Observable Efimov resonances in light-light-heavy systems

Three-body loss resonances associated with heavy-heavy-light Efimov states have been observed for over a decade in ultracold mixtures tuned near interspecies Feshbach resonances. For light-light-heavy systems, observing such resonances has been far more challenging due to the substantially large Efimov spacing. In these Efimov-unfavored systems, the intraspecies scattering length ${a}_{\text{BB}}$ has been shown to significantly affect the overall Efimov scenario, namely, the positions of the Efimov resonances ${a}_{\ensuremath{-}}^{(n)}$ and the three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(0)}$. The present article explains the origin behind this influence by highlighting two primary mechanisms via which both the magnitude and sign of ${a}_{\text{BB}}$ govern the Efimov spectrum and set the resulting 3BP ${a}_{\ensuremath{-}}^{(0)}$. By employing van der Waals interactions for ${^{23}\mathrm{Na}}_{2}^{40}\mathrm{K}$, we attribute the vital role of ${a}_{\text{BB}}$ in Efimov-unfavored systems to the large difference between the Efimov scaling parameters for two and three resonant interactions, ${s}_{0}$ and ${s}_{0}^{*}$. In particular, we account for the unusually large ${a}_{\ensuremath{-}}^{(0)}$ obtained in light-light-heavy systems with ${a}_{\text{BB}}>0$ (e.g., ${^{41}\mathrm{K}}_{2}^{87}\mathrm{Rb}$), and show that the first Efimov resonance can still occur at an experimentally accessible value when ${a}_{\text{BB}}<0$.