The unitary three-body problem in a trap

Felix Werner (1) , Yvan Castin (1)

1 LKB (Lhomond) - Laboratoire Kastler Brossel

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.

Mots clés: unitary quantum gas; zero-range potential; three-body problem; harmonic trap

Domaines: Autre [cond-mat.other]

Felix Werner, Yvan Castin. The unitary three-body problem in a trap. Physical Review Letters, 2006, 97, pp.150401. ⟨hal-00007574v3⟩