Feshbach resonant scattering of three fermions in one-dimensional wells

Abstract

We calculate the spectrum for three atoms in a one-dimensional harmonic well near an s-wave Feshbach resonance using a two-channel model to describe the Feshbach physics. This is relevant to the study of cold K-40 atoms trapped in a one-dimensional optical lattice. 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 nonuniform density.