Dipolar Bose-Einstein condensates with weak disorder

Abstract

A homogeneous polarized dipolar Bose-Einstein condensate is considered in the presence of weak quenched disorder within mean-field theory at zero temperature. By first solving perturbatively the underlying Gross-Pitaevskii equation and then performing disorder ensemble averages for physical observables, it is shown that the anisotropy of the two-particle interaction is passed on to both the superfluid density and the sound velocity.

Bogoliubov theory of dipolar Bose gas in a weak random potential

“…As the dipolar interaction potential (3) has two repulsive and only one attractive direction in real space, it yields a net expulsion of bosons from the ground state which is described by Q 3 2 (ǫ dd ) in (28). In contrast to that the dipolar interaction supports the localization of bosons in the random environment [37,39] …”

“…Note that (5) is not continuous at q = 0, as the limit q → 0 is direction dependent. This is the origin for various anisotropic properties, which are characteristic for dipolar Bose gases [37,39,42,43]. The operatorsâ k and a † k are the annihilation and creation operators in Fourier space, respectively, which turn out to satisfy the bosonic commutation relations…”

“…In the first case we have C dd = µ 0 d 2 m , with the magnetic dipole moment d m and the magnetic permeability of vacuum µ 0 , and in the latter case we have C dd = d 2 e /ǫ 0 , with the electric dipole moment d e and the vacuum dielectric constant ǫ 0 . Note that, due to the anisotropic character of the dipolar interaction, many static and dynamic properties of a dipolar Bose gas become tunable [4,5,40,41], consequences for a random environment have only recently be explored [37,39].…”

“…With this we go beyond the zero-temperature mean-field approach where the Gross-Pitaevskii equation is solved perturbativly with respect to the random potential [37,39]. This extension to the finite-temperature regime allows us to study in detail how the anisotropy of superfluidity can be tuned, a phenomenon which also occurs at zero-temperature [37,39], but turns out to be enhanced by the thermal fluctuations. We observe in addition that contact and dipolar interaction have different effects upon quantum, thermal, and disorder depletion of condensate and superfluid.…”

“…For a delta-correlated disorder it was found that both a condensate and a superfluid depletion occurs due to the localization of bosons in the respective minima of the external random potential which is present even at zero temperature. A generalization to the corresponding situation, where the disorder correlation function falls off with a characteristic correlation length as, for instance, a Gauss function [36,37], laser speckles [38] or a Lorentzian [39] is straightforward.…”