# Quantum magnetomechanics: towards the ultra-strong coupling regime

## TL;DR

This paper explores a hybrid quantum system where a magnetic-coated mechanical oscillator couples to an LC resonator, achieving ultra-strong coupling regimes with potential applications in quantum state transfer and sensing.

## Contribution

It derives the system's Hamiltonian showing a charge-momentum coupling with geometric dependence and demonstrates feasibility of reaching ultra-strong coupling experimentally.

## Key findings

- Coupling rate can reach ultra-strong regime with feasible parameters
- Derived Hamiltonian reveals charge-momentum interaction with geometric dependence
- Potential applications include quantum state transfer and weak-force sensing

## Abstract

In this paper we investigate a hybrid quantum system comprising a mechanical oscillator coupled via magnetic induced electromotive force to an $LC$ resonator. We derive the Lagrangian and Hamiltonian for this system and find that the interaction can be described by a charge-momentum coupling with a strength that has a strong geometric dependence. We focus our study on a mechanical resonator with a thin-film magnetic coating which interacts with a nano-fabricated planar coil. We determine that the coupling rate between these two systems can enter the strong, ultra-strong, and even deep-strong coupling regimes with experimentally feasible parameters. This magnetomechanical configuration allows for a range of applications including electro-mechanical state transfer and weak-force sensing.