Revealing the origin of super-Efimov states in the hyperspherical formalism

Abstract

Super-Efimov states are a new kind of universal three-body bound states predicted for three identical fermions with $p$-wave resonant interactions in two dimensions by a recent field-theoretic calculation [Phys.~Rev.~Lett.~\textbf{110}, 235301 (2013)]. The binding energies of these states obey a dramatic double exponential scaling $E_n=E_{\ast }\exp (-2e^{\pi n/s_0+\theta })$ with universal scaling $s_0=4/3$ and three-body parameters $E_{\ast }$ and $\theta$. We use the hyperspherical formalism and show that the super-Efimov states originate from an emergent effective potential $-1/4{\rho }^2-(s_0^2+1/4)/{\rho }^2{\ln }^2\left(\rho \right)$ at large hyperradius $\rho$. Moreover, for pairwise interparticle potentials with van der Waals tails, our numerical calculation indicates that the three-body parameters $E_{\ast }$ and $\theta$ are also universal and the ground super-Efimov state shall cross the threshold when the $2$D $p$-wave scattering area is about $-42.0l_{\text{vdW}}^2$ with $l_{\text{vdW}}$ the van der Waals length.

Published version, chosen as Editors' Suggestion, 6 pages, 5 figures

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Cited by in corpus (21)

• Efimov Physics: a review
• Universal few-body physics and cluster formation
• Observation of the Efimovian Expansion in Scale Invariant Fermi Gases
• Strongly Interacting p-wave Fermi Gas in Two-Dimensions: Universal Relations and Breathing Mode
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Quantitative analysis of $p$-wave three-body losses via cascade process
• Semisuper Efimov effect of two-dimensional bosons at a three-body resonance
• Sigature of the universal super Efimov Effect: three-body contact in two dimensional Fermi gases
• Stable p-wave resonant two-dimensional Fermi-Bose dimers
• Three-body forces and Efimov physics in nuclei and atoms
• Universality in a one-dimensional three-body system
• Dynamic Super Efimov Effect
• Observation of Dynamical Super Efimovian Expansion in a Unitary Fermi Gas
• Universal three-body bound states in mixed dimensions beyond the Efimov paradigm
• Oscillatory-like Expansion of a Fermionic Superfluid
• Scattering Hypervolume of Fermions in Two Dimensions
• Efimov Effect in Long-range Quantum Spin Chains
• Window for Efimov physics for few-body systems with finite-range interactions
• Universal Bound States in Long-range Spin Chains with an Impurity
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement
• Pseudopotentials for Two-dimentional Ultracold Scattering in the Presence of Synthetic Spin-orbit-coupling