Broad versus narrow Fano-Feshbach resonances in the BCS-BEC crossover with trapped Fermi atom

TL;DR

This paper compares broad and narrow Fano-Feshbach resonances in 6Li atoms, showing that broad resonances allow a simplified single-channel description of the BCS-BEC crossover across a wide magnetic field range, unlike narrow resonances.

Contribution

It demonstrates that broad Fano-Feshbach resonances enable an effective single-channel model for the BCS-BEC crossover, simplifying theoretical descriptions and experimental realizations.

Findings

Broad resonance maps to a single-channel contact interaction model.

Narrow resonance's effective model is limited to a narrow magnetic field range.

The broad resonance facilitates a comprehensive BCS-BEC crossover in trapped Fermi gases.

Abstract

With reference to the broad and narrow Fano-Feshbach resonances of 6Li at about 822 G and 543 G, we show that for the broad resonance a molecular coupled-channel calculation can be mapped with excellent accuracy onto an effective single-channel problem with a contact interaction. This occurs for a wide enough range of the magnetic field, that the full BCS-BEC crossover can be realized with a typical trap. For the narrow resonance, the mapping onto a single-channel problem and the realization of the BCS-BEC crossover are restricted to too narrow a range of the magnetic field to obtain them in practice. In this way, the BCS-BEC crossover for Fermi atoms with the broad resonance is placed on the same footing as the corresponding crossover for different physical systems.