Disorder-induced shift of condensation temperature for dilute trapped Bose gases

Abstract

We determine the leading shift of the Bose-Einstein condensation temperature for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by treating both a Gaussian and a Lorentzian spatial correlation for the quenched disorder potential. Increasing the correlation length from values much smaller than the geometric mean of the trap scale and the mean particle distance to much larger values leads first to an increase of the positive shift to a maximum at this critical length scale and then to a decrease.

Hartree–Fock mean-field theory for trapped dirty bosons

“…Also the disorderinduced shift of the critical temperature for the homogeneous case was analyzed in Refs. [27,28], which also has implications for a harmonic confinement [29]. Furthermore, it was shown in Refs.…”

Dipolar Bose-Einstein condensates in weak anisotropic disorder

“…For a strong enough disorder in a homogeneous system, the depletion increases to such an extent that even a critical disorder strength exists, above which a Bose-glass phase appears, consisting only of localized mini-condensates [33][34][35][36][37][38]. Effects of disorder were also studied for harmonically trapped BECs [35,37,39,40] and BECs in optical lattices [20,23,30,[41][42][43], while the temperature behavior of dirty boson properties was examined in Refs. [15,19,28,32,38,39,42,44].…”

Dipolar Bose-Einstein condensates with weak disorder

“…In the case of a spatially decaying disorder correlation R(x), the results of the theory do not depend significantly on its shape [22]. Therefore, in what follows, we restrict ourselves to the case of a Gaussian correlation with the Fourier transform R(k) = R e −σ 2 k 2 /2 , where R and σ characterize the strength and the correlation length of the disorder, respectively.…”