Achieving the ultimate precision limit in quantum NMR spectroscopy

TL;DR

This paper demonstrates that in quantum nano-NMR spectroscopy, the ultimate precision limit for estimating the Larmor frequency can be achieved despite practical measurement constraints, through optimal control and measurement tuning.

Contribution

It shows how to reach the fundamental precision limit in quantum nano-NMR despite the inability to perform perfect single-spin measurements.

Findings

Ultimate precision limit is achievable with control and measurement tuning.

Practical measurement constraints do not prevent reaching the fundamental limit.

The approach applies to unentangled spins in quantum nano-NMR.

Abstract

The ultimate precision limit in estimating the Larmor frequency of $N$ unentangled rotating spins is well established, and is highly important for magnetometers, gyroscopes and many other sensors. However this limit assumes perfect, single addressing, measurements of the spins. This requirement is not practical in NMR spectroscopy, as well as other physical systems, where a weakly interacting external probe is used as a measurement device. Here we show that in the framework of quantum nano-NMR spectroscopy, in which these limitations are inherent, the ultimate precision limit is still achievable using control and a finely tuned measurement.