11 research outputs found
Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder
The effect of a weak three-dimensional (3d) isotropic laser speckle disorder
on various thermodynamic properties of a dilute Bose gas is considered at zero
temperature. First, we summarize the derivation of the autocorrelation function
of laser speckles in 1d and 2d following the seminal work of Goodman. The goal
of this discussion is to show that a Gaussian approximation of this function,
proposed in some recent papers, is inconsistent with the general background of
laser speckle theory. Then we propose a possible experimental realization for
an isotropic 3d laser speckle potential and derive its corresponding
autocorrelation function. Using a Fourier transform of that function, we
calculate both condensate depletion and sound velocity of a Bose-Einstein
condensate as disorder ensemble averages of such a weak laser speckle potential
within a perturbative solution of the Gross-Pitaevskii equation. By doing so,
we reproduce the expression of the normalfluid density obtained earlier within
the treatment of Landau. This physically transparent derivation shows that
condensate particles, which are scattered by disorder, form a gas of
quasiparticles which is responsible for the normalfluid component
Tailoring Anderson localization by disorder correlations in 1D speckle potentials
We study Anderson localization of single particles in continuous, correlated,
one-dimensional disordered potentials. We show that tailored correlations can
completely change the energy-dependence of the localization length. By
considering two suitable models of disorder, we explicitly show that disorder
correlations can lead to a nonmonotonic behavior of the localization length
versus energy. Numerical calculations performed within the transfer-matrix
approach and analytical calculations performed within the phase formalism up to
order three show excellent agreement and demonstrate the effect. We finally
show how the nonmonotonic behavior of the localization length with energy can
be observed using expanding ultracold-atom gases