Genetic fitting techniques for precision ultracold spectroscopy

TL;DR

This paper introduces a genetic algorithm-based method for fitting potential energy curves of diatomic molecules directly to experimental data without assuming a specific functional form, achieving high accuracy.

Contribution

It presents a novel, general fitting technique using genetic algorithms that improves potential energy curve fitting accuracy over traditional methods.

Findings

Achieves better than 1% uncertainty in potential fitting

Successfully compares with state-of-the-art fitting techniques

Applicable to various diatomic molecules and potentials

Abstract

We present development of a genetic algorithm for fitting potential energy curves of diatomic molecules to experimental data. Our approach does not involve any functional form for fitting, which makes it a general fitting procedure. In particular, it takes in a guess potential, perhaps from an $ab \ initio$ calculation, along with experimental measurements of vibrational binding energies, rotational constants, and their experimental uncertainties. The fitting procedure is able to modify the guess potential until it converges to better than 1% uncertainty, as measured by $\bar{\chi}^2$. We present the details of this technique along with a comparison of potentials calculated by our genetic algorithm and the state of the art fitting techniques based on inverted perturbation approach for the $X \ ^1\Sigma^+$ and $C \ ^1\Sigma^+$ potentials of lithium-rubidium.