Dirty Bosons in Disordered Optical Potentials

Pearl J. Y. Louis, Makoto Tsubota

Pearl J. Y. Louis, Makoto Tsubota

Thierry Giamarchi

Matthew Case, Igor F. Herbut

We show that the self-consistency requirement on random potentials causes the decrease of correlations with disorder in the large- N theory of commensurate dirty bosons, leaving the possibility that there is no superfluid transition intact.

Daniel S. Goldbaum, Erich J. Mueller

Tama Khellil, Antun Balaž, Axel Pelster

The time-independent Gross-Pitaevskii equation describing a quasi one-dimensional Bose-Einstein-condensed gas in a harmonic trapping potential with an additional delta-correlated disorder potential at zero temperature is numerically solved for the condensate wave function, and disorder ensemble averages are evaluated. In particular, we analyze quantitatively the emergence of mini-condensates in the local minima of the random potential, which occurs for weak disorder preferentially at the border of the condensate, while for intermediate disorder strength this happens in the trap center. In view of a more detailed physical understanding of this phenomenon, we extend a quite recent non-perturbative approach towards the weakly interacting dirty boson problem, which relies on the Hartree-Fock theory and is worked out on the basis of the replica method, from the homogeneous case to a harmonic confinement. In the weak disorder regime we apply the Thomas-Fermi approximation, while in the intermediate disorder regime we use a variational ansatz in order to describe analytically the numerically observed redistribution of the fragmented mini-condensates with increasing disorder strength.