collective mode damping in superfluid Bose gases using an effective spin-1 model and Green's function methods, providing analytical and numerical results.

Findings

Higgs mode damping increases with temperature but remains underdamped in experiments.

Nambu-Goldstone mode can be overdamped due to Landau damping at typical experimental temperatures.

Damping rates are calculated up to 1-loop order, showing temperature-dependent behavior.

Abstract

We study collective modes of superfluid Bose gases in optical lattices at commensurate fillings. We focus on the vicinity of the quantum phase transition to the Mott insulator, where there exists the Higgs amplitude mode in addition to the Nambu-Goldstone phase mode associated with the spontaneous U(1) symmetry breaking. We analyze finite-temperature effects on the damping of the collective modes by using an effective spin-1 model and the field theoretical methods based on the finite-temperature Green's function. We calculate the damping rates up to 1-loop order and evaluate them analytically and numerically. We show that the damping rate of the Higgs mode increases with increasing the temperature but it remains underdamped up to a typical temperature achieved in experiments. Moreover, we find that the Nambu-Goldstone mode attenuates via a Landau damping process resulting from interactions with the Higgs mode and it can be overdamped at the typical temperature in a certain parameter region.