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Optimized sympathetic cooling of atomic mixtures via fast adiabatic strategies

We discuss fast frictionless cooling techniques in the framework of sympathetic cooling of cold atomic mixtures. It is argued that optimal cooling of an atomic species - in which the deepest quantum degeneracy regime is achieved - may be obtained by means of sympathetic cooling with another species whose trapping frequency is dynamically changed to maintain constancy of the Lewis-Riesenfeld adiabatic invariant. Advantages and limitations of this cooling strategy are discussed, with particular regard to the possibility of cooling Fermi gases to a deeper degenerate regime.