Observable Resonances in Efimov-unfavored 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 $a_{-}^{(n)}$ and the three-body parameter (3BP) $a_{-}^{(0)}$. 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 $a_{-}^{(0)}$. By employing van der Waals interactions for $^{23}$Na$_2{}^{40}$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 $a_{-}^{(0)}$ obtained in light-light-heavy systems with $a_\text{BB}>0$ (e.g., $^{41}$K$_2{}^{87}$Rb), and show that the first Efimov resonance can still occur at an experimentally accessible value when $a_\text{BB}<0$.