Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates

TL;DR

This paper analytically and numerically investigates the Anderson localization of Bogolyubov quasiparticles in interacting Bose-Einstein condensates within random potentials, revealing how localization depends on healing length and correlation length.

Contribution

It derives an analytical expression for the Lyapunov exponent of quasiparticles and identifies the conditions for maximum localization in disordered BECs.

Findings

Localization strongest when healing length is comparable to correlation length.

Analytical Lyapunov exponent matches numerical simulations.

Localization effects are observable in current ultracold atom experiments.

Abstract

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with healing length \xi) subjected to a random potential (with finite correlation length \sigma_R). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k and we study the localization maximum k_{max}. For 1D speckle potentials, we find that k_{max} is proportional to 1/\xi when \xi is much larger than \sigma_R while k_{max} is proportional to 1/\sigma_R when \xi is much smaller than \sigma_R, and that the localization is strongest when \xi is of the order of \sigma_R. Numerical calculations support our analysis and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in current experiments with ultracold atoms.