Orbital Feshbach Resonance with Small Energy Gap between Open and Closed Channels

TL;DR

This paper investigates orbital Feshbach resonances in ultracold alkali-earth-like atoms with small energy gaps between open and closed channels, showing how they can be induced and accurately modeled using two-channel pseudopotentials.

Contribution

It demonstrates that OFRs can be induced by coupling to bound or scattering states of the closed channel in systems with small threshold gaps, and validates the use of two-channel Huang-Yang pseudopotentials for low-energy scattering calculations.

Findings

OFR can be induced by coupling to CC bound or scattering states.

Two-channel Huang-Yang pseudopotential is applicable for low-energy scattering.

Scattering states of the CC should be included in theoretical models.

Abstract

Recently a new type of Feshbach resonance, i.e., orbital Feshbach resonance (OFR) was proposed for the ultracold alkali-earth (like) atoms, and experimentally observed in the ultracold gases of $^{{\rm 173}}$Yb atoms. Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when the OFR of $^{{\rm 173}}$Yb atoms appears, the energy gap between the thresholds of the open channel (OC) and the closed channel (CC) is much smaller than the characteristic energy of the inter-atomic interaction, i.e., the van der Waals energy. In this paper we study the OFR in the systems with small CC-OC threshold gap. We show that in these systems the OFR can be induced by the coupling between the OC and either an isolated bound state of the CC or the scattering states of the CC. Moreover, we also show that in each case the two-channel Huang-Yang pesudopoential is always applicable for the approximate calculation of the low-energy scattering amplitude. Our results imply that in the theoretical calculations for these systems it is appropriate to take into account the contributions from the scattering states of the CC.