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

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 $R^{\ast }$ 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.

20 pages, 6 figures, accepted for publication in PRA, appendix on the derivation of an integral formula for the Hurvitz zeta function

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• Observation of Bose-Einstein Condensation of Molecules
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Three-boson problem near a narrow Feshbach resonance
• An exactly solvable model of the BCS-BEC crossover
• Atom-dimer scattering for confined ultracold fermion gases

Cited by in corpus (13)

• Analytical solution of the bosonic three-body problem
• Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
• Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides
• Universal low-energy properties of three two-dimensional particles
• Confinement-induced resonance in quasi-one-dimensional systems under transversely anisotropic confinement
• Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas
• Universality of excited three-body bound states in one dimension
• Controlling integrability in a quasi-1D atom-dimer mixture
• Ultracold-atom collisions in atomic waveguides : A two-channel analysis
• Three-body bound states of two bosons and one impurity in one dimension
• Three-body bound states in a harmonic waveguide with cylindrical symmetry
• Effects of nonintegrability on stabilization of Feshbach molecules in atom waveguides
• Faddeev equations in one-dimensional problems with resonant interactions