Resonant scattering of ultracold atoms in low dimensions
Résumé
Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic wave guides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the resonances which cannot be set arbitrarily to zero is shown to have important implications for the confinement induced resonances. For spin polarized fermions in a linear wave guide in the limit of infinitely strong odd-wave scattering length it imposes a strong constraint for achieving the Fermi Tonks Girardeau gas. For a planar wave guide, the $p$- and $d$-wave scattering resonances are analyzed in terms of the appearance of a low energy quasi-bound state.
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