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...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2004-08, Vol.70 (2), Article 023611
Main Authors: Tsuchiya, Shunji, Griffin, Allan
Format: Article
Language:English
Subjects:
ATOM COLLISIONS
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSE-EINSTEIN CONDENSATION
COOLING
COUPLING
ENERGY CONSERVATION
EXCITATION
HELIUM 4
HUBBARD MODEL
LANDAU DAMPING
MATRIX ELEMENTS
ONE-DIMENSIONAL CALCULATIONS
PHONONS
SUPERFLUIDITY
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
VECTORS
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Summary: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 {sup 4}He. This leads to the disappearance of all damping processes when Un{sup c0}{>=}6J, where U is the on-site interaction, J is the hopping matrix element, and n{sup 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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.70.023611