# Spectral characterization of couplings in a mixed optomechanical model

## TL;DR

This paper analyzes the spectral features of a mixed optomechanical system with linear and quadratic interactions, revealing phonon sidebands and sub peaks, and shows how spectral analysis can infer coupling strengths.

## Contribution

It provides an exact spectral analysis of single-photon emission and scattering in a mixed optomechanical model with both linear and quadratic couplings.

## Key findings

- Presence of phonon sideband peaks in spectra
- Existence of sub peaks around phonon sidebands
- Spectral features can infer optomechanical coupling strengths

## Abstract

We study the spectrum of single-photon emission and scattering in a mixed optomechanical model which consists of both linear and quadratic optomechanical interactions. The spectra are calculated based on the exact long-time solutions of the single-photon emission and scattering processes in this system. We find that there exist some phonon sideband peaks in the spectra and there are some sub peaks around the phonon sideband peaks under proper parameter conditions. The correspondence between the spectral features and the optomechanical interactions is confirmed, and the optomechanical coupling strengths can be inferred by analyzing the resonance peaks and dips in the spectra.