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We numerically determine the very rich phase diagram of mass-imbalancedbinary mixtures of hardcore bosons (or equivalently -- fermions, orhardcore-Bose/Fermi mixtures) loaded in one-dimensional optical lattices.Focusing on commensurate fillings away from half filling, we find a strongasymmetry between attractive and repulsive interactions. Attraction is found toalways lead to pairing, associated with a spin gap, and to pair crystallizationfor very strong mass imbalance. In the repulsive case the two atomic componentsremain instead fully gapless over a large parameter range; only a very strongmass imbalance leads to the opening of a spin gap. The spin-gap phase is theprecursor of a crystalline phase occurring for an even stronger mass imbalance.The fundamental asymmetry of the phase diagram is at odds with recenttheoretical predictions, and can be tested directly via time-of-flightexperiments on trapped cold atoms.

Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices