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

TL;DR

This paper develops simple analytic models of the S-matrix for ultra-cold atomic collisions at negative energies, enabling the study of confinement-induced resonances that are difficult to analyze with direct numerical methods.

Contribution

The authors introduce analytic S-matrix models for negative-energy scattering, incorporating resonances and background effects, applicable to multi-channel cold atom collision scenarios.

Findings

Models successfully describe negative-energy scattering phenomena.

Extended analysis to multichannel cases with Feshbach resonances.

Facilitates study of confinement-induced resonances in cold atoms.

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.