Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

TL;DR

This paper investigates how weak 3D isotropic laser speckle disorder affects the thermodynamic properties of a dilute Bose gas at zero temperature, providing theoretical derivations and proposing an experimental setup.

Contribution

It derives the autocorrelation function for 3D isotropic speckle disorder and calculates condensate depletion and sound velocity using a perturbative Gross-Pitaevskii approach.

Findings

Reproduces the normalfluid density expression consistent with Landau's theory

Shows that Gaussian approximation of speckle autocorrelation is inconsistent with speckle theory

Proposes an experimental realization for isotropic 3D laser speckle potential

Abstract

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.