Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

TL;DR

This paper investigates how Bogoliubov quasiparticles in weakly interacting disordered Bose gases become localized, deriving analytical localization lengths and identifying energy regimes with suppressed or enhanced localization effects.

Contribution

The authors develop a general mapping of Bogoliubov-de Gennes equations to a Schrödinger-like equation and analytically derive localization lengths for correlated disorder in one dimension.

Findings

Localization length varies with energy and disorder correlation.

Localization is suppressed at low energy due to screening.

Maximum localization occurs when healing length matches disorder correlation length.

Abstract

We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $\mu$ subjected to a disordered potential $V$. 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 $V/\mu$, 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.