Two-channel Feshbach physics in a structured continuum

TL;DR

This paper investigates the scattering and bound states of atom pairs in a one-dimensional optical lattice near a Feshbach resonance, revealing structured continuum effects, Fano resonances, and universal behaviors of weakly bound dimers.

Contribution

It extends Feshbach physics to a structured continuum in a lattice, defining a lattice scattering length and analyzing bound states and resonances with numerical examples.

Findings

Bound dimer states exist both below and above the continuum bands.

Fano resonance profiles are observed inside the band due to Feshbach coupling.

The scattering length diverges at band edges, indicating Feshbach resonances.

Abstract

We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center of mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by RF- or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wavefunction of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.