We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic energy density profiles we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill-out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.

The random-dimer model is probably the most popular model for a one-dimensional disordered system where correlations are responsible for delocalization of the wave functions. This is the primary model used to justify the insulator-metal transition in conducting polymers and in DNA. However, for such systems, the localization-delocalization regimes have only been observed by deeply modifying the system itself, including the correlation function of the disordered potential. In this article, we propose to use an ultracold atomic mixture to cross the transition simply by externally tuning the interspecies interactions, and without modifying the impurity correlations.PACS numbers: 64.60. Cn,67.60.Bc In a one-dimensional disordered system, Anderson localization is known to occur at any energy when the disorder is δ correlated [1,2]. Nevertheless, if one introduces particular short-range correlations, delocalization of a significant subset of the eigenstates can appear. This happens in the random-dimer model (RDM) [3], in which the sites of a lattice are assigned energies ǫ a or ǫ b at random, with the additional constraint that sites of energy ǫ b always appear in pairs, or dimers. The same occurs in its dual counterpart (DRDM) [3], in which lattice sites with energy ǫ b never appear as neighbors. In these models, extended states arise from resonant modes of the (dual)dimers which present vanishing backscattering at energy E res . In the thermodynamic limit, the ratio √ N /N between the number of delocalized states and the total number of states vanishes, and there is no mobility edge separating extended and localized energy eigenstates. Nevertheless in finite size systems, thus in real systems, a localization-delocalization transition can be induced by driving E res inside the spectrum.This model was proposed to be the possible mechanism which leads to the insulator-metal transition in a wide class of conducting polymers such as polyaniline and heavily doped polyacetylene (see, for instance, [4]) and in some biopolymers such as DNA [5,6]. The evidence of delocalized electronic states was experimentally demonstrated in a random-dimer GaAs-AlGaAs superlattice [7], while for photons, a RDM dielectric system was used [8]. Recently, a RDM setup has been proposed to demonstrate the delocalization of acoustic waves [9]. For polymers, semiconductor lattices, photonic crystals and elastic chains, the dimer resonant energies cannot be modified without changing the sample itself. Thus the localization-delocalization transition for a (D)RDM chain as a function of the relative position of the resonant modes with respect to the band modes cannot easily be studied using these physical systems.In this article, we propose an experimental procedure to realize a DRDM experiment with a one-dimensional (1D) two-component ultracold atomic mixture in an optical lattice, and we demonstrate that the localizationdelocalization transition can be explored by tuning the interparticle interactions.To introduce disorder, a component (B d ) has ...

We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-onedimensional lattice and to attractive interactions from fermionic atoms that are localized in various configurations inside the lattice wells. The system is treated within a Bose-Hubbard tight binding model by an out-of-equilibrium Green's function approach.A new band gap opens up when the lattice period is doubled by locating the fermions in alternate wells and yields an interference pattern in the transmittivity on varying the intensity of the driving force. The positions of the transmittivity minima are determined by matching the period of Bloch oscillations and the time for tunnelling across the band gap. Massive disorder in the distribution of the fermions will wash out the interference pattern, but the same period doubling of the lattice can be experimentally realized in a four-beam set-up. We report illustrative numerical results for a mixture of 87 Rb and 40 K atoms in an optical lattice created by laser beams with a wavelength of 763 nm.