Confinement-Induced Resonances in Two-Center Problem via Pseudopotential Approach

TL;DR

This paper analyzes how confinement in a waveguide affects quantum scattering by two fixed centers, deriving conditions for confinement-induced resonances using a pseudopotential approach, with potential applications in atomic physics.

Contribution

It extends the understanding of confinement-induced resonances to systems with two fixed scattering centers using a regularized pseudopotential method.

Findings

Derived conditions for CIRs in two-center systems.

Showed that single-center CIR results are recovered in the limit.

Applicable to atomic scattering by fixed impurities like ions or Rydberg atoms.

Abstract

We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for even state tends to the well-known result obtained by Olshanii. Our result can be applicable to confined atomic scattering by fixed impurities, like ions or Rydberg atoms, with possible extension to $N$ impurities, or by two-atomic molecules.