Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

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.

References in corpus (10)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Three-Dimensional Anderson Localization of Ultracold Matter
• Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate
• Anisotropic 2D diffusive expansion of ultra-cold atoms in a disordered potential
• Dipolar Bose-Einstein Condensates with Weak Disorder
• Density modulations in an elongated Bose-Einstein condensate released from a disordered potential
• Matter Wave Transport and Anderson Localization in Anisotropic 3D Disorder
• Transport regimes of cold gases in a two-dimensional anisotropic disorder
• Anderson localization in optical lattices with speckle disorder

Cited by in corpus (10)

• Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder
• Bogoliubov Theory of Dipolar Bose Gas in Weak Random Potential
• Dipolar Bose gas in a weak isotropic speckle disorder
• Superfluidity and Bose-Einstein condensation in a dipolar Bose gas with weak disorder
• Cloud shape of a molecular Bose-Einstein condensate in a disordered trap: a case study of the dirty boson problem
• Hartree-Fock Mean-Field Theory for Trapped Dirty Bosons
• Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap
• Effects of the Lee-Huang-Yang quantum corrections on a disordered dipolar Bose gas
• Non-equilibrium evolution of Bose-Einstein condensate deformation in temporally controlled weak disorder
• Two dimensional Quantum droplets in random repulsive potential