An analytical approach to atomic multichannel collisions in tight harmonic waveguides

Abstract

We perform an analytical investigation in the framework of generalized $K$ matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular we present the unitarity bounds which emerge when considering a quasi one dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de-)excitations by means of CIRs. We analyze the CIR for $d$-waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.

17 pages, 11 figures

References in corpus (11)

• Radiofrequency spectroscopy of a strongly interacting two-dimensional Fermi gas
• Dipolar gases in quasi one-dimensional geometries
• Scattering in Mixed Dimensions with Ultracold Gases
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Resonant Scattering of Ultracold Atoms in Low Dimensions
• Suppression of Quantum Scattering in Strongly Confined Systems
• Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
• Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides
• Modeling interactions for resonant p-wave scattering
• Confinement-induced p-wave resonances from s-wave interactions
• Dynamics of parametric matter wave amplification

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• K-matrix formulation of two-particle scattering in a wave guide in the presence of one-dimensional spin-orbit coupling
• Ultracold atoms in quasi-1D traps: a step beyond the Lieb-Liniger model
• Magnetic-field gradiometer based on ultracold collisions
• Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping
• Bound and scattering states in harmonic waveguides in the vicinity of free space Feshbach resonances
• Universal energy-dependent pseudopotential for the two-body problem of confined ultracold atoms
• Dipolar confinement-induced molecular states in harmonic waveguides
• Energy Band Engineering of Periodic Scatterers by Quasi-1D Confinement