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The effect of a weak three-dimensional (3d) isotropic laser speckle disorderon various thermodynamic properties of a dilute Bose gas is considered at zerotemperature. First, we summarize the derivation of the autocorrelation functionof laser speckles in 1d and 2d following the seminal work of Goodman. The goalof this discussion is to show that a Gaussian approximation of this function,proposed in some recent papers, is inconsistent with the general background oflaser speckle theory. Then we propose a possible experimental realization foran isotropic 3d laser speckle potential and derive its correspondingautocorrelation function. Using a Fourier transform of that function, wecalculate both condensate depletion and sound velocity of a Bose-Einsteincondensate as disorder ensemble averages of such a weak laser speckle potentialwithin a perturbative solution of the Gross-Pitaevskii equation. By doing so,we reproduce the expression of the normalfluid density obtained earlier withinthe treatment of Landau. This physically transparent derivation shows thatcondensate particles, which are scattered by disorder, form a gas ofquasiparticles which is responsible for the normalfluid component.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder