Eur. Phys. J. B 68, 435-443 (2009)
https://doi.org/10.1140/epjb/e2009-00069-7

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

¹ Université Joseph Fourier, Laboratoire de Physique et Modélisation des Mileux Condensés, CNRS B.P. 166, 38042 Grenoble, France
² Department of Physics “E.R. Caianiello” and C.N.I.S.M., Università di Salerno, via S. Allende, 84081 Baronissi, Salerno, Italy
³ Université de Lyon, Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS UMR5672, 46 Allée d'Italie, 69364 Lyon Cedex 07, France

Corresponding author: ^a minguzzi@grenoble.cnrs.fr

Received: 1 August 2008
Revised: 15 December 2008
Published online: 3 March 2009

Abstract

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