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Related Experiment Video

Updated: Jan 28, 2026

Absolute Quantum Yield Measurement of Powder Samples

Absolute Quantum Yield Measurement of Powder Samples

Published on: May 12, 2012

Limits on Spectral Resolution Measurements by Quantum Probes.

Amit Rotem¹, Tuvia Gefen¹, Santiago Oviedo-Casado²

¹Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Givat Ram, Israel.

Physical Review Letters

|March 2, 2019

Summary

In nano-NMR experiments, frequency resolution is not fundamentally limited. Both resolving multiple frequencies and precisely estimating a single one are constrained only by the Cramér-Rao bound, regardless of signal timescale.

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Area of Science:

Physics
Spectroscopy
Nanotechnology

Background:

Frequency resolution limits in nano-NMR are debated.
A perceived difference exists between resolving multiple frequencies and estimating a single frequency's precision.

Purpose of the Study:

To investigate the theoretical and experimental relationship between frequency resolution and estimation precision in nano-NMR.
To determine the fundamental limits governing these capabilities.

Main Methods:

Theoretical analysis of nano-NMR signal processing.
Experimental validation of theoretical predictions.

Main Results:

The study reveals a more subtle relationship between frequency resolution and single frequency estimation precision.
Both capabilities are theoretically and experimentally shown to be limited by the Cramér-Rao bound for single frequency estimation.

Conclusions:

The perceived fundamental difference in limits between resolving and estimating frequencies in nano-NMR is not accurate.
The Cramér-Rao bound provides a unified limit for both frequency resolution and precision in nano-NMR experiments.