Feshbach Molecules in a One-dimensional Optical Lattice

TL;DR

This paper develops a theoretical framework for Feshbach molecules in a one-dimensional optical lattice, deriving analytic results for scattering and bound states, and exploring Fano resonances and molecular survival probabilities.

Contribution

It introduces a two-channel theoretical model for Feshbach molecules in 1D lattices, providing analytic solutions and insights into resonance profiles and molecular dynamics.

Findings

Analytic expressions for scattering states and bound states.

Identification of Fano resonance profiles.

Analysis of molecular survival probability during magnetic field sweeps.

Abstract

We present the theory of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. Using a two-channel description of the resonance, we derive analytic results for the scattering states inside the continuum band and the discrete bound states outside the band. We identify a Fano resonance profile, and the survival probability of a molecule when swept through the Bloch band of scattering states by varying an applied magnetic field. We discuss how these results may be used to investigate the importance of the structured nature of the continuum in experiments.