Fano-Liouville Spectral Signatures in Open Quantum Systems

TL;DR

This paper extends the Fano model to include dissipation in open quantum systems, deriving a modified spectral profile that combines Fano and Lorentzian features for various optical responses.

Contribution

It provides a comprehensive analytical framework for the optical response of dissipative Fano systems, incorporating dissipation effects into the spectral lineshape.

Findings

Derived the full optical response including dissipation effects

Established a modified Fano profile with Lorentzian contribution

Provided formulas for extracting model parameters from observables

Abstract

The scattering amplitude from a set of discrete states coupled to a continuum became known as the Fano profile, characteristic for its asymmetric lineshape and originally investigated in the context of photoionization. The generality of the model, and the proliferation of engineered nanostructures with confined states gives immense success to the Fano lineshape, which is invoked whenever an asymmetric lineshape is encountered. However, many of these systems do not conform to the initial model worked out by Fano in that i) they are subject to dissipative processes and ii) the observables are not entirely analogous to the ones measured in the original photoionization experiments. In this letter, we work out the full optical response of a Fano model with dissipation. We find that the exact result for absorption, Raman, Rayleigh and fluorescence emission is a modified Fano profile where the typical lineshape has an additional Lorentzian contribution. Expressions to extract model parameters from a set of relevant observables are given.