Confinement-induced resonance (CIR) in classical vs. quantum scattering under 2D harmonic confinement

TL;DR

This study explores the classical analogue of confinement-induced resonance (CIR) in 2D harmonic traps, showing that classical systems with finite-range potentials exhibit CIR-like features similar to quantum systems, including dependence on angular momentum.

Contribution

It demonstrates that classical scattering under 2D harmonic confinement can exhibit CIR-like phenomena, extending the understanding of classical-quantum analogies in confined atomic systems.

Findings

Classical CIR manifests as a minimum in transmission coefficient.

Classical CIR can occur for non-zero angular momentum $L_z$, unlike in quantum cases.

The results support a classical-quantum analogy in confinement-induced resonances.

Abstract

Using complex analysis, we have investigated classical quasi-one-dimensional atom-atom scattering under 2D harmonic confinement with two different interaction potential (Yukawa and Lennard-Jones) and found that the Confinement-Induced Resonance (CIR) that occurs in the quantum system seems to have a classical analogy. We observed CIR in our classical results in the sense that a clear minimum appeared in the transmission coefficient for the different interaction potentials. We also investigated the change in the value and position of this minimum by varying the characteristic parameters of the system including the angular momentum $L_z$ along the longitudinal axis. In the quantum case, it has already been shown that for the zero range Huang potential, CIR occurs only for $L_z = 0$. Our results indicate that classical CIR can also occur for $L_z \ne 0$ using finite range potentials. We have endeavoured to provide extensive physical arguments to explain the observed results and to support the proposed analogy between the classical and quantum regimes where applicable.