{
  "id": "cond-mat/0412225",
  "version": "v2",
  "published": "2004-12-09T11:06:34.000Z",
  "updated": "2005-03-15T09:13:53.000Z",
  "title": "Three-body problem for ultracold atoms in quasi-one-dimensional traps",
  "authors": [
    "C. Mora",
    "R. Egger",
    "A. O. Gogolin"
  ],
  "comment": "20 pages, 6 figures, accepted for publication in PRA, appendix on the derivation of an integral formula for the Hurvitz zeta function",
  "journal": "Phys. Rev. A 71, 052705 (2005)",
  "doi": "10.1103/PhysRevA.71.052705",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.mes-hall",
    "physics.atom-ph",
    "quant-ph"
  ],
  "abstract": "We study the three-body problem for both fermionic and bosonic cold atom gases in a parabolic transverse trap of lengthscale $a_\\perp$. For this quasi-one-dimensional (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, $a_{ad}$ and $b_{ad}$. In the tightly bound `dimer limit', $a_\\perp/a\\to\\infty$, we find $b_{ad}=0$, and $a_{ad}$ is linked to the 3D atom-dimer scattering length. In the weakly bound `BCS limit', $a_\\perp/a\\to-\\infty$, 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 non-universal: $a_{ad}$ and $b_{ad}$ depend both on $a_\\perp/a$ 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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-15T09:13:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ultracold atoms",
      "quasi-one-dimensional traps",
      "atom-dimer scattering length",
      "single confinement-induced three-body bound state",
      "bosonic cold atom gases"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}