Superfluidity and Bose–Einstein Condensation in a Dipolar Bose Gas with Weak Disorder

Abstract

We investigate the properties of a three-dimensional homogeneous dipolar Bose gas in a weak random potential with a Gaussian correlation function at finite temperature. Using the Bogoliubov theory (beyond the mean field), we calculate the superfluid and the condensate fractions in terms of the interaction strength on the one hand and in terms of the width and the strength of the disorder on the other. The influence of the disordered potential on the second-order correlation function, the ground state energy, and the chemical potential is also analyzed. We find that for fixed strength and correlation length of the disorder potential, the dipole-dipole interaction leads to modify both the condensate and the superfluid fractions. We show that for a strong disorder strength the condensed fraction becomes larger than the superfluid fraction. We discuss the effect of the trapping potential on a disordered dipolar Bose in the regime of large number of particles.

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.…”

Dirty bosons in a three-dimensional harmonic trap

“…Thus we use here again the TF approximation, and neglect the kinetic term in the self-consistency equation (35), which becomes in the superfluid region:…”

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.…”