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