The unitary three-body problem in a trap

TL;DR

This paper analytically and numerically investigates the energy spectrum and eigenstates of three identical particles (bosons or fermions) in a harmonic trap at infinite scattering length, revealing universal and Efimovian states with implications for stability.

Contribution

It provides an exact analytical solution for the three-body problem in a trap at unitarity and explores the coupling and stability of universal and Efimovian states for bosons and fermions.

Findings

All fermionic states are universal.

Bosonic states include both universal and Efimovian states.

Universal bosonic states are long-lived with minimal three-body loss.

Abstract

We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.