Three-body problem for ultracold atoms in quasi-one-dimensional traps

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dc.creatorMora, C.
dc.creatorEgger, R.
dc.creatorGogolin, A. O.
dc.date2004-12-09
dc.date2005-03-15
dc.date.accessioned2026-07-07T06:26:14Z
dc.date.available2026-07-07T06:26:14Z
dc.descriptionWe 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.
dc.description20 pages, 6 figures, accepted for publication in PRA, appendix on the derivation of an integral formula for the Hurvitz zeta function
dc.identifierhttps://arxiv.org/abs/cond-mat/0412225
dc.identifierhttp://arxiv.org/abs/cond-mat/0412225
dc.identifierPhys. Rev. A 71, 052705 (2005)
dc.identifierdoi:10.1103/PhysRevA.71.052705
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97051
dc.subjectStatistical Mechanics
dc.subjectMesoscale and Nanoscale Physics
dc.subjectAtomic Physics
dc.subjectQuantum Physics
dc.titleThree-body problem for ultracold atoms in quasi-one-dimensional traps
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