Quantum Phases of Ultra Cold Bosons in Incommensurate 1D Optical Lattices

We study theoretically a BEC loaded into an optical lattice in the tight-binding regime, with a second, weak incommensurate lattice acting as a perturbation. We find, using direct diagonalization of small systems and a large scale, number conserving Gutzwiller-based mean field approach, the phase diagram of the model. We show that the superfluid, Mott-insulator and Bose-glass phases familiar from disordered systems appear here as well, with a localization transition occurring already in a 1D geometry, contrary to the well known Anderson localization. We complement these results with GPE simulations, and stress the fundamental difference between commensurate and incommensurate lattices. These results, together with calculations we have performed for realistic scenarios, suggest that this setup is well suited for available experimental realizations.