Effective Potential for Ultracold Atoms at the Zero-Crossing of a Feshbach Resonance

TL;DR

This paper introduces an effective potential to accurately describe ultracold atoms near a zero-crossing Feshbach resonance, accounting for finite-range effects where traditional methods fail, with implications for Bose-Einstein condensates and Fermi gases.

Contribution

The authors develop a new effective potential that captures finite-range effects at zero-crossing of Feshbach resonances, improving upon the traditional effective-range expansion.

Findings

Higher-order effects are negligible for broad resonances.

Signatures of the effective potential may be observable in narrow resonances.

Potential relevance for microstructured traps at the atom-solid interface.

Abstract

We consider finite-range effects when the scattering length goes to zero near a magnetically controlled Feshbach resonance. The traditional effective-range expansion is badly behaved at this point and we therefore introduce an effective potential that reproduces the full T-matrix. To lowest order the effective potential goes as momentum squared times a factor that is well-defined as the scattering length goes to zero. The potential turns out to be proportional to the background scattering length squared times the background effective range for the resonance. We proceed to estimate the applicability and relative importance of this potential for Bose-Einstein condensates and for two-component Fermi gases where the attractive nature of the effective potential can lead to collapse above a critical particle number or induce instability toward pairing and superfluidity. For broad Feshbach resonances the higher-order effect is completely negligible. However, for narrow resonances in tightly confined samples signatures might be experimentally accessible. This could be relevant for sub-optical wavelength microstructured traps at the interface of cold atoms and solid-state surfaces.