Damping of Bogoliubov Excitations in Optical Lattices

TL;DR

This paper investigates how finite temperature affects the damping of Bogoliubov excitations in optical lattices, revealing a threshold beyond which damping processes vanish due to anomalous dispersion conditions.

Contribution

It extends the analysis of Landau damping in optical lattices to finite temperatures within a 1D Bose-Hubbard model, identifying conditions for the disappearance of damping.

Findings

Damping vanishes when $U n^{c0} \,\geq\, 6t$ due to anomalous dispersion.

Disappearance of damping occurs in 1D, 2D, and 3D optical lattices.

Threshold wavevector marks the cessation of Beliaev damping.

Abstract

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion'', analogous to phonons in superfluid $^4\rm{He}$. This leads to the disappearance of all damping processes when $U n^{\rm c 0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{\rm c 0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in 2D and 3D optical lattices. The disappearance of Beliaev damping above a threshold wavevector is noted.