Fermionic trimers in spin-dependent optical lattices

We investigate the formation of three-body bound states (trimers) in two-component Fermi gases confined in one dimensional optical lattice with spin-dependent tunneling rates. The binding energy and the effective mass of the trimer are obtained from the solution of the Mattis integral equation generalized to the case of unequal Bloch masses. We show that this equation admits multiple solutions corresponding to excited bound states, which are only stable for large mass asymmetry.