Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length

TL;DR

This paper investigates how background scattering influences Efimov states near a Feshbach resonance, revealing shifts in universality regimes and the limited impact of short-range three-body forces, aligning with experimental observations.

Contribution

It introduces a model accounting for finite interaction range and background scattering, elucidating their effects on Efimov spectra and universality limits near Feshbach resonances.

Findings

Background scattering significantly alters Efimov spectra.

Van der Waals universality shifts with background scattering sign and strength.

Short-range three-body forces have minimal impact on universality.

Abstract

We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}$K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $-8$ and $-10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.