Exotic few-body bound states in a lattice

TL;DR

This paper explores exotic bound states of few bosonic atoms in a one-dimensional optical lattice, revealing novel trimer configurations and their binding mechanisms within the Hubbard model framework.

Contribution

It provides a complete characterization of two- and three-body bound and scattering states, including new weakly-bound trimer states and their binding mechanisms.

Findings

Existence of invariant dimer states for attractive and repulsive interactions.

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

Binding mechanisms involving effective particle exchange interactions.

Abstract

Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle -- "monomer" -- we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.