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The Efimov effect was first predicted for three particles interacting at an$s$-wave resonance in three dimensions. Subsequent study showed that the sameeffect can be realized by considering two-body and three-body interactions inmixed dimensions. In this work, we consider the three-body problem of twobosonic $A$ atoms interacting with another single $B$ atom in mixed dimensions:The $A$ atoms are confined in a space of dimension $d_A$ and the $B$ atom in aspace of dimension $d_B$, and there is an interspecies $s$-wave interaction ina $d_{\rm int}$-co-dimensional space accessible to both species. We find thatwhen the $s$-wave interaction is tuned on resonance, there emerge an infiniteseries of universal three-body bound states for $\{d_A,d_B,d_{\rmint}\}=\{2,2,0\}$ and $\{2,3,1\}$. Going beyond the Efimov paradigm, thebinding energies of these states follow the scaling$\ln|E_n|\sim-s(n\pi-\theta)^2/4$ with the scaling factor $s$ being unity forthe former case and $\sqrt{m_B(2m_A+m_B)}/(m_A+m_B)$ for the latter. We discusshow our mixed dimensional systems can be realized in current cold atomexperiment and how the effects of these universal three-body bound states canbe detected.

Universal three-body bound states in mixed dimensions beyond the Efimov paradigm