Superfluid - Insulator transition for bosons in disordered and quasi-periodic potentials

On the theory side, one dimensional bosons in random [1] and quasiperiodic potentials [2] have been shown to undergo superfluid to insulator phase transitions, upon variation of the strength of the disorder or of the interactions. We discuss here such a transition in connection with the experiments in a system of $^39$K atoms for which both the disorder (quasiperiodic potential) and the interactions can be experimentally varied in a controlled way [3]. We analyze three probes of the nature of the system, namely a measurement of the coherence, the transport and the excitation spectrum obtained by shaking of the lattice. The combination of these measurements shows evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluid-like regime, in general agreement with the theory. [1] T. Giamarchi and H. J. Schulz, Phys. Rev B {\bf 37} 325 (1988). [2] G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollw\"ock and T. Giamarchi, Phys. Rev. A {\bf 78} 023628 (2008). [3] Chiara D'Errico, Eleonora Lucioni, Luca Tanzi, Lorenzo Gori, Guillaume Roux, Ian P. McCulloch, Thierry Giamarchi, Massimo Inguscio and Giovanni Modugno Phys. Rev. Lett. {\bf 113}, 095301 (2014).