# Coupled square well model and Fano-phase correspondence

## TL;DR

This paper explores the Fano-Feshbach resonance using a coupled-square-well model, revealing a general phase-$q$ relationship in Fano resonances across frequency and time domains.

## Contribution

It demonstrates that the phase-$q$ correspondence is universal for Fano resonances in the weak coupling regime, regardless of the transition mechanism.

## Key findings

- Fano lineshape profiles observed in energy absorption spectrum
- Time-dependent dipole response exhibits a phase shift related to the Fano $q$ parameter
- Phase-$q$ correspondence is shown to be general for weak coupling Fano resonances

## Abstract

This paper investigates the Fano-Feshbach resonance with a two-channel coupled-square-well model in both the frequency and time domains. This systems is shown to exhibit Fano lineshape profiles in the energy absorption spectrum. The associated time-dependent dipole response has a phase shift that has recently been understood to be related to the Fano lineshape asymmetric $q$ parameter by $\phi=2arg(q-i)$. The present study demonstrates that the phase-$q$ correspondence is general for any Fano resonance in the weak coupling regime, independent of the transition mechanism.