Three-body bound states in a lattice

We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly-bound "trimer" state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly-bound trimers with energies below and above the continuum of scattering states of a single particle ("monomer") and a bound particle pair ("dimer"). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.