Resonant Scattering of Ultracold Atoms in Low Dimensions

Abstract

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 resonance which was neglected in previous works is shown to have important implications in the properties of the confinement induced resonances. For spin polarized fermions in quasi-1D wave guides it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar wave guide, the charateristics of the 2D induced scattering resonances in $p$- and d-wave are determined as a function of the 3D scattering parameters and of the wave guide frequency.

References in corpus (5)

• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Two-dimensional Bose-Einstein condensate in an optical surface trap
• Three fully polarized fermions close to a p-wave Feshbach resonance
• Modeling interactions for resonant p-wave scattering
• Three fermions in a box at the unitary limit: universality in a lattice model

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• Stretching p-wave molecules by transverse confinements
• Quantitative analysis of $p$-wave three-body losses via cascade process
• Two-body state with p-wave interaction in one-dimensional waveguides under transversely anisotropic confinement
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Optical spin transport theory of spin-1/2 topological Fermi superfluids
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• General features and contact modeling of $N$-body isolated resonances near threshold
• Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
• Confinement-Induced Resonances in Rabi-Coupled Bosonic Mixtures
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement
• Elastic collision rates of spin-polarized fermions in two dimensions