Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances

TL;DR

This paper introduces an analytic model that derives atomic scattering lengths from molecular binding energy measurements near Feshbach resonances, applicable to various resonance types, and demonstrates its accuracy with Cs$_2$ molecules.

Contribution

The paper presents a new analytic approach considering finite-range potentials to determine scattering lengths from binding energies near overlapping Feshbach resonances.

Findings

Accurately determined Cs atomic scattering length.

Measured positions and widths of specific Feshbach resonances.

Validated the model with experimental data on Cs$_2$ molecules.

Abstract

We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on Cs$_2$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectroscopy in a range where one broad and two narrow Feshbach resonances overlap. From the data we accurately determine the Cs atomic scattering length and the positions and widths of two particular resonances.