Anderson localization of bogolyubov quasiparticles in interacting Bose-Einstein condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a leading length ξ) subjected to a random potential (with a finite correlation length σR). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k, and we study the localization maximum kmax. For 1D speckle potentials, we find that kmax 1/ξ when ξ σR while kmax 1/σR when ξ σR, and that the localization is strongest when ξ∼σR. Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.