# Magnetometry via spin-mechanical coupling in levitated optomechanics

## TL;DR

This paper explores magnetometry using a levitated nanodiamond with spin-mechanical coupling, analyzing sensitivity limits under various conditions and proposing a versatile platform for magnetic sensing.

## Contribution

It introduces a hybrid levitated nanomechanical magnetometer leveraging spin-mechanical coupling for sensitive magnetic field gradient detection.

## Key findings

- Sensitivity of 1 μTm$^{-1}$/$
oot{Hz}$ in ultrahigh vacuum
- Sensitivity of ~100 mTm$^{-1}$/$
oot{Hz}$ at room temperature
- Potential sensitivity of 100 μTm$^{-1}$/$
oot{Hz}$ using Ramsey interferometry

## Abstract

We analyze magnetometry using an optically levitated nanodiamond. We consider a configuration where a magnetic field gradient couples the mechanical oscillation of the diamond with its spin degree of freedom provided by a Nitrogen vacancy center. First, we investigate measurement of the position spectrum of the mechanical oscillator. We find that conditions of ultrahigh vacuum and feedback cooling allow a magnetic field gradient sensitivity of 1 $\mu$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. At high pressure and room temperature, this sensitivity degrades and can attain a value of the order of 100 $m$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. Subsequently, we characterize the magnetic field gradient sensitivity obtainable by maneuvering the spin degrees of freedom using Ramsey interferometry. We find that this technique can offer photon-shot noise and spin-projection noise limited magnetic field gradient sensitivity of 100 $\mu$Tm$^{-1}$/$\sqrt{\mbox{Hz}}$. We conclude that this hybrid levitated nanomechanical magnetometer provides a favorable and versatile platform for sensing applications.