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We study transport of fermions in a system composed of a short opticallattice connecting two finite atomic reservoirs at different filling levels.The average equilibration current through the optical lattice, for stronglattice-reservoir coupling and finite temperatures, is calculated within theLandauer formalism using a nonequilibrium Green's functions approach. Wemoreover determine quantum and thermal fluctuations in the transport and findsignificant shot-to-shot deviations from the average equilibration current. Weshow how to control the atomic current by engineering specific optical latticepotentials without requiring site-by-site manipulations and suggest therealization of a single level model. Based on this model we discuss theblocking effect on the atomic current resulting from weak interactions betweenthe fermions.

Mesoscopic transport of fermions through an engineered optical lattice connecting two reservoirs