Trion and Dimer Formation of Three-Color Fermions

We study the problem of three ultracold fermions in different hyperfine states loaded into a lattice with spatial dimension D=1,2. We consider SU(3)-symmetric attractive interactions and also eventually include a three-body constraint, which mimics the effect of three-body losses in the strong-loss regime. We combine exact diagonalization with the Lanczos algorithm, and evaluate both the eigenvalues and the eigenstates of the problem. In D=1, we find that the ground state is always a three-body bound state (trion) for arbitrarily small interaction, while in D=2, due to the stronger influence of finite-size effects, we are not able to provide conclusive evidence of the existence of a finite threshold for trion formation. Our data are however compatible with a threshold value which vanishes logarithmically with the size of the system. Moreover we are able to identify the presence of a fine structure inside the spectrum, which is associated with off-site trionic states. The characterization of these states shows that only the long-distance behavior of the eigenstate wavefunctions provides clear-cut signatures about the nature of bound states and that onsite observables are not enough to discriminate between them. The inclusion of a three-body constraint due to losses promotes these off-site trions to the role of lowest energy states, at least in the strong-coupling regime.