The transmittivity of a Bose–Einstein condensate on a lattice: interference from period doubling and the effect of disorder

Abstract

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.

Ultracold bosons in lattices with binary disorder

“…In addition to that, the atomic interaction energies can be made random [11], if the lattice loaded by cold atoms is placed near a wire inducing a spatially random magnetic field [12]. Disorder with discrete probability distribution can be created introducing a second atomic species strongly localized on random sites [13,14,15] which leads only to random shifts of the onsite energies. With the aid of incommensurate lattices one can make the tunneling amplitudes and the on-site energies quasirandom [16,17,18].…”

Localization-delocalization transition in the random dimer model

“…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 to be classically trapped in the minima of the potential [10][11][12]. For this purpose, one can choose a spin-polarized Fermi component or a strongly repulsive hardcore Bose gas.…”

“…To introduce disorder, a component (B d ) has to be classically trapped in the minima of the potential [10][11][12]. For this purpose, one can choose a spin-polarized Fermi component or a strongly repulsive hardcore Bose gas.…”

Anderson localization in optical lattices with speckle disorder

“…. n s − 1) [17,23]. The Green's function of the effective Hamiltonian (6),G(E) = (E −H) −1 , coincides with G(E) in the subspace {1, n s } by construction.…”