Effects of Interactions and Temperature in Disordered Ultra-Cold Bose Gases

We simulate ultra-cold interacting bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We use the Hartree-Fock-Bogoliubov formalism in the Bose-Hubbard model to explore the parameter regimes that lead to exponential localization of the ground state in a 3-colour optical lattice and investigate the role of repulsive interactions, harmonic confinement and finite temperature.