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

Abstract

The Efimov effect was first predicted for three particles interacting at an $s$-wave resonance in three dimensions. Subsequent study showed that the same effect can be realized by considering two-body and three-body interactions in mixed dimensions. In this work, we consider the three-body problem of two bosonic $A$ 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 a space of dimension $d_B$, and there is an interspecies $s$-wave interaction in a $d_{\mathrm{int}}$-co-dimensional space accessible to both species. We find that when the $s$-wave interaction is tuned on resonance, there emerge an infinite series of universal three-body bound states for $\{d_A,d_B,d_{\mathrm{int}}\}=\{2,2,0\}$ and $\{2,3,1\}$. Going beyond the Efimov paradigm, the binding energies of these states follow the scaling $\ln |E_n|\sim -s(n\pi -\theta {)}^2/4$ with the scaling factor $s$ being unity for the former case and $\sqrt{m_B(2m_A+m_B)}/(m_A+m_B)$ for the latter. We discuss how our mixed dimensional systems can be realized in current cold atom experiment and how the effects of these universal three-body bound states can be detected.

5 pages, 2 figures, 2 tables

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Cited by in corpus (9)

• D-dimensional three-body bound-state problem with zero range interactions
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Universal relations for spin-orbit coupled Fermi gas near an s-wave resonance
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Efimov Effect in Long-range Quantum Spin Chains
• Universal Bound States in Long-range Spin Chains with an Impurity
• Universal Relations in Long-range Quantum Spin Chains