Anderson Localization of Bogolyubov Quasiparticles in Interacting Bose-Einstein Condensates

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We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with healing length ξ) subjected to a random potential (with 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 is proportional to 1/ξwhen ξis much larger than σᵣ while kmax is proportional to 1/σᵣ when ξis much smaller than σᵣ, and that the localization is strongest when ξis of the order of σᵣ. Numerical calculations support our analysis and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in current experiments with ultracold atoms.