Feshbach resonant scattering of three fermions in one-dimensional wells

TL;DR

This paper investigates three-fermion interactions near a Feshbach resonance in a one-dimensional optical lattice, revealing differences between models and potential quantum phase transitions.

Contribution

It provides a detailed analysis of three-fermion spectra near Feshbach resonance using a two-channel model, highlighting model differences and phase transition possibilities.

Findings

Differences between one- and two-channel models near resonance.

Identification of level crossings indicating possible quantum phase transitions.

Discussion on the stability of non-uniform density phases.

Abstract

We study the weak-tunnelling limit for a system of cold 40K atoms trapped in a one-dimensional optical lattice close to an s-wave Feshbach resonance. We calculate the local spectrum for three atoms at one site of the lattice within a two-channel model. Our results indicate that, for this one-dimensional system, one- and two-channel models will differ close to the Feshbach resonance, although the two theories would converge in the limit of strong Feshbach coupling. We also find level crossings in the low-energy spectrum of a single well with three atoms that may lead to quantum phase transition for an optical lattice of many wells. We discuss the stability of the system to a phase with non-uniform density.