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Using exact diagonalisation and Density Matrix Renormalisation group (DMRG)approach, we analyse the transition to a localised state of a weaklyinteracting quasi-1D Bose gas subjected to a quasiperiodic potential. Theanalysis is performed by calculating the superfluid fraction, density profile,momentum distribution and visibility for different periodicities of the secondlattice and in the presence (or not) of a weak repulsive interaction. It isshown that the transition is sharper towards the maximally incommensurate ratiobetween the two lattice periodicities, and shifted to higher values of thesecond lattice strength by weak repulsive interactions. We also relate ourresults to recent experiments.

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential