Atom-dimer scattering for confined ultracold fermion gases

Abstract

We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_{\perp }$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_{\perp }/a\approx 1.46$, and a dimer state for arbitrary $a_{\perp }/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_{\perp }/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_{\perp }/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. There is no trimer state, and despite $a_{ad}=0$ at $a_{\perp }/a\approx 2.6$, there is no resonance enhancement of the interaction.

5 pages, 2 figures; to appear in PRL (revised version)

References in corpus (3)

• Observation of Bose-Einstein Condensation of Molecules
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• An exactly solvable model of the BCS-BEC crossover

Cited by in corpus (5)

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• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Charge and spin dynamics of interacting Fermions in a one dimensional harmonic trap
• Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas
• Nanoscale atomic waveguides with suspended carbon nanotubes