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One-dimensional systems allow for a detailed study of the competing eects of disor- der and interactions on the localization of a Fermi or Bose gas.[1] While non-interacting fermions are always localized in a random potential, a transition to a superconducting phase occurs for strong enough attractive interactions. Similarly, strong repulsive in- teractions will trigger the localization of a Bose gas.[1,2] During this talk, I will present the study of an interacting mixture of bosons and spinless fermions in a random po- tential. Super uid correlations are enhanced by interspecies interactions, while the disordered potential tries to pin each component of the gas. Using renormalization group methods, supplemented by a variational calculation, we have found several lo- calized or super uid phases, including a new insulating phase, similar to the Bose glass, in which both species are coupled and localized.[3] We also computed the dynamical structure factor for typical parameters of various ultra-cold atoms experiments. Each phase exhibits its own signature, that could be probed in Bragg scattering experiments. [1] T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988) [2] M. P. A. Fisher et al., Phys. Rev. B 40, 546 (1989) [3] F. Crépin, G. Zaránd, P. Simon, Phys. Rev. Lett. 105, 115301 (2010)

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François Crépin, Laboratoire de Physique des Solides, Université Paris Sud
Seminar room of the Institute of Theoretical Physics
Contact: not specified