Three-body bound states in a lattice

TL;DR

This paper investigates three-body bound states in a one-dimensional Bose-Hubbard lattice, revealing new weakly-bound trimers with energies outside the scattering continuum, explained by an effective exchange interaction, and highlighting their potential observation in cold atom experiments.

Contribution

The study uncovers two novel types of weakly-bound three-body states in a lattice, extending understanding beyond the simple trimer, with a detailed analysis of their binding mechanisms.

Findings

Identification of weakly-bound trimers with energies outside the scattering continuum.

Derivation of an effective Hamiltonian showing exchange interactions responsible for binding.

Universal binding energy value in the strong-coupling limit.

Abstract

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.