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arXiv:1412.4921 · Physical Review A

Ultracold-atom collisions in atomic waveguides: A two-channel analysis

Tom Kristensen, Ludovic Pricoupenko

Published Apr 8, 2015• 7 citations
arXivHTMLPDF

Abstract

Low-dimensional behavior of two ultracold atoms trapped in two- and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used, allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement-induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with those of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound-state properties.

DOI
10.1103/physreva.91.042703

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Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic waveguides 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 waveguides, it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar waveguide, the characteristics of the 2D induced scattering resonances in p- and d-waves are determined as a function of the 3D scattering parameters and of the waveguide frequency.
We have developed a method for treating ultracold pair collisions in confined geometry of tight atomic waveguides. With this approach we have predicted and analyzed a few novel resonant and multichannel effects induced by confining traps in ultracold atomic collisions. In this report we discuss our model yielding the shifts and widths of magnetic Feshbach resonances in tight atomic waveguides. We also briefly discuss a resonant mechanism of molecule formation in atomic traps with transferring the energy release to the center-of-mass excitation while forming molecule and dipolar confinement-induced resonances in waveguides. These results could potentially be used experimentally.
We develop a grid method for multichannel 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 $\ensuremath{\omega}$ 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 the case of the multimode regime up to four open transverse channels are considered. Previously obtained analytical results are extended significantly here. Series of Feshbach resonances in the transmission behavior are identified and analyzed. The behavior 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 multichannel scattering processes. Possible applications include, e.g., cold and ultracold atom-atom collisions in atomic waveguides and electron-impurity scattering in quantum wires.
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