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. In this context we also point out that the concept of a quasi-three dimensional speckle, which appears due to an extension of the autocorrelation function in the longitudinal direction of a transverse 2d speckle, is not applicable for the true 3d speckle, since it requires an additional space dimension. 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.

Analytical and numerical study of dirty bosons in a quasi-one-dimensional harmonic trap

“…Therefore, we expect that a quantum phase transition will also appear in the trapped case within the Thomas-Fermi approximation. Now we check whether our results are compatible with the Huang-Meng theory [20][21][22][23][24][25][26][27][28][29][30][31], where the Boseglass order parameter of a homogeneous dilute Bose gas at zero temperature in case of weak disorder regime is deduced within the seminal Bogoliubov theory. The Bose-glass order parameter in one dimension is according to the Huang-Meng theory proportional to the disorder strength, which yields in dimensionless form In our Hartree-Fock mean-field theory the Bose-glass order parameter in case of weak disorder strength turns out to be:…”

“…But a more quantitative investigation of that elusive phase is still lacking both from an experimental and a theoretical point of view.One of the first important theoretical results of the dirty boson problem was obtained by Huang and Meng in 1992 [20]. Within a Bogoliubov theory for a weakly interacting Bose-Einstein condensate it was found that a weak random disorder potential leads to a depletion of both the global condensate density and the superfluid density due to the localisation of bosons in the respective minima of the random potential [20][21][22][23][24][25][26][27][28][29][30][31]. Beyond the weak disorder, a perturbative approach was worked out in [32,33], where the impact of the external random potential upon the quantum fluctuations was studied in detail.…”

Cloud shape of a molecular Bose–Einstein condensate in a disordered trap: a case study of the dirty boson problem

“…In particular, it was also demonstrated that, despite the randomness of the potential, superfluidity persists and that its depletion is larger than the condensate depletion since the bosons scattered by the disorder landscape represent randomly distributed obstacles for the motion of the superfluid. An extension to the situation when the disorder correlation function falls off with a characteristic correlation length, as in the case of a Gaussian [32,[38][39][40], a Lorentzian [41], or laser speckle disorder [42,43] revealed that condensate and superfluid depletions decrease with increasing correlation length. Note that, to the best of our knowledge, so far no prediction of the Huang-Meng theory has yet been checked experimentally although it stems from 1992.…”

Hartree–Fock mean-field theory for trapped dirty bosons

“…[24], whereas laser speckles are treated in Refs. [25,26]. Also the disorderinduced shift of the critical temperature for the homogeneous case was analyzed in Refs.…”