# Lattice quantum magnetometry

## TL;DR

This paper introduces lattice quantum magnetometry, a method for detecting magnetic fields using a charged particle on a 2D lattice, highlighting its potential for high-precision magnetic field estimation.

## Contribution

It proposes a novel lattice-based quantum sensing approach and analyzes its quantum Fisher information, revealing optimal measurement strategies for magnetic field estimation.

## Key findings

- Quantum Fisher information peaks depend on spectral properties.
- Certain magnetic field values are estimated more accurately.
- Coarse-grained position measurements can approach optimal estimation.

## Abstract

We put forward the idea of lattice quantum magnetometry, i.e. quantum sensing of magnetic fields by a charged (spinless) particle placed on a finite two-dimensional lattice. In particular, we focus on the detection of a locally static transverse magnetic field, either homogeneous or inhomogeneous, by performing ground state measurements. The system turns out to be of interest as quantum magnetometer, since it provides a non-negligible quantum Fisher information (QFI) in a large range of configurations. Moreover, the QFI shows some relevant peaks, determined by the spectral properties of the Hamiltonian, suggesting that certain values of the magnetic fields may be estimated better than the others, depending on the value of other tunable parameters. We also assess the performance of coarse-grained position measurement, showing that it may be employed to realize nearly optimal estimation strategies.