arXiv:1501.07811 · Annalen der Physik

Anderson localization of Bogoliubov excitations on quasi‐1D strips

Christopher Gaul, Pierre Lugan, Cord Axel Müller

Published Apr 2, 2015• 3 citations

Abstract

Anderson localization of Bogoliubov excitations is studied for disordered lattice Bose gases in planar quasi–one‐dimensional geometries. The inverse localization length is computed as function of energy by a numerical transfer‐matrix scheme, for strips of different widths. These results are described accurately by analytical formulas based on a weak‐disorder expansion of backscattering mean free paths. image

DOI: 10.1002/andp.201500106

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arXiv:1501.07811 · Annalen der Physik

Anderson localization of Bogoliubov excitations on quasi‐1D strips

Christopher Gaul, Pierre Lugan, Cord Axel Müller

Published Apr 2, 2015• 3 citations

arXiv HTML PDF

Abstract

DOI: 10.1002/andp.201500106

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V

. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov--de Gennes equations onto a single-particle Schr\"odinger-like equation with an effective potential. For disordered potentials, the Schr\"odinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in $V/\ensuremath{\mu}$, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed.