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

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.

17 pages, 7 figures

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• Response of the Higgs amplitude mode of superfluid Bose gases in a three dimensional optical lattice
• Quantum many-body scars in the Bose-Hubbard model with a three-body constraint
• Localized Higgs modes of superfluid Bose gases in optical lattices: A Guzwiller mean-field study
• SU(3) truncated Wigner approximation for strongly interacting Bose gases
• Effective field theory of the Higgs mode in a two-dimensional dilute Bose gas
• Higgs and Nambu-Goldstone modes in a spin-1 $XY$ model with long-range interactions