Quantum thermodynamic derivation of the energy resolution limit in magnetometry

TL;DR

This paper derives the fundamental energy resolution limit in magnetometry from quantum thermodynamics principles, linking measurement work and Landauer erasure to the magnetic sensing sensitivity.

Contribution

It provides the first-principles derivation of the energy resolution limit in magnetometry using quantum thermodynamic arguments, connecting work, measurement, and sensing sensitivity.

Findings

Energy resolution limit ranges from 1 to 10^7 times Planck's constant.

Quantum thermodynamics explains the fundamental limits of magnetic sensing.

Application to various magnetometers demonstrates the universality of the limit.

Abstract

It was recently demonstrated that a multitude of realizations of several magnetic sensing technologies satisfy the energy resolution limit, which connects a quantity composed by the variance of the magnetic field estimate, the sensor volume and the measurement time, and having units of action, with $\hbar$. A first-principles derivation of this limit is still elusive. We here present such a derivation based on quantum thermodynamic arguments. We show that the energy resolution limit is a result of quantum thermodynamic work necessarily associated with quantum measurement and Landauer erasure, the work being exchanged with the magnetic field. We apply these considerations to atomic magnetometers, diamond magnetometers, and SQUIDs, spanning an energy resolution limit from $10^0\hbar$ to $10^7\hbar$. This connection between quantum thermodynamics and magnetometry can help advance quantum sensing technologies towards even more sensitive devices.