A toy model for the dipolar-induced resonance in quasi-one-dimensional systems

TL;DR

This paper introduces a simplified model to understand the dipolar-induced resonance in quasi-one-dimensional systems, revealing how a single resonance emerges from the interplay of repulsive and attractive interactions.

Contribution

It presents a toy-model potential that captures the key features of dipolar interactions and analytically confirms the existence of a single resonance in such systems.

Findings

A non-zero-range repulsive potential can induce a resonance.

The toy model reproduces the main features of the effective interaction.

Analytical confirmation of the single dipolar-induced resonance.

Abstract

We discuss the properties of the effective dipolar interaction for two particles tightly confined along a one-dimensional tube, stressing the emergence of a single dipolar-induced resonance in a regime for which two classical dipoles would just repel each other. We present a toy-model potential reproducing the main features of the effective interaction: a non-zero-range repulsive potential competing with an attractive contact term. The existence of a single resonance is confirmed analytically. The toy model is than generalized to investigate the interplay between dipolar and contact interaction, giving an intuitive interpretation of the resonance mechanism.