# Enhanced magnetic sensitivity with non-gaussian quantum fluctuations

## TL;DR

This paper demonstrates that non-gaussian quantum states of dysprosium atoms can achieve magnetic sensitivity surpassing squeezed states and approaching the Heisenberg limit, using non-linear spin coupling and magnetic sublevel resolution.

## Contribution

It introduces a method to create and measure non-gaussian quantum states with enhanced magnetic sensitivity in atomic spins.

## Key findings

- Non-gaussian states outperform squeezed states in magnetic sensitivity.
- Sensitivity reaches about half the Heisenberg limit.
- Magnetic sublevel resolution is crucial for optimal measurement.

## Abstract

The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of non-classical states of the electronic spin $J = 8$ of dysprosium atoms, created using light-induced non-linear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.