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We investigate the strong-coupling limit of a three-component Fermi mixturein an optical lattice with attractive interactions. In this limit bound states(trions) of the three components are formed. We derive an effective Hamiltonianfor these composite fermions and show that it is asymptotically equivalent toan antiferromagnetic Ising model. By using Monte-Carlo simulations, weinvestigate the spatial arrangement of the trions and the formation of atrionic density wave (CDW), both in a homogeneous lattice and in the presenceof an additional harmonic confinement. Depending on the strength of theconfinement and on the temperature, we found several scenarios for the trionicdistribution, including coexistence of disordered trions with CDW and bandinsulator phases. Our results show that, due to a proximity effect, staggereddensity modulations are induced in regions of the trap where they would nototherwise be present according to the local density approximation.

Monte Carlo study of fermionic trions in a square lattice with harmonic confinement