Unitary quantum three-body problem in a harmonic trap

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 sta...

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Bibliographic Details
Published in:Physical review letters 2006-10, Vol.97 (15), p.150401-150401, Article 150401
Main Authors: Werner, Félix, Castin, Yvan
Format: Article
Language:English
Subjects:
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EIGENFUNCTIONS
FERMIONS
HARMONIC POTENTIAL
INTERACTION RANGE
SCATTERING LENGTHS
SPIN
THREE-BODY PROBLEM
TRAPPING
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.97.150401