Frequency Multiplexed Magnetometry via Compressive Sensing

TL;DR

This paper introduces a compressive sensing approach for frequency multiplexed magnetometry using NV center sensors, achieving Heisenberg-like scaling and increased sensitivity over traditional phase estimation methods.

Contribution

It presents a novel application of compressive sensing to quantum magnetometry, enabling frequency multiplexing and improved precision scaling beyond existing phase estimation techniques.

Findings

Achieves approximately 1/T precision scaling with CS methods.

Provides 5-fold increase in sensitivity over dynamic-range gain.

Reduces resource requirements for frequency multiplexed signals.

Abstract

Quantum sensors based on single Nitrogen-Vacancy (NV) defects in diamond are state-of-the-art tools for nano-scale magnetometry with precision scaling inversely with total measurement time $\sigma_{B} \propto 1/T$ (Heisenberg scaling) rather than as the inverse of the square root of $T$, with $\sigma_{B} =1/\sqrt{T}$ the Shot-Noise limit. This scaling can be achieved by means of phase estimation algorithms (PEAs) using adaptive or non-adaptive feedback, in combination with single-shot readout techniques. Despite their accuracy, the range of applicability of PEAs is limited to periodic signals involving single frequencies with negligible temporal fluctuations. In this Letter, we propose an alternative method for precision magnetometry in frequency multiplexed signals via compressive sensing (CS) techniques. We show that CS can provide for precision scaling approximately as $\sigma_{B} \approx 1/T$, both in the case of single frequency and frequency multiplexed signals, as well as for a 5-fold increase in sensitivity over dynamic-range gain, in addition to reducing the total number of resources required.