Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates

Abstract

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a healing length $\ensuremath{\xi}$) subjected to a random potential (with a finite correlation length ${\ensuremath{\sigma}}_{R}$). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum $k$, and we study the localization maximum ${k}_{\mathrm{max}}$. For 1D speckle potentials, we find that ${k}_{\mathrm{max}}\ensuremath{\propto}1/\ensuremath{\xi}$ when $\ensuremath{\xi}\ensuremath{\gg}{\ensuremath{\sigma}}_{R}$ while ${k}_{\mathrm{max}}\ensuremath{\propto}1/{\ensuremath{\sigma}}_{R}$ when $\ensuremath{\xi}\ensuremath{\ll}{\ensuremath{\sigma}}_{R}$, and that the localization is strongest when $\ensuremath{\xi}\ensuremath{\sim}{\ensuremath{\sigma}}_{R}$. Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.