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Atom-dimer scattering for confined ultracold fermion gases

C. Mora·R. Egger·A. O. Gogolin·A. Komnik
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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.

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C. Mora, R. Egger, A. O. Gogolin, A. Komnik. 2004-09-17. Atom-dimer scattering for confined ultracold fermion gases. https://doi.org/10.1103/physrevlett.93.170403

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