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arXiv:1202.2298 · Physical Review A

Analytical treatment of bosonic d -wave scattering in isotropic harmonic waveguides

Panagiotis Giannakeas, Vladimir S. Melezhik, Peter Schmelcher

Published Apr 3, 2012• 4 citations
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Abstract

We analyze $d$-wave resonances in atom-atom scattering in the presence of harmonic confinement by employing a higher-partial-wave pseudopotential. Analytical results for the scattering amplitude and transmission are obtained and compared to corresponding numerical ones, which employ the Lennard-Jones potential. Qualitative agreement is observed for weak confinement. For strong confinement the pseudopotential does not capture the $s$- and $d$-wave interference phenomena, yielding an asymmetric Fano profile for the transmission resonance.

DOI
10.1103/physreva.85.042703

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A semianalytical approach to atomic waveguide scattering for harmonic confinement is developed, taking into account all partial waves. As a consequence $\ensuremath{\ell}$-wave confinement-induced resonances are formed, being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the KKK-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.
We observe and analyze ddd-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the ddd-wave resonance emerges in the quasi-1D regime as an imprint of a 3D ddd-wave shape resonance. A scaling relation for the position of the ddd-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from sss-wave to ddd-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a possibility for studying strongly correlated atomic systems beyond sss-wave physics.
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