Efimov states embedded in the three-body continuum

We present analytical solutions for the three-body problem with multichannel interactions and identify a class of quasibound Efimov states that can be viewed as three-body Fano-Feshbach resonances. Our method employs a multichannel generalization of the Fermi pseudopotential to model low-energy atom-atom interactions near a magnetically tunable Fano-Feshbach resonance. We discuss the conditions under which quasibound Efimov states may be supported and identify the interaction parameters that limit the lifetimes of these states. We speculate that it may be possible to observe these states using spectroscopic methods, perhaps allowing for the measurement of multiple Efimov resonances.

Figure 1

(Color online) A schematic representation of our two-body model is shown. As the range $r_0$ is taken to zero, the potential is regularized by the derivative in Eq. (1)

Figure 2

(Color online) In (a), we show approximately the lowest 300 potential curves up to $3.5ϵ$, while (b) shows an enlarged view of the region near the $E=ϵ$ threshold and the attractive $R^{-2}$ diabatic Efimov potential. Note also the series of avoided crossings in (a) near $E=0.6ϵ$ indicating the presence of a two-body quasibound state. In (c) we show the eigenvalue near $E=ϵ$ converging to the universal value for two identical bosons and one distinguishable particle ${\lambda }^2\to -0.171145=-s_0^2$ indicated by the dashed red line.