Three-fermion problems in optical lattices

TL;DR

This paper provides exact solutions for three-fermion systems in optical lattice wells, revealing Borromean and three-body bound states near Feshbach resonances, with implications for cold atom experiments.

Contribution

It offers the first exact spectral analysis of three-fermion atoms in optical lattice wells, including the identification of Borromean states and three-body bound states near Feshbach resonances.

Findings

Discovery of Borromean states in Li6 atoms.

Identification of three-body bound states in K40 atoms.

Sensitivity analysis of results to atomic details.

Abstract

We present exact results for the spectra of three fermionic atoms in a single well of an optical lattice. For the three lowest hyperfine states of Li6 atoms, we find a Borromean state across the region of the distinct pairwise Feshbach resonances. For K40 atoms, nearby Feshbach resonances are known for two of the pairs, and a bound three-body state develops towards the positive scattering-length side. In addition, we study the sensitivity of our results to atomic details. The predicted few-body phenomena can be realized in optical lattices in the limit of low tunneling.