Damping of Bogoliubov excitations in optical lattices

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional 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 ⁴He. This leads to the disappearance of all damping processes when Un^c0⩾6J, where U is the on-site interaction, J is the hopping matrix element, and n^c0(T) is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.