  We consider two-component one-dimensional quantum gases at special imbalanced
commensurabilities which lead to the formation of multimer (multi-particle
bound-states) as the dominant order parameter. Luttinger liquid theory supports
a mode-locking mechanism in which mass (or velocity) asymmetry is identified as
the key ingredient to stabilize such states. While the scenario is valid both
in the continuum and on a lattice, the effects of umklapp terms relevant for
densities commensurate with the lattice spacing are also mentioned. These ideas
are illustrated and confronted with the physics of the asymmetric
(mass-imbalanced) fermionic Hubbard model with attractive interactions and
densities such that a trimer phase can be stabilized. Phase diagrams are
computed using density-matrix renormalization group techniques, showing the
important role of the total density in achieving the novel phase. The effective
physics of the trimer gas is as well studied. Lastly, the effect of a parabolic
confinement and the emergence of a crystal phase of trimers are briefly
addressed. This model has connections with the physics of imbalanced
two-component fermionic gases and Bose-Fermi mixtures as the latter gives a
good phenomenological description of the numerics in the strong-coupling
regime.
