Landau damping of Bogoliubov excitations in optical lattices at finite temperature

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 $n^{c0}(T)$ 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 ${}^4\mathrm{He}$. This leads to the sudden disappearance of all damping processes in $D$-dimensional simple cubic optical lattice when $U{n}^{c0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element. Beliaev damping in a 1D optical lattice is briefly discussed.

arXiv comment28 pages, 9 figures

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• Dynamics of a Bose-Einstein condensate at finite temperature in an atomoptical coherence filter
• Damping of Bogoliubov Excitations in Optical Lattices
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• Damping of quasiparticles in a Bose-Einstein condensate coupled to an optical cavity
• Absence of damping of low energy excitations in a quasi-2D dipolar Bose gas
• Instability of a superfluid Bose gas induced by a locked thermal gas in an optical lattice
• Bose - Einstein Condensate Superfluid-Mott Insulator Transition in an Optical Lattice
• Damping of the Higgs and Nambu-Goldstone modes of superfluid Bose gases at finite temperatures
• Metastable Bose-Einstein Condensation in a Strongly Correlated Optical Lattice
• Coarse-Grained Finite-Temperature Theory for the Condensate in Optical Lattices
• Decoherence of an impurity in a one-dimensional fermionic bath with mass imbalance
• Damping in two component Bose gas
• Damping of Confined Excitations Modes of 1D Condensates in an Optical Lattice
• Enhancing exotic quantum fluctuations in a strongly entangled cavity BEC system