Three-body problem for ultracold atoms in quasi-one-dimensional traps
- Institut fuer Theoretische Physik, Heinrich-Heine-Universitaet, D-40225 Duesseldorf (Germany)
- Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ (United Kingdom)
We study the three-body problem for both fermionic and bosonic cold-atom gases in a parabolic transverse trap of length scale a{sub perpendicular}. For this quasi-one-dimensional (quasi-1D) problem, there is a two-body bound state (dimer) for any sign of the 3D scattering length a and a confinement-induced scattering resonance. The fermionic three-body problem is universal and characterized by two atom-dimer scattering lengths a{sub ad} and b{sub ad}. In the tightly bound 'dimer limit' a{sub perpendicular}/a{yields}{infinity}, we find b{sub ad}=0 and a{sub ad} is linked to the 3D atom-dimer scattering length. In the weakly bound 'BCS limit' a{sub perpendicular}/a{yields}-{infinity}, a connection to the Bethe ansatz is established, which allows for exact results. The full crossover is obtained numerically. The bosonic three-body problem, however, is nonuniversal: a{sub ad} and b{sub ad} depend both on a{sub perpendicular}/a and on a parameter R* related to the sharpness of the resonance. Scattering solutions are qualitatively similar to fermionic ones. We predict the existence of a single confinement-induced three-body bound state (trimer) for bosons.
- OSTI ID:
- 20717758
- Journal Information:
- Physical Review. A, Vol. 71, Issue 5; Other Information: DOI: 10.1103/PhysRevA.71.052705; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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