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 $ω$ 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.
Shifts and widths of Feshbach resonances in atomic waveguides
我们建立了一个理论模型，并分析了原子波导中费什巴赫共振的位移和宽度。它是基于一个多通道的方法在多模制度的波导中的约束诱导共振（CIR）和原子跃迁。在这个方案中，我们取代单通道标量原子间相互作用的四通道张量势模型共振的宽，窄和重叠的字符根据A. D. Lange等人的双通道参数化。作为输入的费什巴赫共振的实验已知的参数，在波导的情况下使用。我们计算了Cs原子在谐振波导中的s-、d-和g-波磁费什巴赫共振的位移和宽度，以及自由空间散射长度零点处透射的共振增强。我们发现共振宽度与原子的纵向动量成线性关系，与波导宽度成二次关系。我们的模型开辟了新的可能性，定量研究的散射过程中的超冷原子气体在波导超出的框架的s波共振散射。
The influence of evanescent waves on the nature of optical cooperative effects in atomic ensembles in a waveguide
Peter the Great St. Petersburg Polytechnic University（圣彼得堡彼得大帝理工大学）；Institute for Analytical Instrumentation of RAS（俄罗斯科学院分析仪器研究所）；Ioffe Institute（约费研究所）
