Limits on Spectral Resolution Measurements by Quantum Probes

TL;DR

This paper investigates the fundamental limits of spectral resolution in quantum probes, revealing that both frequency resolution and estimation precision are ultimately constrained by the Cramér-Rao bound, challenging previous distinctions.

Contribution

The study provides a unified theoretical and experimental analysis showing that spectral resolution and frequency estimation are limited by the same fundamental bound, clarifying their relationship.

Findings

Both spectral resolution and frequency estimation are limited by the Cramér-Rao bound.

Experimental results confirm the theoretical limits on resolution.

The relationship between resolution and estimation precision is more nuanced than previously thought.

Abstract

The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cram\'er-Rao bound of a single frequency estimation.