Damping of Bogoliubov Excitations in Optical Lattices

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 ${}^4\mathrm{He}$. This leads to the disappearance of all damping processes when $U{n}^{c0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{c0}(T)$ 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.

4pages, 5figures, submitted to Phys. Rev. Lett