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We consider two-component one-dimensional quantum gases at special imbalancedcommensurabilities which lead to the formation of multimer (multi-particlebound-states) as the dominant order parameter. Luttinger liquid theory supportsa mode-locking mechanism in which mass (or velocity) asymmetry is identified asthe key ingredient to stabilize such states. While the scenario is valid bothin the continuum and on a lattice, the effects of umklapp terms relevant fordensities commensurate with the lattice spacing are also mentioned. These ideasare illustrated and confronted with the physics of the asymmetric(mass-imbalanced) fermionic Hubbard model with attractive interactions anddensities such that a trimer phase can be stabilized. Phase diagrams arecomputed using density-matrix renormalization group techniques, showing theimportant role of the total density in achieving the novel phase. The effectivephysics of the trimer gas is as well studied. Lastly, the effect of a parabolicconfinement and the emergence of a crystal phase of trimers are brieflyaddressed. This model has connections with the physics of imbalancedtwo-component fermionic gases and Bose-Fermi mixtures as the latter gives agood phenomenological description of the numerics in the strong-couplingregime.

Multimer formation in 1D two-component gases and trimer phase in the asymmetric attractive Hubbard model