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arXiv · 0712.2070

Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

S. G. Bhongale·S. J. J. M. F. Kokkelmans·Ivan H. Deutsch
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Abstract

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of $^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schr\"{o}dinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.

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S. G. Bhongale, S. J. J. M. F. Kokkelmans, Ivan H. Deutsch. 2007-12-13. Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances. https://doi.org/10.1103/physreva.77.052702

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