Landau damping of Bogoliubov excitations in optical lattices at finite temperature

TL;DR

This paper investigates how Bogoliubov excitations in optical lattices at finite temperature experience Landau damping, revealing conditions under which damping ceases due to anomalous dispersion, with implications for superfluid behavior.

Contribution

It provides a detailed analysis of Landau damping of Bogoliubov excitations in optical lattices, highlighting the role of anomalous dispersion and dimensionality effects, which were not thoroughly explored before.

Findings

Damping vanishes when $U n^{c0} \,\geq\, 6DJ$ in simple cubic lattices.

Anomalous dispersion is necessary for energy conservation in damping processes.

Damping behavior varies across 1D, 2D, and 3D optical lattices.

Abstract

We study the damping of Bogoliubov excitations in an optical lattice at finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding model and limit our analysis to the lowest excitation band. We use the Popov approximation to calculate the temperature dependence of the number of condensate atoms $n^{\rm c 0}(T)$ in each lattice well. We calculate the Landau damping of a Bogoliubov excitation in an optical lattice due to coupling to a thermal cloud of excitations. While most of the paper concentrates on 1D optical lattices, we also briefly present results for 2D and 3D lattices. For energy conservation to be satisfied, we find that the excitations in the collision process must exhibit anomalous dispersion ({\it i.e.} the excitation energy must bend upward at low momentum), as also exhibited by phonons in superfluid $^4\rm{He}$. This leads to the sudden disappearance of all damping processes in $D$-dimensional simple cubic optical lattice when $U n^{\rm c 0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element. Beliaev damping in a 1D optical lattice is briefly discussed.