# Cavity mediated dissipative coupling of distant magnetic moments: theory and experiment

## TL;DR

This paper explores how two distant magnetic moments can interact via a microwave cavity, demonstrating both theoretical and experimental control of their indirect coupling, which depends on their individual coupling mechanisms.

## Contribution

It provides a comprehensive analysis of cavity-mediated interactions between magnetic moments with different coupling types, revealing conditions for level repulsion and attraction.

## Key findings

- Indirect coupling depends on the coupling mechanism (coherent or dissipative).
- Level repulsion occurs when both modes share the same coupling type.
- Level attraction occurs when modes have different coupling types.

## Abstract

We investigate long-range coherent and dissipative coupling between two spatially separated magnets while both are coupled to a microwave cavity. A careful examination of the system shows that the indirect interaction between two magnon modes is dependent on their individual mechanisms of direct coupling to the cavity. If both magnon modes share the same form of coupling to the cavity (either coherent or dissipative), then the indirect coupling between them will produce level repulsion. Conversely, if the magnon modes have different forms of coupling to the cavity (one coherent and one dissipative), then their indirect coupling will produce level attraction. We further demonstrate the cavity-mediate nature of the indirect interaction through investigating the dependence of the indirect coupling strength on the frequency detuning between the magnon and cavity modes. Our work theoretically and experimentally explores indirect cavity mediate interactions in systems exhibiting both coherent and dissipative coupling, which opens a new avenue for controlling and utilizing light-matter interactions.