Shifts and widths of Feshbach resonances in atomic waveguides

Abstract

We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. We replace in this scheme the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow and overlapping character according to the two-channel parametrization of A.D.Lange et. al. [35]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of s-, d-and g-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waiveguide width. Our model opens novel possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of s-wave resonant scattering.

Confinement-induced resonances in ultracold atom-ion systems

“…Note that in this limit we have [42,43,49], that is, we have total reflection of the colliding particles. Moreover, the condition (5) defining the appearance of CIR does not have any reliance on the atomic mass.…”

“…To this end, we employ the computational scheme described in Ref. [40], which has been successfully applied to the atom-atom [41][42][43] as well as to the dipole-dipole confined scattering [44,45].…”

Energy-dependentℓ-wave confinement-induced resonances

“…Recent experimental advances allowed to explore the corresponding physics of CIRs in quasi-one-and quasi-two-dimensional (quasi-1D and quasi-2D) waveguide geometries [11][12][13][14][15] or in mixed dimensional scattering processes [16]. Complementing the experimental studies, substantial theoretical efforts exhibit a kaleidoscope of confinement-induced processes, such as dual [17] and higher partial wave CIRs [18,19], multichannel [20][21][22][23] or anharmonic CIRs [24][25][26] and CIR molecule formation [27] or dipolar CIRs [28][29][30]. Further studies on CIR effects focus on the impact of various confining geometries, such as quasi-2D either harmonic [31,32] or square well [33], and lattice potentials [34][35][36], or collisions in mixed dimensions [37].…”

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

“…This issue has been already the subject to many theoretical studies [4,5,[18][19][20][21][22][23] where a zero-range potential approach was used and much more sophisticated multichannel studies have been performed in Refs. [24][25][26]. In this paper, we use a finite-range two-channel modeling of the FR resonance.…”