Coupledℓ-wave confinement-induced resonances in cylindrically symmetric waveguides

Abstract

A semi-analytical approach to atomic waveguide scattering for harmonic confinement is developed taking into account all partial waves. As a consequence ℓ-wave confinement-induced resonances are formed being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the K-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.

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].…”

“…The atoms are allowed to perform collisions with higher partial waves where we take into account that the total colliding energy is well above the threshold of the ground state of the transversal confinement. The theoretical conceptualization of the corresponding resonant phenomena is based on a fully analytical and non-perturbative framework of the K-matrix approach [19,28] including appropriate interatomic interactions with e.g. a van der Waals tail.…”

“…We remark, that Eq. (5) holds for arbitrary partial waves ℓ and ℓ ′ , under the assumption that either both are even or odd and at all energies within the continuum between the ground-and first excited channel, where the main difference to the K-Matrix derived in [19] is, that the K-Matrix there only holds as long as a ⊥ q 0 ≪ 1. In particular we also note, that in the case of ∆ ℓ ′ = 0, namely the single partial wave approximation, the formula reduces to…”

“…(2) interrelates the wave functions of the asymptotic and the inner region. Consequently, the corresponding K matrices are connected according to the relation 18,19,28,33], where the K 3D -Matrix is a diagonal matrix in the ℓ-wave representation with entries given by the tangent of the phase shifts.…”

Generalized local-frame-transformation theory for excited species in external fields

“…Furthermore, the LFT theory gives a compact description of a variety of physical processes such as dielectronic recombination [12], negative-ion photodetachment in magnetic [13] or electric fields [14][15][16] or under generic external confinement [17], or ultracold atomic and/or * pgiannak@purdue.edu † chgreene@purdue.edu ‡ robichf@purdue.edu dipolar collisions in the presence of external trapping potentials [18][19][20][21]. In molecular applications frame transformation theory has been decisive in describing the rich rovibrational Rydberg spectra of diatomic molecules [22], and the dissociative recombination of H + 3 [23,24].…”