# Coherent coupling completes an unambiguous optomechanical classification framework

## TL;DR

This paper introduces a comprehensive Hamiltonian-based framework to classify and distinguish different types of optomechanical couplings, including a novel coherent coupling, aiding in the design of optomechanical systems.

## Contribution

It develops a general Hamiltonian framework for unambiguously identifying optomechanical coupling types, including a new coherent coupling concept, with practical examples and implications for system design.

## Key findings

- Coherent coupling can enhance cooling of mechanical oscillators.
- The framework distinguishes between resonance frequency modulation, environment coupling, and coherent coupling.
- Application to a ring cavity demonstrates the practical relevance of the classification.

## Abstract

In most optomechanical systems a movable mirror is a part of an optical cavity, and its oscillation modulates either the resonance frequency of the cavity, or its coupling to the environment. There exists the third option -- which we call a "coherent coupling" -- when the mechanical oscillation couples several non-degenerate optical modes supported by the cavity. Identifying the nature of the coupling can be an important step in designing the setup for a specific application. In order to unambiguously distinguish between different optomechanical couplings, we develop a general framework based on the Hamiltonian of the system. Using this framework we give examples of different couplings, and discuss in details one particular case of a purely coherent coupling in a ring cavity with a movable mirror inside. We demonstrate that in certain cases coherent coupling can be beneficial for cooling the motion of the mechanical oscillator. Our general framework allows to approach the design of optomechanical experiments in a methodological way, for precise exploitation of the strengths of particular optomechanical couplings.