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Résumé |
One-dimensional systems allow for a detailed study of the competing
effects of disorder 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
interactions 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 potential. Superfluid 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
localized or superfluid 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); F. Crépin et al.,arxiv:1111:2706 |
