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The Heisenberg time-energy relation prevents determination of an atomictransition to better than the inverse of the measurement time. The relationgenerally applies to frequency estimation of a near-resonant field [1-3], sinceinformation on the field frequency can be used to infer the atomic transition[4, 5]. Here we demonstrate a frequency estimation technique that provides anuncertainty orders of magnitude below the Heisenberg limit with a single atom.With access to $N$ atoms, we propose a fundamental uncertainty limit improvingas $\sqrt{N}$, regardless of whether entanglement is employed. We describeimplementation of the quantum fourier transform to estimate an unknownfrequency without using entanglement. A comparison to classical algorithmsseverely limits the benefit that quantum algorithms provide for frequencyestimation and that entanglement provides to quantum sensing in general.

Frequency measurements beyond the Heisenberg time-energy limit with a single atom