Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides

TL;DR

This paper introduces a grid method for multi-channel atomic scattering in waveguides, analyzing resonances and confinement effects across various regimes, with implications for cold atom experiments and quantum wire technologies.

Contribution

The paper extends analytical results for multi-channel scattering in waveguides, providing a comprehensive numerical approach and identifying new Feshbach and dual confinement-induced resonances.

Findings

Reproduces known CIRs in zero-energy, single-mode regime.

Identifies series of Feshbach resonances in multi-channel scattering.

Discovers dual CIR causing complete scattering suppression.

Abstract

We develop a grid method for multi-channel scattering of atoms in a waveguide with harmonic confinement. This approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes. Collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency $\omega$ permitting the center-of-mass (c.m.) separation are explored in depth. In the zero-energy limit and single mode regime we reproduce the well-known confinement-induced resonances (CIRs) for bosonic, fermionic and heteronuclear collisions. In case of the multi-mode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behaviour are identified and analyzed. The behaviour of the transmission with varying energy and scattering lengths is discussed in detail. The dual CIR leading to a complete quantum suppression of atomic scattering is revealed in multi-channel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.