Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp

TL;DR

This paper develops a theoretical model based on coupled atom-molecule Boltzmann equations to predict features of Feshbach molecule formation in a dilute gas during magnetic field ramps, aligning well with experimental data.

Contribution

It introduces a simplified, predictive model for molecule formation dynamics that accounts for density, temperature, and phase space effects without adjustable parameters.

Findings

Effective adiabatic rate constant scales with density

Molecular fraction vs. magnetic field resembles an error function

Molecular production efficiency depends universally on initial phase space density

Abstract

Starting with coupled atom-molecule Boltzmann equations, we develop a simplified model to understand molecule formation observed in recent experiments. Our theory predicts several key features: (1) the effective adiabatic rate constant is proportional to density; (2) in an adiabatic ramp, the dependence of molecular fraction on magnetic field resembles an error function whose width and centroid are related to the temperature; (3) the molecular production efficiency is a universal function of the initial phase space density, the specific form of which we derive for a classical gas. Our predictions show qualitative agreement with the data from [Hodby et al, Phys. Rev. Lett. {\bf{94}}, 120402 (2005)] without the use of adjustable parameters.