# Spin-mechanics with levitating ferromagnetic particles

## TL;DR

This paper demonstrates the coupling of levitating ferromagnetic particles to NV center spins in diamond, enabling potential quantum spin-mechanics applications with high-frequency librations and coherent control.

## Contribution

It introduces a novel scheme for coupling levitating ferromagnets to NV center spins, showing experimental feasibility and coherent control of the system.

## Key findings

- Librational frequencies in the hundreds of kHz range with high Q factors.
- Coherent spin control and read-out of levitated particles.
- Potential for spin-mechanical quantum experiments.

## Abstract

We propose and demonstrate first steps towards schemes where the librational mode of levitating ferromagnets is strongly coupled to the electronic spin of Nitrogen-Vacancy (NV) centers in diamond. Experimentally, we levitate ferromagnets in a Paul trap and employ magnetic fields to attain oscillation frequencies in the hundreds of kHz range with Q factors close to $10^4$. These librational frequencies largely exceed the decoherence rate of NV centers in typical CVD grown diamonds offering prospects for sideband resolved operation. We also prepare and levitate composite diamond-ferromagnet particles and demonstrate both coherent spin control of the NV centers and read-out of the particle libration using the NV spin. Our results will find applications in ultra-sensitive gyroscopy and bring levitating objects a step closer to spin-mechanical experiments at the quantum level.